G Sartori Natal

A Chemori

F Pierrot

Dual-Space Adaptive Control of Redundantly Actuated Parallel Manipulators for Extremely Fast Operations With Load Changes

This paper deals with the dual-space adaptive control of R4 redundantly actuated parallel manipulator for applications with very high accelerations. This controller is compared experimentally with a dual-space feedforward controller (which may have good performances for specific cases, but has crucial losses of performance when there is any operational change (such as a change of load)), for a pickand-place task with accelerations of 30G (without payload) and 20G (with a payload of 200g). The objective of this paper is to show that the proposed dual-space adaptive controller not only keeps a very good performance independently of the operational case, but also has a better performance than the dual-space feedforward controller even when this last one is best configured to the given case.

I. INTRODUCTION

It is known that parallel manipulators have important advantages in comparison to serial manipulators in terms of speed/acceleration, stiffness, accuracy and payload. In order to deal with their main disadvantage (abundance in singularities in the workspace [START_REF] Kock | A parallel x-y manipulator with actuation redundancy for high-speed and active-stiffness applications[END_REF]), actuation redundancy was proposed in [START_REF] Park | Singularity analysis of closed kinematic chains[END_REF]. A degree of actuation redundancy of a parallel manipulator is the difference, represented by a positive integer, between the number of its actuators and its degrees-of-freedom (dof) [START_REF] Ganovski | Modeling, simulation and control of redundantly actuated parallel manipulators[END_REF]. Actuation redundancy might also be a way to reach higher accelerations or to improve the homogeneity of acceleration performance over the workspace (this was the basic conjecture in [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF]). It can also allow for more safety in case of breakdown of individual actuators [START_REF] Yi | Fault tolerance of parallel manipulators using task space and kinematic redundancy[END_REF], [START_REF] Roberts | Fundamental limitations on designing optimally fault-tolerant redundant manipulator[END_REF].

In order to apply the vast control literature developed for serial counterparts to parallel manipulators with redundant actuation, there is a need to develop an efficient dynamical model for parallel manipulators [START_REF] Cheng | Dynamics and control of redundantly actuated parallel manipulators[END_REF]. A dynamics formulation that could be applied to redundant parallel manipulators was presented in [START_REF] Nakamura | Dynamics computation of closedlink robot mechanisms with nonredundant and redundant actuators[END_REF]. Based on this formulation, redundant actuation was used to eliminate undesired singularity effects in parallel manipulators in [START_REF] Cheng | Dynamics and control of redundantly actuated parallel manipulators[END_REF], [START_REF] Liu | Analysis and control of redundant parallel manipulators[END_REF]. In these works, kinematic and dynamic control methods were satisfactorily implemented experimentally in the task space, where the effect of the redundant actuators to the end-effector motion can be fully considered [START_REF] Shang | Nonlinear adaptive task space control for a 2-dof redundantly actuated parallel manipulator[END_REF]. Important and probably very perspective research results were achieved by Müller in [START_REF] Müller | Control of simply-redundant full-actuated parallel manipulators[END_REF] and [START_REF] Müller | Internal preload control of redundantly actuated parallel manipulators[END_REF]. In his recent works, he took profit from a general solution for the inverse dynamics of redundantly This work is supported by ECHORD PRADA: an European project. G. Sartori Natal, A. Chemori and F. Pierrot are with LIRMM, Univ. Montpellier 2 -CNRS, 161 rue Ada, 34392 Montpellier, France sartorinatal@lirmm.fr actuated parallel manipulators to develop a computationallyefficient open-loop preload control scheme (depending on a single preload parameter), the simplicity of which makes it applicable in real-time control applications with backlash avoidance, especially for the cases of simply-redundant (i.e. one redundant actuator) parallel robots. In [START_REF] Shang | Nonlinear computed torque control for a high-speed planar parallel manipulator[END_REF], in order to overcome the influences of modeling errors and nonlinear friction, a nonlinear computed torque control was introduced. In [START_REF] Hui | Hybrid position/force adaptive control of redundantly actuated parallel manipulators[END_REF], a hybrid position/force adaptive control for redundantly actuated parallel manipulators has been proposed, and an adaptive controller for redundantly actuated parallel manipulator was designed in [START_REF] Shang | Nonlinear adaptive task space control for a 2-dof redundantly actuated parallel manipulator[END_REF]. It is important to emphasize, however, that in none of these works the effect of load changes was analyzed (neither how the proposed controllers would deal with such operational changes).

In this paper, a dual-space adaptive controller is proposed (based on the adaptive control scheme proposed in [START_REF] Lee | Adaptive output feedback control of robot manipulators using high-gain observer[END_REF]) in order to guarantee the best possible performance of a redundantly actuated parallel manipulator not only in an unloaded condition, but also when carrying a relevant payload at a very high speed.

This paper is organized as follows. In section II, a brief description of the R4 redundantly actuated parallel manipulator is presented. The proposed control scheme is detailed in section III. Section IV is devoted to the pick-and-place trajectory generation. The obtained experimental results are presented in section V. Conclusion and future works are discussed in section VI.

II. R4 PARALLEL MANIPULATOR

A. Description of the R4 robot

The R4 parallel manipulator (cf. Fig. 1) has the following main characteristics: i) 3-do f (translations along x-y-z axis) and 4 actuators (redundantly actuated), ii) Each motor has a maximum torque of 127N.m, iii) A workspace of at least a cylinder of 300mm radius and 100mm height. Its geometrical parameters are summarized in table I and the reader is referred to [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF] for their illustration.

B. Simplified Direct Dynamics

Some simplifications on the dynamics of the robot were made during its design phase in order to evaluate which configuration would be the optimal in terms of performance and cost, such as the neglect of joint friction, the inertia of the forearms and the gravity acceleration, as well as the consideration that the mass of the forearms is split in two parts (half of the mass is transferred to the end of the arm whereas the other half is transferred to the traveling plate). These assumptions are discussed in [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF] and in [START_REF] Nabat | Robots parallèles à nacelle articulée -du concept à la solution industrielle pour le pick-and-place[END_REF]. The expression of the simplified direct dynamic model of this robot is given by [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF]:

ẍ = (M T + J m T I T J m ) -1 J T m (Γ -I T Jm ẋ) (1)
where ẋ ∈ R m and ẍ ∈ R m are the vectors of Cartesian velocities and accelerations; M T = Diag{M t p +n M f orearm 2

} m×m = M tot I m×m is a diagonal matrix with m diagonal terms, being M t p the mass of the traveling plate, M f orearm the mass of the forearm, M tot the scalar value of the diagonal of M T , m the number of degrees-of-freedom (m = 3) and n the number of motors (n = 4); I T = Diag{I act + I arm } n×n = I tot I n×n is a diagonal matrix with n diagonal terms, where I act and I arm are the inertia of the actuators and the inertia of the arms, respectively, and I tot is the scalar value of the diagonal of I T ; J m ∈ R n×m and Jm ∈ R n×m are the generalized inverse Jacobian matrix and its first derivative, respectively; and Γ ∈ R n represents the torques generated by the actuators. For further details on the mechanical design of the R4 parallel manipulator, the reader is referred to [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF]. After some algebraic manipulations, this dynamic model can be rewritten as:

Γ = H T M T ẍ + I T q (2)
being H the pseudo-inverse of J m , that is H = J + m = (J T m J m ) -1 J T m , and q the vector of joint accelerations. As mentioned in section I, the R4 parallel manipulator is redundantly actuated (4 actuators vs. 3-do f ). This characteristic has important advantages in terms of mechanical capabilities of the robot, but in terms of control, new issues arise: not only classical joint control schemes are unable to deal with dynamic effects on the Cartesian space [START_REF] Ganovski | Modeling, simulation and control of redundantly actuated parallel manipulators[END_REF], but they are also unable to cope with the actuation redundancy (the integral term will be disturbed by kinematic inconsistencies). In order to deal with these issues, it is better to implement the control law in Cartesian space. It will be shown in the following that such a controller can easily be completed by a dual-space feedforward that has an effect similar to the computed torque controller.

III. PROPOSED DUAL-SPACE CONTROL SCHEMES: A FEEDFORWARD CONTROLLER AND AN ADAPTIVE CONTROLLER

A. The dual-space feedforward controller

The dual-space feedforward controller consists basically in a PID in the Cartesian space with a feedforward of both desired Cartesian/joint accelerations to improve the tracking performance. This control approach is illustrated through the block diagram of Fig. 2: The desired trajectory x d is given in the Cartesian space. As only the joint positions q m are measured (the Cartesian positions are computed using the Forward Kinematic of the robot), this desired trajectory is converted to its counterpart q d in the joint space through the inverse kinematics (I.K. block in Fig. 2) of the robot [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF], such that the corresponding tracking error can be obtained. The joint tracking errors ∆q must then be reconverted to the Cartesian space ∆x in order to be used by the PID controller. As the joint tracking errors are assumed to be significantly small, and the sampling time ∆t is of only 0.1ms (10 -4 s), let ∆q ∆t dq dt . Then, it is recalled that q = J m ẋ, being q the joint velocity, ẋ the Cartesian velocity of the platform and J m the generalized inverse Jacobian matrix, as defined in [START_REF] Corbel | Towards 100g with pkm. is actuation redundancy a good solution for pick-andplace?[END_REF]. This relation has a unique solution if J m is square, however in the case of redundantly actuated manipulators (n > m), the inverse relation will have infinite solutions. In order to cope with this issue, the pseudo-inverse of J m is used instead (the pseudo-inverse has the property of generating a solution with the minimum Euclidian norm). Therefore, one has that ẋ = H q, where H is the pseudoinverse of J m , that is

PID c I.K. + - d² Kffj MANIPULATOR Kffc + + + .. .. Γ + dt d² dt
H = J + m = (J m T J m ) -1 J m T .
The following relation between the joint errors ∆q and the Cartesian errors ∆x can then be obtained:

dx dt = H dq dt ⇒ ∆x ∆t H ∆q ∆t ⇒ ∆x H∆q (3)
By straightforward analysis of Fig. 2, the proposed dualspace feedforward control law is given by:

Γ = H T f + K f f j qd (4) being f = K p e + K i e(t)dt + K d de(t)
dt + K f f c ẍd the force applied on the traveling plate, e = ∆x, K p , K i and K d the Cartesian PID gains, K f f c the Cartesian acceleration feedforward gain and K f f j is the joint acceleration feedforward gain. In order to compensate for the effects of the dynamics of the system, it is possible to see from the simple rewritten dynamic model (2) that the feedforward gains that should multiply ẍd and qd are simply the system parameters (K f f c = M tot and K f f j = I tot ). For information purposes, the gains of the PID in the Cartesian space was tuned experimentally through the procedure of small steps and the feedforward gains were tuned manually until the best performances could be achieved for the case with and without payload. These gains are presented in table II.

B. The dual-space adaptive controller

The proposed dual-space adaptive controller is based on the adaptive control scheme proposed in [START_REF] Lee | Adaptive output feedback control of robot manipulators using high-gain observer[END_REF]. The most important characteristic of this controller is its capability of taking into consideration the dynamics of the system and estimate its parameters automatically in real-time. Considering the rewritten dynamics of the system (2), we propose the implementation of this controller in dual-space, being its general expression given as follows:

Γ = M(q) qd + Ĉ(q, q) qd + Ĝ(q) + K p e + K d ė (5)
where e = q dq, M, Ĉ, Ĝ are the estimates of M, C and G (being M(q) ∈ R n×n the inertia matrix, C(q, q) ∈ R n×1 the vector of Coriolis and centrifugal forces, and G(q) the gravity vector), respectively. Considering the dynamic model of R4 manipulator, the following control law is then proposed:

Γ = H T MT ẍd + ÎT qd + K p e + K d ė (6)
which can be rewritten in the Cartesian space as:

F = Y r θ + K p e c + K d ėc (7)
where K p and K d are positive gains, e c = x dx, ėc = ẋdẋ, and:

Y r = I 3×3 ẍd J T m I 4×4 qd ; θ = Mtot Îtot ( 8
)
being Y r and θ the regressor vector and the vector of estimated parameters, respectively. These estimated parameters vary according to the following adaptation rule (i = 1, 2):

θi =              γ ii φ i , if a i < θi < b i or θi ≥ b i and φ i ≤ 0 or θi ≤ a i and φ i ≥ 0 γ ii (1 + b i -θi δ ), if θi ≥ b i and φ i ≥ 0. γ ii (1 + θi -a i δ ), if θi ≤ a i and φ i ≤ 0. ( 9
)
where • γ ii is the i th element of the diagonal adaptation gain matrix γ,

• θi represents the estimates of each unknown parameter,

• a i and b i are the lower and upper bounds of each estimative, respectively, • φ ii is the i th element of the column matrix φ = -Y T r s; being s = ėc + λ e c , where λ = λ 0 1+||e|| , being λ 0 and δ positive constants. The chosen adaptive gains were γ 11 = 0.2 and γ 22 = 1.5x10 -4 . In order to decide the good range for the estimated parameters, the behavior of the feedforward controller with relation to its best gains for each specific case were taken into account. Considering that the best K f f c gains of the feedforward controller were 0.625 for the case without payload and 0.825 for the case with a payload of 200g, and also considering that bigger payloads may be used in future experiments, the chosen range for the Mtot parameter (in kg) was of [0.525; 1], which means a 1 = 0.525 and b 1 = 1. Concerning the inertia Îtot parameter (in kg.m 2 ), which is equivalent to the K f f j feedforward gain, the range was chosen as [0.006; 0.018], which means a 2 = 0.006 and b 2 = 0.018. In this paper, only the behavior of the Mtot parameter will be detailed, as this is the parameter that directly compensates for the load changes. The chosen parameters of the dual-space adaptive controller are summarized in table III.

IV. TRAJECTORY GENERATION: 3D PICK-AND-PLACE MOVEMENTS

The objective of this case study is to evaluate the capability of the proposed control approach to deal with very high accelerations in a pick-and-place like trajectory. This kind of trajectory is largely used in the industry for many different applications, such as food/medicaments packaging, lasercutting, electronic components assembly, etc.

In this case study, the desired trajectory is chosen such that movements of different distances would have to be performed in the same amount of time, which would require different accelerations for each one of them, demonstrating the good applicability of the proposed control scheme. The sequence of movements to be executed in this case study is the following (as illustrated in Fig. 3):

1) Pick 1 -Place 1: From (-0.1,0.1)m to (0.1,-0.1)m, 2) Place 1 -Pick 2: From (0.1,-0.1)m to (0.1,0.1)m, 3) Pick 2 -Place 2: From (0.1,0.1)m to (-0.1,-0.1)m, 4) Place 2 -Pick 1: From (-0.1,-0.1)m to (-0.1,0.1)m.

Each movement was performed in 0.08s without payload (0.32s for the whole cycle), and in 0.1s with payload (0.4s for the whole cycle). Their maximum height was equal to 2.5cm. The trajectory generation algorithm used in this case is based on a polynomial interpolation of degree five [START_REF] Khalil | Modeling, identification and control of robots[END_REF]. This algorithm guarantees the continuity of the movement in position, velocity and also in acceleration.

V. REAL-TIME EXPERIMENTAL RESULTS

In this section, real-time experimental results obtained by the application of the proposed control schemes described in section III on the parallel manipulator R4 described in section II in order to track the reference trajectories detailed

A. The experimental testbed

The proposed control schemes were implemented in Simulink/Matlab of Mathworks, being compiled using XPC Target real-time toolbox, and uploaded to a target PC, which managed the real-time task execution with a sampling frequency of 10KHz.

In the following experiment, the robot goes from the rest position to the desired initial position (-0.1, 0.1, -0.55)m and then executes two cycles of the proposed pick-and-place trajectory while carrying a payload of 200g.

B. 3D pick-and-place movements with a payload of 200g at 20G

In this scenario, the adaptive controller is compared to the feedforward controller (configured with its best value of K f f c for the case with a payload of 200g (K f f c = 0.825)) at 20G (≈ 200m/s 2 ) of acceleration. The objective of this experiment is to show that the feedforward controller may have a good performance when configured with its best value of K f f c for a specific scenario, but even in this case it will remain worse than the adaptive controller. The obtained results for this scenario are depicted in Figs. 45. By analyzing Fig. 4, it is possible to notice that the adaptive controller is able to provide a better overall tracking performance than the feedforward controller even with its best value of K f f c for this case. For the X-Y axes, even though the feedforward has provided a good performance, the adaptive controller was able to keep the tracking errors inside a smaller interval, as shown in table IV. For the Z-axis, the difference between the performances of both controllers is bigger and easily visible. The superior performance of the adaptive controller in this case is further confirmed by the Root Mean Square Errors (RMSE) presented in table IV. This RMSE takes into consideration the Root Mean Square Errors of all axes equally, as detailed in the following:

e rms = e 2 rms x + e 2 rms y + e 2 rms z (10)
The torques generated by each controller are presented in Fig. 5, which demonstrates that the adaptive controller generated a signal with a slightly bigger amplitude than the feedforward controller.

In the next scenario, it will be shown that the feedforward controller loses much performance when not having an adequate manual update of K f f c for a different case, while the adaptive controller maintains its very good performance independently of the scenario without any need of manual adjustments of its parameters.

C. 3D pick-and-place movements without payload at 30G

In this scenario, the robustness of the adaptive controller to load changes and the lack of robustness of the feedforward controller to load changes are confirmed. From Fig. 6, it is possible to notice that the feedforward controller, when not manually updated to a new scenario, has a crucial loss of performance (more than 100% peak-to-peak (difference between the highest peak and the lowest valley of a signal) error increase in the X-Y axes in this case), which shows that it is not robust to operational changes. As in the previous scenario, the adaptive controller maintains its very good Smooth/far from limits Adaptive controller: Slightly bigger amplitude performance without any need of manual adjustment of its parameters. Table IV shows that the adaptive controller maintained an overall similar performance with relation to the previous case (especially for the RMSE that remained nearly unchanged) while the feedforward controller had critical losses, which would only be compensated by an adequate manual adjustment of the K f f c gain. Fig. 7 confirms that the adaptive controller generated a control signal with a slightly bigger amplitude than the feedforward controller. These experiments have been registered on the accompanying video.

D. Evolution of the estimated parameter Mtot

In order to compensate for the load changes, the parameter M tot was estimated in real-time by the adaptive controller. The feedforward gain K f f c , which will be considered as an offline estimation of M tot , remains constant during all the experiments. The behavior of both estimations of M tot is depicted in Figs. 89for different accelerations.

For the first scenario, the value of K f f c which provides the best performance of the feedforward controller is equal to 0.825 (dashed curves in both Figs. 89). The first thing to be mentioned is that the convergence of the estimation of the adaptive controller from the initial value to a region around 0.825 is fast enough to be accomplished before the first stop point is reached (which is the expected performance in a pick-and-place task, where the robot will perform movements with payload followed by movements without payload). This confirms the fact that the tracking performance of the adaptive controller will barely be affected by an initial value which is different from the best value for the specific case, and also justifies the good performance of the feedforward controller when keeping this value constant during this experiment.

For the second scenario, the crucial loss of performance of the feedforward controller is justified. In Fig. 9, it is shown that when not manually updating the feedforward gain K f f c , this estimation will now remain with an inadequate value. The estimation of the adaptive controller converges to a region around Mtot = 0.625, which is the best value of K f f c for this case. Another point to be mentioned is the increased oscillations in parameter estimation with the increase of acceleration. Between the most reasonable causes, one can mention the increase of unmodeled dynamics effects (such as the dry and viscous frictions, counter-electromotice forces, etc.), which become more important with higher accelerations, thus becoming a relevant disturbance source. However, the robustness of the adaptive controller enables it to maintain both smoothness and good performance of the closed-loop system in terms of tracking, as well as in terms of evolution of the control inputs (the same general form for both controllers, without addition of oscillations by the adaptive controller, cf. Figs. 5,7), despite oscillations on parameters.

VI. CONCLUSION AND FUTURE WORKS

In this paper, in order to guarantee the best possible tracking performance of the redundantly actuated parallel manipulator R4 independently of the operational scenario, a dual-space adaptive controller was proposed. For evaluation purposes, it was compared with a dual-space feedforward controller, which is able to provide a good performance when best configured for a specific case, but loses much performance when any operational change occurs. The realtime experimental results show clearly that the proposed adaptive controller is able to compensate for the load changes quickly enough to be applied on a pick-and-place task, even with very high accelerations. As future works, the addition of the friction in the dynamic model will be analyzed, such that a corresponding adaptation term can be added in the adaptive controller, and other applications such as laser cutting with complex trajectories shall be performed.

Fig. 1 .

 1 Fig. 1. The R4 parallel manipulator: Schematic view of the CAD design (left), side view of the robot prototype (right)

Fig. 2 .

 2 Fig. 2. Block diagram of the proposed dual-space feedforward controller

Fig. 3 .

 3 Fig. 3. Isometric view of the 3D pick-and-place trajectory

Fig. 4 .Fig. 5 .

 45 Fig. 4. 3D pick-and-place tracking errors with a payload of 200g for an acceleration of 20G

Fig. 6 .Fig. 7 .

 67 Fig.6. 3D pick-and-place tracking errors without payload for an acceleration of 30G

Fig. 9 .

 9 Fig. 9. Evolution of the parameters Mtot and K f f c (dashed) for different accelerations (without payload)

TABLE I GEOMETRIC

 I

		/DYNAMICS PARAMETERS
	r b [m]	r t p [m]	l i [m]	L i [m]
	0.135	0.05	0.2	0.53
	M t p [kg] M f orearm [kg] I act [kg.m 2 ] I arm [kg.m 2 ]
	0.2	0.065	0.003	0.005

TABLE II PARAMETERS

 II OF THE DUAL-SPACE FEEDFORWARD CONTROLLER

	K p	K i	K d	K f f c	K f f j
	8000 600	40	0.825	0.012
		TABLE III
	CONFIGURATION OF THE DUAL-SPACE ADAPTIVE CONTROLLER
	Adaptive gains		γ 11 = 0.2 / γ 22 = 1.5e -4
	Range of Mtot (kg)		[0.525;1]
	Range of Îtot (kg.m 2 )		[0.006;0.018]
	λ 0				100
	δ			0.0001
	K p				8000
	K d				40


Zeineb Zarrouk

Ahmed Chemori

Philippe Poignet

Adaptive Force Feedback Control for 3D Compensation of Physiological Motion in Beating Heart Surgery

In this paper the problem of 3D physiological motion compensation in beating heart surgery is resolved by an adaptive control architecture based on Model Reference Adaptive Control (MRAC). The proposed control architecture uses the measures of the contact efforts applied by the surgical tool on the heart to assure force feedback. No apriori information about motion characteristics is necessary. It includes a nonlinear feedback linearizing the robot dynamics and a velocity loop. Simulation results are presented to show the effectiveness of the proposed control architecture for 3D compensation of physiological motions in beating heart surgery. Furthermore, its robustness toward uncertainties on dynamic parameters and environment stiffness is shown.

I. INTRODUCTION AND RELATED WORK

In cardiac surgery, physiological motions induced by the heartbeat and respiration can make it very problematic for the surgeon to perform skillful and precise operations on the heart. These motions represent a source of perturbations that make surgical tasks very difficult to perform. It is proved that manual tracking of heart motion cannot be achieved without phase and amplitude errors [START_REF] Falk | Manual control and tracking-a human factor analysis relevant for beating heart surgery[END_REF]. For many years, cardiac surgery has been performed using an external machine that insures blood circulation and body's oxygenation. This technique allows the surgeon to operate on a stopped heart and perform precise gestures. However, the use of the heart-lung machine implies more risks and a longer recovery time [START_REF] Okamura | Haptics for robot-assisted minimally invasive surgery[END_REF]. An alternative technique to cancel beating heart motion is the use of a passive mechanical stabilizer. This device stabilizes a small region on the heart surface by suction or pressure. However, the stabilizer may damage the myocardium tissue and experiments performed on pigs show a residual cardiac motion that is still important to achieve heartbeat surgery [START_REF] Lemma | Do cardiac stabilizers really stabilize? experimental quantitative analysis of mechanical stabilization[END_REF]. To avoid the use of the heart-lung machine and overcome the problems related to the physiological motions, robotized systems using vision or force control to compensate them have been developed. In this context, several control architectures have been proposed to deal with motion compensation in minimally invasive beating heart surgery. Based on a vision sensor, Nakamura et al. [START_REF] Nakamura | Heatbeat synchronization for robotic cardiac surgery[END_REF] developed the first system for estimating the heart motion using high-speed cameras by tracking markers fixed on the heart surface. In [START_REF] Ginhoux | Active filtering of physiological motion in robotized surgery using control[END_REF], Ginhoux et al. proposed a vision based approach for motion canceling using model predictive control to get higher precision tracking. Once again, a camera is Zeineb Zarrouk, Ahmed Chemori and Philippe Poignet are with LIRMM, Univ. Montpellier 2 -CNRS, 161 rue Ada, 34392 Montpellier, France chemori@lirmm.fr employed to track artificial markers placed on the heart surface. However, the use of additional markers is not desirable in real surgical procedures due to the space limitation and to the problems related to their fixation. To avoid such problems, Ortmaier et al. [START_REF] Ortmaier | Motion estimation in beating heart surgery[END_REF] have used the natural textures on the heart surface for estimating the heart motion using vision. In this approach, salient features on the heart surface were tracked using a motion model. In [START_REF] Bebek | Intelligent control algorithms for robotic-assisted beating heart surgery[END_REF], Bebek et al. demonstrated that the tracking motion can be improved by the use of electrocardiogram (ECG) signal in the motion estimation. Their approach is based on the fusion of the heart motion measured by mechanical motion sensors and the ECG signal. This information is used to predict the feedforward reference signal. Both control approaches developed in [START_REF] Ginhoux | Active filtering of physiological motion in robotized surgery using control[END_REF] and [START_REF] Bebek | Intelligent control algorithms for robotic-assisted beating heart surgery[END_REF] used algorithms predicting the future heart motion based on recorded heart cycles. However during a contact task, the forces applied on the heart introduce disturbances modifying the natural motion. In this case, the predictive algorithms may fail to accurately predict and compensate the future heart motion. Besides the problem of the heartbeat in minimally invasive cardiac surgery, an important obstacle encountered by surgeons is the significant degradation of haptic feedback about the surgical instrument interaction with tissues. Indeed, surgeons can only estimate contact forces through the tissue deformation. Therefore, focusing on motion compensation using force feedback, Cagneau et al. [START_REF] Cagneau | Physiological motion compensation in robotized surgery using force feedback control[END_REF] proposed an approach based on a PI scheme coupled with an Iterative Learning Control (ILC). The proposed algorithm assumes that the heart motion is periodic. This hypothesis may be too restrictive and the experiments performed on an animated contact show large tracking errors. In [START_REF] Cortesao | Motion compensation for robotic-assisted surgery with force feedback[END_REF], a novel technique is proposed to compensate physiological motions using force control. This approach is based on two independent Active OBservers (AOB) designed for force control and motion compensation. The first AOB has its estimation strategy tuned for haptic telemanipulation, providing control actions through estimated states to achieve a desired closed loop dynamics. The second AOB performs control actions referred to the system input. The obtained simulation of this control approach shows good compensation of sinusoidal and non-sinusoidal physiological motions. In [START_REF] Dominici | Compensation of physiological motion using linear predictive force control[END_REF], Dominici et al. proposed a predictive force control for compensating physiological motions based on a process model to predict future plant behavior using past and current forces applied values. Simulation results show the efficiency of the proposed control approach to compensate heart motion along Z axis. This present paper deals with a technique to compensate physiological motions in minimally invasive beating heart surgery based on an adaptive force feedback scheme. The paper is organized as follows : Section II describes the D2M2 robot manipulator whose dynamic model is used for simulations. Section III describes the proposed control architecture used in the compensation problem. Simulation results are presented and commented in Section IV. Finally, Section V deals with some concluding remarks.

II. THE D2M2 ROBOT MANIPULATOR

The D2M2 (cf. Fig. 1) is a robot manipulator designed for surgery experiments. It has 5 degrees of freedom with direct drive actuators providing high-bandwidth motion tracking and low friction. These properties allow the robot endeffector to track the heart motion characterized by high frequencies and may ensure motion compensation. An ATI Mini 40 force sensor is fixed at the extremity of the endeffector to measure in real time the forces applied by the robot on the environment. The dynamic model [START_REF] Dombre | Modeling, Identification and Control of Robots[END_REF] of the D2M2 robot in contact with its environment is given by :

Γ = M(q) q +V (q, q) + G(q) + J T (q)F e (1)
where

• Γ : the vector of the generalized torques • M : the inertia matrix • V : the Coriolis and Centrifugal vector • G : the gravity vector • J : the Jacobian matrix

• F e : the measured contact force at the end-effector • q, q and q : the vectors respectively of articular positions, velocities and accelerations. This model can be rewritten as follows :

M x (q) Ẍs +V x (q, q) + G x (q) = F sc -F e (2)
with: M x (q) = J -T (q)M(q)J -1 (q)

V x (q) = J -T (q)V (q, q) -M x J(q, q) q G x (q) = J -T (q)G(q) M x , V x and G x are respectively the inertial matrix, the Coriolis and centrifugal force vector and the gravity term written in Cartesian space. F sc denotes the commanded force and J = dJ dt is the first derivative of the Jacobian matrix.

Let us now consider the control input F sc as :

F sc = M x (q) f * +V x (q, q) + G x (q) + F e (3)
This leads to the following fully linearized and decoupled second order system :

Ẍs = f * (4)
where f * is an acceleration, being an input parameter.

In this work, the singularity of the Jacobian matrix is not considered. In fact, the low amplitude of the heart motion signal may not put the robot in a singular configuration. Equation ( 4) represents the dynamics of a unitary mass for each Cartesian dimension described by Fig. 2.

Introducing the gain K 2 of the velocity loop (cf. Fig. 3), the Fig. 2. Decoupled and linearized system equivalent linear transfer function is given by :

G(p) = F e u = 1 p(p + K 2 )
where p represents Laplace operator and F e is the Cartesian force applied by the robot and u is the control input.

III. PROPOSED ADAPTIVE FORCE FEEDBACK CONTROL ARCHITECTURE A. Global control architecture

The global control scheme, shown in Fig. 3, is composed of five parts, namely:

• The system plant linearized in Cartesian space

• The contact environment

• The adaptive controller • The reference model which characterizes the closedloop desired performance • A linear pre-filter H m that determines the reference signal. It is given by :

H m (p) = ω 2 p 2 + 2ξ ω p + ω 2 (5)
In the following section, the different blocks of the global control architecture are detailed.

B. Exact feedback linearization of the robot dynamics

To ensure the heart compensation, the proposed control architecture is based on a linear adaptive controller. The use of a linear controller implies full exact input-state linearization of the robot dynamics. The linearized model is presented and described in section II.

C. Environment

The block "Contact (K s )" presented in Fig. 3 is the environment with which the robot's end-effector interacts. In our case, it represents the heart surface which is in perpetual motion. The contact between the end-effector and the heart surface is modeled as a spring with a stiffness K s . According to this assumption, the force F e applied by the robot's endeffector on its environment is giving by:

F e = K s X
where X assigns the penetration of the end-effector in the heart tissue.

D. Model Reference Adaptive Force Control

The Model Reference Adaptive Controller (MRAC) is one of the most important adaptive controllers [START_REF] Bodal | Digital Self-tuning Controllers: Algorithms, Implementation and Applications[END_REF]. It can be seen as an adaptive servo system in which the desired performance is specified through a reference model. The goal of the adaptive controller is to adjust the parameters of the controller to deal with eventual variations in the dynamics of the controlled system and/or uncertainties. The adjustment mechanism is defined by minimizing a determined cost function to keep the output of the process as close as possible to that of the reference model. The proposed controller MRAC is based on output feedback [START_REF] Astrom | Adaptive Control[END_REF]. It is designed for a SISO process with one input and one output. To ensure 3D motion compensation, three MRAC Controllers are used (one controller for each dimension). The proposed MRAC controllers are based on the MIT rule in the adjustment mechanism. This rule is defined by the following expression :

dθ dt = γφ ε (6)
where

• θ is a vector of the controller's parameters,

• γ is a parameter that characterizes the adaptation rate,

• φ is a vector of filtered output, input and command signal, • ε is the augmented error. The derivation of the MRAC in RST form is described as follows:

• The structure of the controller (cf. Fig. 4) [START_REF] Landau | Digital Control Systems: Design, Identification and Implementation[END_REF] is defined by the following equation :

Ru(t) = -Sy(t) + Tu c (t)
where u and y are respectively the input and the output of the controlled system, and u c is the reference signal.

According to the control architecture of Fig. 3, the reference signal u c corresponds to the force which the robot's end-effector must apply on its environment. This structure allows the process to get a perfect output tracking. The polynomials R, S, and T , specified by equations ( 7), [START_REF] Cagneau | Physiological motion compensation in robotized surgery using force feedback control[END_REF], and ( 9), are resolved by the so-called Diophantine equation.

R(p) = p + r 1 (7)
S(p) = s 0 p + s 1 ( 8)

T (p) = t 0 p + t 1 (9)
The vector θ of adjustment is then given by :

θ = [r 1 , s 0 , s 1 ,t 0 ,t 1 ] T Fig. 4. RST controller
At each instant, the parameters of the polynomials R, S and T are updated according to the change in the system parameters.

• Derive an error model ε by adding a correction term to the error between the output of the process and that of the model. • The parameters adjustment law is defined by equation [START_REF] Ortmaier | Motion estimation in beating heart surgery[END_REF]. The MRAC controller aims to minimize the error between the outputs of the process and the model. The goal of this approach is to keep the applied force equal to the desired one. This means that the output of the reference model must be as close as possible to the desired force. To satisfy this condition, the reference model is described by a second order function with a static gain close to 1 and a phase close to 0.

H m (p) = ω 2 p 2 + 2ξ ω p + ω 2 (10)
with ω = 500 and ξ = 1.

E. Closed-loop stability analysis using augmented error

According to [START_REF] Astrom | Adaptive Control[END_REF] (chapter 5, section 5.7), THEOREM 5.9 elaborates the stability of the closed-loop system controlled by the MRAC controller. Indeed, the transfer G can be factorized as G 1 G 2 such that G 1 is strictly positive real. Then the proposed adaptation law [START_REF] Ortmaier | Motion estimation in beating heart surgery[END_REF] gives an asymptotically stable closed-loop system, that is the error tends to zero as t tends to ∞.

IV. SIMULATION RESULTS AND ROBUSTNESS ANALYSIS

This section focuses on the simulation results of the proposed control architecture described in section III. Simulations are performed using MATLAB R2007a software. The beating heart signals simulating the heart motion are those of [START_REF] Sauvée | 3d heart motion estimation using endoscopic monocular vision system[END_REF]. They have been recorded on a pig beating heart using a vision based system. The obtained 3D motions data are displayed in Fig. 5. The force reference is the output Fig. 5. Recorded physiological 3D motion data [START_REF] Sauvée | 3d heart motion estimation using endoscopic monocular vision system[END_REF] of the pre-filter H m described by equation ( 5) with ω = 50 and ξ = 1. This pre-filter inhibits the sudden changes of forces that may generate important torques. Three simulation scenarios are performed, namely :

• motion compensation in nominal case,

• robustness toward parameters uncertainty,

• robustness toward stiffness uncertainty, they are detailed in the following sections.

A. Simulation 1: Nominal case

The initial condition of this first simulation assumes that the robot's end-effector is in contact with the organ. The realtime motion data, which are previously presented, are used to simulate the 3D motion of the beating heart. According to the real-time experiments achieved in [START_REF] Zarrad | Stability and transparency analysis of a haptic feedback controller for medical applications[END_REF], the contact stiffness in our simulator is set to 800 N/m. Three MRAC controllers are used along X, Y , and Z to ensure compensation in 3D. In this simulation scenario, the robot parameters are considered perfectly identified and the external disturbances are supposed to be zero. A variable force reference is applied along each axis. The three first graphs in Fig. 6,7, and 8 display the evolution of the desired forces in solid line and the applied forces in dashed line along the axis X, Y , and Z respectively. The maximal force error is about 3% corresponding to a position error of about 3.7 × 10 -3 %. Fig. 9 shows the heart position (dashed line) and the robot endeffector position (solid line). The difference between the two is due to the D2M2 end-effector penetration of the heart surface, in order to track the desired force. Fig. 10 represents the evolution of the torques generated by the motors of the robot, where it can be clearly seen that they remain within the admissible limits given by the manufacturer of the actuators (150 N.m). The peaks that appear in these curves correspond to the changes in the reference forces. This first simulation is carried out without errors introduced. It shows the good performance of the proposed force feedback control architecture to ensure 3D heartbeat compensation. In the next simulations, different uncertainties are considered to show the effectiveness and the robustness of the proposed control architecture.

B. Simulation 2: Robustness toward dynamic parameters uncertainty

In this simulation scenario, uncertainties on parameters are considered. In view of the fact that the amplitude of the heart motion is more important along Z axis, we introduce 25% of uncertainties on parameters corresponding to the Z axis and 5% on the other parameters. The maximal force error recorded along X axis is almost 5,3% and 2% along Y and Z axis. This resuts can be explained by the number of parameters that are greater along X axis. This simulation proves that the controller is able to adapt its parameters to conform to another system whose parameters are different from the nominal one. The results of the tracking heart motion are shown in Fig. 11.

C. Simulation 3: Robustness toward environment stiffness uncertainty

In this simulation, we consider the situation where the robot's end-effector interacts with tissues of a stiffness different from the nominal one. The environment stiffness is set to 1200 N/m. This means that the stiffness uncertainty introduced is 50% of the nominal value. The 3D compensation of heart motion is shown in Fig. 12. Requiring more energy to apply the desired forces, the torques represented in Fig. 13, are greater comparing to the nominal case, nevertheless, they remain within the admissible limits.

D. Comparison with other control architectures

The force control architectures developed in [START_REF] Dominici | Compensation of physiological motion using linear predictive force control[END_REF] and [START_REF] Cortesao | Motion compensation for robotic-assisted surgery with force feedback[END_REF] are based on a force feedback and linear controllers. These architectures were performed in task space and tested in simulation. A comparison of the proposed approach with these approaches is summarized in table I :

Our controller

Predictive controller [START_REF] Dominici | Compensation of physiological motion using linear predictive force control[END_REF] AOB controller [START_REF] Cortesao | Motion compensation for robotic-assisted surgery with force feedback[END_REF] 3D [START_REF] Dominici | Compensation of physiological motion using linear predictive force control[END_REF] AND [START_REF] Cortesao | Motion compensation for robotic-assisted surgery with force feedback[END_REF] V. CONCLUSION AND FUTURE WORK This paper deals with an adaptive based force control architecture for 3D physiological motion compensation in mini-invasive cardiac surgery. The proposed control approach takes into consideration the breathing and heartbeat motion without adding markers in the workspace to measure the motion. Instead, a force sensor, located at the extremity of robot's end-effector, is used to measure contact forces applied by the surgical tool on the heart surface. Three simulation scenarios have been implemented on the D2M2 robot manipulator. The first one deals with the nominal case, whereas the two others deal with robustness test of the proposed control scheme toward uncertainties on dynamic parameters and environment stiffness. The next step of our work will be focused on real-time implementation of the proposed control architecture on the D2M2 experimental setup. Furthermore, to improve the effectiveness of the proposed control architecture, future work can also include a study of the possibility of taking into account actuators' saturations in the design of the control approach.

Fig. 1 .

 1 Fig. 1. The D2M2 robot

Fig. 3 .

 3 Fig. 3. Global control scheme with linear adaptive force controller

Fig. 6 .Fig. 7 .

 67 Fig.6. Evolution of the contact force and its variable reference along X axis in the nominal case

Fig. 8 .

 8 Fig. 8. Evolution of the contact force and its variable reference in the nominal case along Z axis

Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .Fig. 13 .

 910111213 Fig. 9. Compensation of the heart motion along X, Y , and Z axis (solid line : end-effector position, dashed line : heart position), in the nominal case


G Sartori

A Chemori

F Pierrot

O Company

An Experimental Comparison of State Observers for the Control of a Parallel Manipulator Without Velocity Measurements

This paper deals with the problem of unavailability of velocity measurements for the control of parallel manipulators for pick-and-place applications. As most controllers require the measurement of the joint positions as well as joint velocities, the latter need to be estimated. Three observers have been implemented while keeping the same nonlinear controller: a Lead-lag filter based observer, an Alpha-beta-gamma observer and a High-gain observer. The resulting performances obtained in Real-time experiments by each observer have been detailed and compared.

I. INTRODUCTION

Over the years, mechanical systems have served as an interesting benchmark for the design and validation of novel nonlinear control strategies. One problem that has attracted a good deal of interest is the output feedback control of mechanical systems. This problem is of practical importance since many commercially-available mechanical systems are not commonly equipped with velocity sensors (e.g., industrial robots) [START_REF] Xian | A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems[END_REF], which is our case with the two degree-of-freedom (dof) parallel robot Par2 [START_REF] Pierrot | Above 40g acceleration for pick-and-place with a new 2-dof pkm[END_REF], that can reach accelerations above 40G. The main reasons for the absence of velocity sensors on these mechanical systems are: (i) Signals delivered by tachometers might be contaminated with noise; (ii) Increased costs when more sensors are used in the plant [START_REF] Arteaga | Robot control and parameter estimation with only joint position measurements[END_REF].

It is well known that in most control algorithms it is assumed that the joint velocities are available. For this reason, they need to be calculated/estimated. The easiest way to compute the joint velocities consists in a numerical derivative of the measured joint positions. However, if the measured positions are noisy or do not have a good enough resolution, this technique will amplify the noise/quantization effect. An estimation of the joint velocities by means of observer-based techniques should then be considered.

The choice of the estimation mechanism is strongly influenced by the existence of uncertainty in the system model. Whereas model-based observers are usually restricted to cases where the model is exactly known, filters can provide model-independent means of estimating velocity [START_REF] Xian | A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems[END_REF].

Model-based schemes were presented in [START_REF] Nicosia | Robot control using only joint position measurements[END_REF], where an exact knowledge based observer-controller was designed, which yielded a semi-global asymptotic tracking result, while in [START_REF] Berghuis | A passivity approach to controllerobserver design for robots[END_REF] and [START_REF] Lim | Re-examining the Nicosia-Tomei robot observer-controller from a backstepping perspective[END_REF] were designed for the case of exact knowledge-based controller [START_REF] Erlic | Manipulator control with en exponentially stable velocity observer[END_REF] and adaptive controller [START_REF] Erlic | A reduced-order adaptive velocity observer for manipulator control[END_REF]. For the case where the system was considered uncertain, variable structure modelbased observers for the design of adaptive [START_REF] De Wit | Trajectory tracking in robot manipulators via nonlinear estimated state feedback[END_REF] and robust [START_REF] De Wit | Robot control via robust estimated state feedback[END_REF] controllers were proposed. For more details about the control of PKMs, the user is referred to [START_REF] Sartori-Natal | Nonlinear dual mode adaptive control of par2: a 2-dof planar parallel manipulator, with real-time experiments[END_REF].

Filter-based control schemes were designed in [START_REF] Loria | Force/position regulation for robot manipulators with unmeasured velocities and uncertain gravity[END_REF], [START_REF] Kaneko | Repetitive and adaptive control of robot manipulators with velocity estimation[END_REF], [START_REF] Yuan | Robust control of robotic manipulators without velocity measurements[END_REF], [START_REF] Zergeroglu | On global output feedback tracking control of robot manipulators[END_REF]. In [START_REF] Loria | Force/position regulation for robot manipulators with unmeasured velocities and uncertain gravity[END_REF], a simple first order filter was proposed to estimate the velocity for the force-position regulation of robotic manipulators through a PI 2 D controller. A filter on the position signal was used to create a velocity signal which was used to design a robust controller with feedforward terms with fixed parameter estimates and a linear feedback term was proposed in [START_REF] Yuan | Robust control of robotic manipulators without velocity measurements[END_REF]. In [START_REF] Kaneko | Repetitive and adaptive control of robot manipulators with velocity estimation[END_REF], a filter-based observer was used with an adaptive output feedback controller which yielded semi-global asymptotic link position tracking. In [START_REF] Zergeroglu | On global output feedback tracking control of robot manipulators[END_REF], a filter was implemented to obtain the velocity error in an adaptive controller which was shown to guarantee global asymptotic trajectory tracking. A detailed comparison between three different methods of adaptive output feedback control for robotic manipulators (the first one with a Highgain observer (HGO), the second one with a linear secondorder observer and the third one with an Extended Kalman Filter (EKF)) was presented in [START_REF] Daly | Experimental results for output feedback adaptive robot control[END_REF].

While in [START_REF] Sartori-Natal | Nonlinear dual mode adaptive control of par2: a 2-dof planar parallel manipulator, with real-time experiments[END_REF] an experimental comparison between two controllers was made using the same velocity estimator (HGO), in the present work three velocity estimators have been implemented experimentally on Par2 parallel manipulator with the Dual Mode (DM) controller [START_REF] Hsu | B-mrac global exponential stability with a new model reference adaptive controller based on binary control theory[END_REF]: The Leadlag (LL) [START_REF] Norman | Control Systems Engineering[END_REF] based observer, the Alpha-beta-gamma (ABG) observer [START_REF] Penoyer | The alpha-beta filter[END_REF] and the High-gain observer [START_REF] Lee | Adaptive output feedback control of robot manipulators using high-gain observer[END_REF]. The control performance obtained with each observer will be detailed and compared. It is important to emphasize that the parameters of the controller were not changed, as the main objective of this study is to evaluate the performance improvements obtained by using different observers with the same controller.

This paper is organized as follows. Section II introduces briefly the proposed control algorithm. In section III, the implemented observers are described. In section IV, the application is described. Section V is devoted to the experimental results, being the performances of the proposed observers compared and commented. In section VI, a conclusion about the current results is made.

II. PROPOSED CONTROL SCHEME: A NONLINEAR DUAL MODE CONTROLER

The control method proposed in this work is a nonlinear Dual Mode controller [START_REF] Hsu | B-mrac global exponential stability with a new model reference adaptive controller based on binary control theory[END_REF] (originally referred as 'binary'), derived from the nonlinear adaptive controller proposed in [START_REF] Slotine | Adaptive manipulator control: A case study[END_REF], with the addition of the projection on the law of the parametric adaptation. It consists basically in the utilization of a high adaptation gain together with a projection of the estimated parameters. Then, to large tracking errors in the transitory stage, the controller behaves approximately as a sliding mode controller, generating an exponential convergence to a residual domain arbitrarily small, and to smaller errors, it behaves as a parametric adaptation law. Other important advantages of the adaptation law in dual mode with respect to other adaptive controllers or known robust control algorithms are the generation of continuous control signals, the improvement of the robustness of the system and the limitation of the values of the estimated parameters thanks to the projection, which has the effect of reducing the effective gain of the controller when the tracking error increases (reducing the sensitivity to measuring noises).

This control law is given by:

τ = Y â + K.s + dSat(αs) (1)
where s = q + λ q, being q = q dq, q = qdq (q, q and q ∈ R n are the vectors of positions, velocities and accelerations and q d , qd and qd ∈ R n are their desired trajectories, respectively); λ , d, α and K are positive constants, Sat(αs) = αs ||αs||+1 is a smooth and continuous saturation function with respect to its argument (with continuous partial derivatives and components limited to the interval [-1, +1]). The mx1 vector â represents an estimate of the unknown parameters of the system given by the vector a, and Y (q, q, q) ∈ R n×m is the regressor vector (based on the dynamic model of the system). The reader is referred to [START_REF] Sartori-Natal | Nonlinear dual mode adaptive control of par2: a 2-dof planar parallel manipulator, with real-time experiments[END_REF] for more details about this controller.

According to equation [START_REF] Xian | A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems[END_REF], it is possible to notice that the proposed control scheme needs the measured positions and velocities. As mentioned before, it is assumed that the velocity measurements are not available, so an estimator must be proposed and implemented. In the present work, three estimators have been implemented and compared. They are described in the following section.

III. IMPLEMENTED OBSERVERS

To deal with the unavailability of velocity measurements, three estimation techniques have been implemented. They are presented in the sequel:

A. LEAD-LAG BASED OBSERVER

The Lead-lag filter [START_REF] Norman | Control Systems Engineering[END_REF] has the following modified structure:

G ll (p) = p τ 1 p + 1 ( 2
)
where p is the Laplace variable. So, the smaller τ 1 is chosen, the more accurate the velocity estimation will be, but the more noise the estimated velocity will have. Its basic idea is to approximately derivate the input signals (in our case, the joint positions), as shown in Eq. ( 3):

q(t) = g ll (t) * q(t) (3)
where q(t) is the estimated joint velocity, g ll (t) is the inverse Laplace transform of G ll (p), i.e, g ll (t) = L -1 [G ll (p)] and the operator * denotes the convolution between the two functions.

The main advantages of this method are its simplicity and computational efficiency, but its main drawbacks are:

1) If τ 1 is given a big value, a delay will be generated and it will cause an inaccurate velocity estimation; 2) If τ 1 is given a small value, there may be a considerable amplification of the noise/quantization effect. Then, τ 1 must be chosen such that a compromise between 1) and 2) is achieved.

B. ALPHA-BETA-GAMMA OBSERVER

The Alpha-beta (or Alpha-beta-gamma) observer [START_REF] Penoyer | The alpha-beta filter[END_REF] consists in a simplified form of Kalman Filter [START_REF] Kalman | A new approach to linear filtering and prediction problems[END_REF] for mechanical systems that have as states the positions and velocities. Its main idea consists in estimating the next step's states of the system according to the usual equations of kinematics and to correct these estimations through the multiplication of the positions' estimation errors by constant gains. The structure of this observer is detailed as follows:

• Estimation of the next step's positions and velocities:

x prev (k + 1) = x innov (k) + T v innov (k) + 1 2 T 2 a innov (k) v prev (k + 1) = v innov (k) + Ta innov (k) (4)
where x prev (k +1) and v prev (k +1) are the estimated positions and velocities for the next step, x innov (k), v innov (k) and a innov (k) are respectively the updated positions, velocities and accelerations obtained through a correction based on the estimation error of the position, detailed as follows,

• Update of the estimated positions and velocities (also called innovation) based on the position measurement:

   x innov (k) = x prev (k) + α(x meas (k) -x prev (k)) v innov (k) = v prev (k) + β T (x meas (k) -x prev (k)) a innov (k) = γ T 2 (x meas (k) -x prev (k)) (5)
being α, β and γ the update gains, x meas the measured positions and T the sampling time.

In our case, the initial joint positions are known and the initial joint velocities are equal to zero, since the robot starts its movements from rest. So, x prev (1) and v prev (1) are initialized with these values, respectively. On the next step, based on the new measured joint positions, there is the innovation process, in which x innov , v innov and a innov are computed and then used to compute the new estimated states of the system (x prev and v prev ) for the next step.

As the Lead-lag based observer, this observer has also the advantage of being very computationally efficient and simple to implement, but it can provide a better performance and robustness (cf. experimental results in section V). One of its main disadvantages is that its gains must be chosen such that a considerable amplification of the noises/quantization effect is avoided, but even with less aggressive gains, fairly decent performances can be achieved.

C. HIGH-GAIN OBSERVER

The High-gain observer (HGO) is a model-based observer that was proposed in [START_REF] Lee | Adaptive output feedback control of robot manipulators using high-gain observer[END_REF]. The main characteristic of this observer is that it takes into account the model of the system, so it can generate a very good performance if a precise model is available. However, even if this is not the case, this observer is robust because at each step a correction of the estimated states is made according to the comparison between the estimated positions and the measured ones. Its description is given as follows:

ẋ1 = x2 + 1 ε α HGO1 (x 1 -x1 ) ẋ2 = 1 ε 2 α HGO2 (x 1 -x1 ) -qd + F( x, q d , qd ) + Ĥ( x1 , q d )τ s (

6) where

• x 1 represents the position error (x 1 = q) and x 2 , its first derivative (x 2 = q), • x = [ x1 x2 ] T represents the vector of estimated states, • ε, α HGO1 and α HGO2 are positive gains, • F( x, q d , qd ) and Ĥ( x1 , q d ) are terms that depend on the dynamic model of the system, • τ s is the saturated torque (to avoid the 'peaking phenomena'). Its main characteristics are: 1) It is robust to uncertainties on the model of the system, although a precise model is needed in order to obtain better performances; 2) It is more complex (computationally and also concerning its implementation) than the two previously described observers; 3) If the gain is selected high enough, it becomes very sensitive to the noise in the position measurement.

IV. APPLICATION: PAR2 PARALLEL MANIPULATOR

The three proposed observers, complied with the proposed nonlinear controller, were applied on the Par2 parallel manipulator illustrated in Fig. 1. Its main characteristics are:

• the platform 6 is a rigid body,

• only the two inner arms 3 are actuated, • the two other arms 4 are linked to the frame 1 through passive revolute joints, • inner arms 3 and 4 are connected to 6 with pairs of rods 5 mounted on ball joints 7 , • the rotations of the arms 4 are coupled in order to guarantee planar motions along x and z axes. For more details about the prototype Par2, the reader is referred to [START_REF] Pierrot | Above 40g acceleration for pick-and-place with a new 2-dof pkm[END_REF].

V. REAL-TIME EXPERIMENTAL RESULTS

The objective of this section is to present and discuss realtime experimental results obtained by the application of the three proposed observers described in section III associated with the control scheme described in section II to the Par2 parallel manipulator described in section IV. The Real-time experimental setup is displayed in Fig. 2. The platform of the robot evolves in the XOZ plane (cf. figure 1). The desired Cartesian trajectory to be tracked by Par2 is a usual 'pick-and-place' trajectory (which has an S-curve profile, being the reader referred to [START_REF] Red | A dynamic optimal trajectory generator for cartesian path following[END_REF] for more details). Its parameters are described in table I.

The parameters of the proposed control approach are summarized in table II and the parameters of the three proposed observers are described in table III. These parameters were tuned such that each observer could provide its best performance. The proposed experimental scenario deals with the control The desired joint trajectory denoted by q d (t) is supposed uniformly bounded, twice continuously differentiable with its two first derivatives qd (t) and qd (t) also uniformly bounded.

The trajectory tracking obtained by the DM controller with the three proposed observers for 15G of maximum acceleration is shown in Figs. 4 and5, and the corresponding tracking errors are shown in Fig. 6. The velocity tracking is presented in Fig. 7 and the estimated velocity errors are presented in Figs. 8 and9. The control inputs are shown in Figs. 10 and11. The real-time implementation of these observers was made with a sampling time of 0.5 msec.

It is worth to notice that the experimental testbed does not include a sensor to measure the Cartesian position of the platform [START_REF] Pierrot | Above 40g acceleration for pick-and-place with a new 2-dof pkm[END_REF]. In addition, because of the high frequency rate (which requires a small computing time), other methods such as vision-based control have not been implemented.

By analyzing figures 5 and 6, it is possible to notice that the best tracking performance was obtained with the ABG observer. With this observer, the tracking errors were kept inside the limits of [-0.2 • , 0.55 • ] during all the trajectories, while the LL observer kept them inside the limits of [-0.5 • , 0.7 • ] and the HGO kept them inside the limits of [-0.6 As for the main reasons why the Alpha-beta-gamma observer was able to generate a better tracking performance than the Lead-lag based observer and the High-gain observer, one can mention that:

1) For the implementation of the HGO, important simplifications on the model of the system were made (when neglecting the mass of the platform) such that it would be possible to represent it on the Lagrangian form. As this observer is model-dependent, this may have caused a considerable loss of performance; 2) The ABG observer is naturally more performant than the LL based observer because the last one consists only in a transfer function that will generate an approximate value of the velocity, while the ABG observer not only estimates the velocity but also corrects its estimation at each step time according to the estimation of the position error. From figure 7, it is difficult to distinguish the curves of reference velocities from those of the estimated ones. It is only possible to adequately analyze their estimation performances through the estimated velocity errors in Fig. 8 (for motor 1) and figure 9 (for motor 2). These figures show that the velocity estimation of the ABG observer was the one that, in average, kept the smaller errors for the longest time during the trajectories, while the velocity estimation of the HGO was the one that kept the smaller errors for the shortest time. It is also possible to notice that the ABG observer generated the most noisy velocity signals, while the LL generated smaller noises but bigger oscillations and the HGO generated nearly no noise and small oscillations.

As for the control signals (figure 10 for motor 1 and figure 11 for motor 2), a similar conclusion can be made. The ABG observer generated the most noisy control signals with small vibrations, the HGO generated the smoothest signals with small vibrations and the LL observer generated the signals with the biggest oscilations. The control signals generated by the three observers showed roughly similar amplitudes and remained inside the admissible limits of each actuator (500 N.m) by a large margin.

The performance details of the three observers are summarized on table IV.

VI. CONCLUSIONS

This paper deals with the problem of unavailability of velocity measurements for the control of parallel manipulators. Three state observers have been proposed and implemented, namely the Alpha-beta-gamma (ABG) observer, the Highgain observer (HGO) and a Lead-lag (LL) based observer. A detailed comparison between the trajectory tracking performances obtained by these observers associated with a nonlinear Dual Mode (DM) controller for a parallel manipulator (Par2) has been presented, for a maximum acceleration of 15G. By analyzing the obtained results, it was possible to notice that all observers generated a good estimation of the velocities, which made it possible for the DM controller to have a good tracking performance in all cases. However, the ABG observer generated the best tracking performance.

Fig. 1 .

 1 Fig. 1. The two-dof parallel manipulator Par2: view of the robot (left), schematic view of its mechanical structure (right)

Fig. 2 .

 2 Fig. 2. Par2 parallel manipulator experimental setup

τ 1 =Fig. 3 .

 13 Fig. 3. Illustration of the robot's movements

Fig. 4 .Fig. 5 .

 45 Fig.[START_REF] Nicosia | Robot control using only joint position measurements[END_REF]. One cycle pick-and-place trajectory trackings for 15G obtained by using the ABG (dots), the HGO (dashed) and the LL (dash-dots) observers

  the controlled system yielded semi-global exponential link position tracking. Reduced order observers

This work is supported by ANR Objectif 100G: a French National Project on Parallel Robots. G. Sartori Natal, A. Chemori, F. Pierrot and O. Company are with LIRMM, Univ. Montpellier 2 -CNRS, 161 rue Ada, 34392 Montpellier, France sartorinatal@lirmm.fr


Philippe Poignet

Ahmed Chemori

Nabil Zemiti

Chao Liu

Some control-related issues in mini-robotics for endoluminal surgery

This paper introduces some issues related to the development of robotics for endoluminal surgery from control point of view. Endoluminal surgery are incisionless procedures performed through natural orifices within the natural pathways. New devices are then required to achieve these new surgical procedures. Besides the development of new devices, control issues arise in both technological and theoretical aspects. The paper presents some of them and we propose a teleoperation architecture that has already been tested for needle insertion that could be used for teleoperated endoluminal surgery especially for instance for biopsies or anastomoses.

I. INTRODUCTION

Endoluminal Surgery or Natural Orifice Translumenal Endoscopic Surgery (NOTES) are incisionless procedures performed within the natural pathways (mouth or other natural orifices) or by creating an opening in the lumen to access to abdmoninal organs. Operating through the bodys natural orifices should offer faster recovery times, less scarring and less pain, which could lead to reduced hospitalization.

Then since recently, endoluminal interventions are evolving quickly and different major procedures have emerged through endoscopic treatment. The gastroesophageal reflux disease (GERD) represents the earliest application of this new surgical procedure [START_REF] Richards | Paradigm shift in the management of gastroesophageal reflux disease[END_REF]. But various applications have been reported during the last decade including endoscopic mucosal resection [START_REF] Ono | Endoscopic mucosal resection for treatment of early gastric cancer[END_REF] with a mucosal ablation depth of 600 microns to 700 microns [START_REF] Sharma | Successful ablation of barrett's esophagus with low-grade dysplasia (lgd) using barrx balloon device[END_REF], endoluminal gastroplication or radiofrequency energy delivery to the gastroesophageal junction. Works in [START_REF] Seewald | Aggressive endoscopic therapy for pancreatic necrosis and pancreatic abscess: a new safe and effective treatment algorithm (videos)[END_REF] have also been reported showing the promise of endoscopic therapy for pancreatic necrosis and pancreatic abscess. Hiatal hernia repair was also performed in a pig model [START_REF] Fritscher-Ravens | Transgastric gastropexy and hiatal hernia repair for gerd under eus control: a porcine model[END_REF] using endoscopic ultrasound (EUS) guidance.

The feasibility of endoluminal therapies has also been demonstrated for the transgastric approach to the peritoneal cavity for diagnostic and therapeutic purposes. In [START_REF] Jagannath | Peroral transgastric endoscopic ligation of fallopian tubes with long-term survival in a porcine model[END_REF], [START_REF] Park | Experimental studies of transgastric gallbladder surgery: cholecystectomy and cholecystogastric anastomosis (videos)[END_REF] for instance, the authors report several experiments such as liver biopsies, manipulation of intraabdominal organs, ligation of fallopian tubes, and transgastric cholecystectomy that have been performed in pigs.

The research is now focused on innovative designs and engineering improvements that have the potential to facilitate these interventions. In this context, robotics plays a key role and the objective of the paper is to introduce the issues from the control point of view which are both theoretical poignet,chemori,zemiti,liu@lirmm.fr and technological, and have appeared during development of this new technology.

The Natural Orifice Surgery Consortium for Advancement and Research (NOSCAR, [www.noscar.org]) identifies several wish list of capabilities or requirements depending on the application. For instance in case of NOTES anastomoses, this list highlights different aspects such as length, flexibility, navigation, vizualization, remote control, feedback, permit suturing (large channel endoscopes), ergonomics / human factors (one person operation).

The paper is then organized as follows. In the next section, we will introduce existing devices that are already commercialized or prototypes developed in robotics labs. Section III presents some difficulties associated to actuation, sensing, transmission as well as fixation problems. Section IV describes the challenges from the control point of view as well as the teleoperation architecture that has been developed for minimally invasive surgery and tested in case of needle insertion such as for biopsy or suturing cases . Experimental results highlight the efficiency of the approach that could then be used for tethered robotized endoluminal surgery. The paper ends with conclusion.

II. A BRIEF REVIEW OF INSTRUMENTS DEDICATED TO ENDOLUMINAL SURGERY

During the last ten years, many systems have been patented such as the "method and apparatus for minimallyinvasive fundoplication" proposed by M. El Gazayerli (Patent US6159146) in 2000 and several devices have already been developed to fulfill the requirements of these new surgical procedures.

In the following, we present a brief review of existing systems that have been classified into two categories depending on the actuation or the level of autonomy. In the first set, the user will find steerable instruments and in the second more sophisticated devices actually developed in the laboratories based on the principle of autonomous robots.

A. Towards a classification of sophisticated NOTES instruments 1) Steerable instruments:

As identified by NOSCAR, a key requirement of NOTES surgery is to provide the surgeon with a stable surgical platform that will support and guide the flexible endoscope and instruments. Indeed, in the abdominal cavity, endoscopes alone are usually free-floating and hence unstable, limiting the physician's ability to perform surgery. For this reason, USGI Medical [www.usgimedical.com] develops the Medicals ShapeLock Endoscopic Guide and ShapeLock Cobra, a multilumen ShapeLock Guide for facilitating endoluminal and transgastric surgery [START_REF] Pankaj Pasricha | A next generation therapeutic endoscope: development of a novel surgery system with "birds-eye" visualization and triangulating instruments[END_REF]. The Cobra device offers the benefit of a stable platform for triangulation of instruments and camera and the ability to use multiple instruments at the same time. Olympus Medical Systems Corp. [www.], another competitor in this area, proposes a multibending therapeutic endoscope called R-scope used for transgastric cholecystectomy [START_REF] Sumiyam | Transgastric cholecystectomy: transgastric accessibility to the gallblader improved with the semf method and a novel multibending therapeutic endoscope[END_REF]. In their experiment, the R-scope, equipped with 2 actuated instrument channels (one allows vertical elevation, the other allows a horizontal swing movement) was used to position a knife for the most ideal dissection. The Endocinch suturing system [www. endocinch.com] is another example of a simple device that will help the doctor to place a series of stitches in the lower esophagus to create a pleat in the sphincter.

Although all these studies and products demonstrate the feasibility of the endoluminal approach, they also emphasize limitations of the present techniques, for instance difficulty in exerting sufficient forward force. Most of them are also cable-driven and guided or controlled by turning a wheel limiting the mobility capability or the dexterity of the device inside the cavity. Therefore the need of more autonomous robot becomes clearly identified.

2) Autonomous robot: To overcome the aforementioned limitations, for instance to offer a stable platform for vizualization and to increase the dexterity of the instrument, the authors in [START_REF] Lehman | Robotic natural orifice transluminal endoscopic surgery[END_REF] present a miniature in vivo robot that consists of two prismatic arms connected to a central body by a rotational shoulder joint. One arm has a forceps and the other hold a cautery end-effector. The central bar is equipped with stereoscopic vision. Thanks to its shape, the robot may be inserted into the peritoneal cavity through the upper gastrointestinal tract approach.

B. The ARAKNES concept

The ARAKNES (Array of Robots Augmenting the KiNematics of Endoluminal Surgery) platform, developed in the framework of a european project [www.araknes.org], extends the concept introduced in [START_REF] Lehman | Robotic natural orifice transluminal endoscopic surgery[END_REF] by giving the surgeon the possibility to manipulate a gastric robotic platform constituted of an array of cooperative robots including assistive and operative robots that will be ingurgitated through the esophagus as illustrated in figure 1. Assistive robots may be viewed for instance as grasping systems or robot equipped with vision and operative robots may be active instruments with suturing or cutting devices. The robots are then bimanually telemanipulated by the surgeon through a remote haptic interface. This concept fulfills then at least two of the NOSCAR requirements: possibility to include remote control of the surgical instrument and feedback through contact interaction information coming from inside the cavity.

In this context, several technological as well as theoretical issues arise, as introduced in the following sections.

III. TECHNOLOGICAL ASPECTS ON CONTROL IN ENDOLUMINAL SURGERY

The specifications of the new robotized instrument (architecture, size, Degrees of Freedom (DoFs), workspace, ...) for endoluminal surgery have to be considered mainly according to the pathways used for introducing instruments and to the aimed surgical task. Indeed, access to the organ is limited by the size and the complex geometry of the insertion pathway. This makes it difficult to insert multiple instruments simultaneously through one orifice.

If the aimed task is, for example, a biopsy on the stomach wall, the customized robot has to be inserted trans-orally to reach the stomach. This imposes a limit on the size and the flexibility of the robot to allow the latter to freely rotate for insertion through the complex geometry of the esophagus. Here, since the esophagus is approximately 15mm diameter large for normal subjects [START_REF] Sultan | Esophageal diameter and the treatment of achalasia[END_REF], to avoid injuries, the overall robotized instrument should be of less than 15mm diameter.

Besides these size constraints, one has to overcome first challenging technological problems concerning the robot architecture and its components such as actuators and sensors. Power and data transmission considerations, biocompatibility, sterilization, etc, have also to be taken into account.

A. Actuators and sensors 1) Actuators: Different solutions can be proposed such as 'on-board actuation', 'remote actuation', or combined 'on-board/remote actuation'. For on-board actuation, i.e. the actuators are placed inside the patient body, problems of miniaturization and amount of the developed force at contact have to be considered. Indeed, the developed interaction force necessary for a puncture/suturing gesture, for example, has to be greater than 10N [START_REF] Zarrad | Towards teleoperated needle insertion with haptic feedback controller[END_REF].

In the literature, several existing technologies might answer these problems : Shape Memory Alloys (SMA) actuators [START_REF] Machado | Medical application of shape memory alloys[END_REF], Electro-Active Polymers (EAP) actuators (www.micromuscle.com), [START_REF] Edwin | Microfabricating conjugated polymer actuators[END_REF], [START_REF] Shahinpoor | Potential applications of electroactive polymer sensors and actuators in mems technologies[END_REF], piezoelectric motors and electromagnetic motors [START_REF] Tendick | Applications of micromechatronics in minimally invasive surgery : Focused section on micromechatronics[END_REF]. However, considering the size imposed by the endoluminal surgery, the most mature and efficient technology to date (in term of the amount of developed interaction force) is piezoelectric and electromagnetic. Examples of such commercially available solutions are the micromotors from Faulhaber group (www.faulhaber-group.com) or from Namiki Precision www.namiki.net and the piezo micromotors from New Scale Technologies, Inc. (www.newscaletech. com).

In addition, if a large number of DoFs is chosen, problems of flexibility and backlashes due to the weight of the overall system should be considered.

Remote actuation offers the possibility of placing the actuators outside the patient body implying then much less miniaturization, power and data transmission constraints. In this case, the power transmission can be done pneumatically, hydraulically (using sterile water for example) or through cables. The main feature of this solution is that it offers a large developed force at the robot end-effector while having no limit on the size of the chosen actuators.

One can however combine both on-board and remote actuation solutions. The on-board actuation can be used to move the DoFs that don't need large interaction forces (rotate a camera for example). The remote actuation for the rest (suturing, puncturing, etc).

2) Sensors: One of the requirements for the robot is to assist the surgeon in his/her gestures providing him/her with sensing and display functions, improving thus the surgeon's ability to sense and control the interaction forces.

One of the ARAKNES project objectives is to develop a force feedback teleoperated system. Visual feedback, position and force informations are thus mandatory to be used as inputs in the robot controller.

Miniaturized position sensors already exist (potentiometers, optical encoders or hall-effect sensors) and should not be a big challenge to deal with. This information will be used in the robot position control loop. This allows the robot to perform autonomous or teleoperated tasks.

To offer a visual feedback to the surgeon, miniaturized passive cameras that can be inserted inside the patient body are now available in the context of endoluminal surgery. One can cite for example the PillCam T M from Given Imaging or the Endo-Capsule from Olympus.

Note that the visual feedback can also be exploited as a position measurement to implement a visual servoing control scheme for the robot. This enables to control the robot with more advanced control strategies such as point to point autonomous position control.

To measure and control the interaction contact forces, one needs to use a miniaturized force sensors. Different technological solutions could then be used such as strain gauges, piezo-resistive, optical sensor [START_REF] Peirs | A micro optical force sensor for force feedback during minimally invasive robotic surgery[END_REF] or electro-active polymer based sensors [START_REF] Shahinpoor | Potential applications of electroactive polymer sensors and actuators in mems technologies[END_REF]. However, the MEMS micro force sensors like the ones presented in [START_REF] Sun | Actively servoed multi-axis microforce sensors[END_REF], [START_REF] Shen | An active micro-force sensing system with piezoelectric servomechanism[END_REF], [START_REF] Kim | Calibration of multiaxis mems force sensors using the shape from motion method[END_REF], have to be considered with interest to be implemented and adapted for the endoluminal surgery context.

B. Fixation challenges

One of the most important factors considered in the design of a robotic platform is providing a stable robot adhesion at the stomach wall in order to perform the required forces.

Different solutions presented in the literature can be considered. For instance, external magnetic attachment and positioning using magnetic handle, or needles and hooks configuration to attach the robot physically to the inner abdominal wall were presented in [15]. Dario et al. have recently described an endoscopic pill with an active locomotion system that uses "legs" to push against the gastrointestinal walls [2], [START_REF] Flynn | Tomorrow's surgery: micromotors and microrobots for minimally invasive procedures[END_REF], and a clamping system that uses shape memory alloys [START_REF] Menciassi | Shape memory alloy clamping devices of a capsule for monitoring tasks in the gastrointestinal tract[END_REF].

C. Wire or wireless

In the context of robotized endoluminal surgery, data and energy transmission is an important issue to consider. If the on board solution is chosen, wire (tethered robot) or wireless solution could be chosen depending on the available technology.

The tethered solution seems to be the simplest one if the dimension of the data/energy cables are compatible with the dimension of the patient natural orifice.

In wireless solution, one has to consider this solution since wires may constitute a channel for infection and encumber the insertion pathway.

Wireless data transmission is less complicated than wireless power transmission. For intra-body data exchange, several solutions can be considered such as WiFi, Bluetooth or RFID [START_REF] Simon Wegmueller | Digital data communication through the human body for biomedical monitoring sensor[END_REF], [START_REF] Cho | The human body characteristics as a signal transmission medium for intrabody communication[END_REF].

Wireless intra-body power transmission has more challenging issues : coil design and placement, low efficiency, power dissipation in surrounding tissue, etc. However, up to date there exist few methods for wireless energy propagation that might be considered to be adapted for endoluminal applications: magnetic induction, magnetic resonance coupling, radio transmission, etc [START_REF] Aristeidis Karalis | Efficient wireless non-radiative mid-range energy transfer[END_REF]. These solutions can be combined with on board rechargeable batteries (integrated thin film LiPON batteries, for example) to be recharged wirelessly.

Here again, all these technologies are of interest but deep adaptations to endoluminal robotic surgery are needed.

IV. THEORETICAL AND PRACTICAL ASPECTS ON CONTROL IN ENDOLUMINAL SURGERY

Controlling the array of robots that will be used for the ARAKNES platform may require different control modes from autonomous to teleoperated control modes with switching between control modes or between different robots.

So far, few works can be found in the litterature on autonomous control issues for NOTES robots except maybe for autonomous locomotion control such as the works presented in [START_REF] Rentschler | Mobile in vivo robots provide sole visual feedback for abdominal exploration and cholecystectomy[END_REF], [START_REF] Rentschler | Natural orifice surgery with an endoluminal mobile robot[END_REF].

Regarding the switching issue, two different aspects may be envisaged either from a technical point of view or from the control point of view. For the technical part, it may be solved with the classical use of button or pedal that requires from the surgeon to have a free hand or foot or it may also be solved less classically with eye tracking as proposed at Imperial College of London [START_REF] Stoyanov | Gazecontingent 3d control for focused energy ablation in robotic assisted surgery[END_REF]. Besides this technical point, the stability problem in terms of control also arises when dealing with swtiching. Extensive litterature may be found in the community working on hybrid system [START_REF] Hespanha | Switching between stabilizing controllers[END_REF].

The starting point of our development is the synthesis of a good teleoperated control architecture i) that will offer the surgeon a remote control of his/her instruments, ii) that will give him/her feedback information from what happens inside, especially from the interaction and finally iii) will allow him to perform anastomoses or biopsies for instance. In the following, after giving some details about teleoperation architecture, a promising candidate for a teleoperation scheme is introduced. This scheme has been already tested for needle insertion and could be used for endoluminal surgery.

A. Teleoperated control mode

The first works on teleoperation have been focused on static capabilities and kinematics. The inertia and damping have been considered but from an energy point of view, where the objective was to minimize the effort needed to accomplish the teleoperation task. Initially, two basic teleoperation architectures have been proposed [START_REF] Lawrence | Stability and transparency in bilateral teleoperation[END_REF], [START_REF] Hokayem | Bilateral teleoperation: an historical survey[END_REF], namely:

• position-position teleoperation architecture, and • position-force teleoperation architecture. In position-position teleoperation architecture, the master position is transmitted as a command to the slave servo controller, and slave position is returned to the master as a position command. This makes sense if the position controllers have good tracking capabilities, since the master and slave will closely follow each other. However, master and slave robots are interconnected in a feedback loop, and the dynamics of the closed loop system must also be considered. It is worth to note that for this architecture, an accurate position control system on the master makes the system feel sluggish in free space motion, since the lags between master and slave position movements cause large reaction forces to be supplied to the operator.

In the position-force architecture, the idea is also to transmit master's positions as commands for the slave. However, the interaction force at the slave is sent back directly as a reaction force to the master. If the slave reproduces with faithfulness the master motions, and the master feels accurately the slave forces, the operator should experience the same interaction with the teleoperated task as would the slave. But this architecture does not address the dynamics of the interconnected system. Moreover, in this force reflection architecture, stability is often a problem unless the force transmitted to the master is significantly attenuated.

Later on, other works have been proposed dealing with bilateral teleoperation, focusing more on dynamics and stability and leading to a variety of proposed architectures. For instance, robust controller based on small gain theory has been proposed for force-force teleoperation architecture [START_REF] Kazerooni | Telefunctioning: an approach to telerobotic manipulations[END_REF].

However the issue of transparency, which provides the human operator with a feeling of the remote environment and which is one of the key properties in surgical robotics that a surgeon may expect from the robot, has not been addressed in the above proposed teleoperation architectures. For that reason, other works have concentrated on performanceobjectives for architecture design based on for instance specifying network theory hybrid parameters [START_REF] Hannaford | A design framework for teleoperators with kinesthetic feedback[END_REF]. However, the obtained architecture requires infinite gains to ensure accurate transparency, which is obviously unacceptable. Other proposed architectures have then addressed the problem of the trade-off between stability and transparency such as the one we presented in [START_REF] Zarrad | Stability and transparency analysis of a haptic feedback controller for medical applications[END_REF] whose architecture will be detailed in section IV-B.

B. An example of a teleoperation control architecture for needle insertion

As a pre-requisite for suturing or biopsy, needle insertion is of a great importance during surgical procedure especially in endoluminal surgery. As reported by the NOSCAR, ideally, it should be remote controlled with a good force feedback. To achieve this requirement, we proposed in [START_REF] Zarrad | Stability and transparency analysis of a haptic feedback controller for medical applications[END_REF] a teleoperation control architecture. This scheme ensures stability and provides high fidelity perceptual feedback of the interaction with the environment delivered transparently to the operator w.r.t. heterogeneous environment in the sense that the surgeon should have a good feeling of the tool/tissue interactions inside the body. The architecture, represented in figure 2, is based on a position-position structure.

As presented in figure 3, it combines the use of an active observer (AOB) with online interaction model parameter estimation. Through a haptic device, the surgeon teleoperates the instrument, fixed on a remote robot that may evolve in free or constrained space. In free space, the surgeon feels the motion of the robot due to the position/position control scheme . When contacts with tissues occur, an online environment stiffness estimation is performed using an Extended Kalman Filter. The stiffness estimation of the environment ensures the global stability of the position/position control scheme w.r.t. environment property changes. Moreover, stability and transparency frequency analysis help to improve telepresence thanks to adaptive tuning of contact stiffness.

The use of AOB combined with online interaction model parameter estimation has provided a teleoperation architecture with a good behavior for macro-scale tasks in a surgical-like environment guaranteeing the trade-off between transparency and stability. Figure 4 presents the different phases of the needle insertion and Figure 5 illustrates the corresponding experimental results. This scheme will be now adapted for endoluminal robotized surgery.

V. CONCLUSION

In this paper some control-related issues for endoluminal robotized surgery have been discussed. Mainly, two aspects have been emphasized from the technological point of view to the theoretical/practical aspects. For each of them, open questions have been highlighted. Future works will address different control issues that have been mentioned such as:

• An indepth study of performances, capabilities and limitations of the existing active-observer based teleoperation architecture,

• Increasing performances as well as robustness of this bimanual teleoperation architecture through the introduction of the predictive approach in order to take into account the different saturations that may exist (on the inputs, outputs, actuators, ...)

• Proposition of an extended architecture that may be able to achieve cooperative teleoperation, where the surgeon will be able to teleoperate multiple slave robots with only limited number of haptic interface.

Fig. 1 .

 1 Fig. 1. Assistive and operative platforms in the ARAKNES architecture

Fig. 2 .

 2 Fig. 2. Position-position teleoperation architecture.

d s 2 Fig. 3 .

 23 Fig. 3. Teleoperation control scheme for each Cartesian dimension. The master station (human and phantom), generates the 3D Cartesian force F d through the virtual coupling Kv. βp scales the phantom position X hp , and β f scales back F d to the master station. G(s) has a damping term K 2 , and is controlled by AOB estimates ˆx r,k pk ˜T through the state feedback gain [Lr 1]. Ks is the system stiffness and L 1 is the first element of Lr. G cl is the force closed loop. The environment stiffness is estimated ( Ks) and used to adapt the force controller.

Fig. 4 .

 4 Fig. 4. Needle insertion phases into two layers soft tissue.

This work is supported by FP7 ARAKNES ICT-2007.3.