Olmo A Moreno Franco

Joao Bimbo
email: joao.bimbo@iit.it

Claudio Pacchierotti
email: claudio.pacchierotti@irisa.fr

Domenico Prattichizzo

Davide Barcelli

Gianni Bianchini

Olmo A Moreno
email: olmo.moreno@iit.it

Transparency-optimal passivity layer design for time-domain control of multi-DoF haptic-enabled teleoperation

This paper presents a novel optimization-based passivity control algorithm for haptic-enabled bilateral teleoperation systems involving multiple degrees of freedom. In particular, in the context of energy-bounding control, the contribution focuses on the implementation of a passivity layer for an existing time-domain scheme, ensuring optimal transparency of the interaction along subsets of the environment space which are preponderant for the given task, while preserving the energy bounds required for passivity. The involved optimization problem is convex and amenable to real-time implementation. The effectiveness of the proposed design is validated via an experiment performed on a virtual teleoperated environment.

I. INTRODUCTION

In haptic-enabled teleoperation, the primary concern is to provide a stable and transparent operation of the system. It is well known that haptic feedback can lead to unstable and therefore unsafe behavior of the overall system due to factors such as communication latency in the loop, hard contacts, and relaxed user grasps. Such behavior must be avoided, especially in fields where safety is a paramount and non-negotiable requirement (e.g., medical robotics) [START_REF] Speich | Implementation of loop-shaping compensators to increase the transparency bandwidth of a scaled telemanipulation system[END_REF]. Transparency can be defined as the match between the impedance of the teleoperated environment and the one perceived by the operator [START_REF] Lawrence | Stability and transparency in bilateral teleoperation[END_REF]. This property allows for achieving a good illusion of telepresence [START_REF] Raju | Design issues in 2-port network models of bilateral remote manipulation[END_REF], [START_REF] Sheridan | Space teleoperation through time delay: review and prognosis[END_REF]. Indeed, haptic stimuli play an important role in improving the performance of teleoperation systems in terms of task completion time [START_REF] Moody | Objective surgical performance evaluation based on haptic feedback[END_REF], [START_REF] Pacchierotti | Enhancing the Performance of Passive Teleoperation Systems via Cutaneous Feedback[END_REF], accuracy [START_REF] Meli | Experimental evaluation of magnified haptic feedback for robot-assisted needle insertion and palpation[END_REF], [START_REF] Pacchierotti | Steering and Control of Miniaturized Untethered Soft Magnetic Grippers With Haptic Assistance[END_REF], peak and mean force [START_REF] Wagner | A tactile shape display using RC servomotors[END_REF]. Therefore, guaranteeing stability while preserving transparency has always been a prominent challenge of the fields of robotics and haptics. To this purpose, a great variety of control design approaches have been proposed. In this context, passivity theory [START_REF] Lozano | Dissipative systems analysis and control[END_REF], [START_REF] Schaft | L2 -Gain and Passivity Techniques in Nonlinear Control[END_REF] has been recognized as an effective tool for achieving stable interaction. In [START_REF] Ryu | Stable teleoperation with time-domain passivity control[END_REF], [START_REF] Hannaford | Time-domain passivity control of haptic interfaces[END_REF], passivity is analyzed in the time domain in terms of energy levels of system components. In [START_REF] Niemeyer | Telemanipulation with Time Delays[END_REF], the problem of making a delayed communication channel passive is addressed. Energy-bounding algorithms to guarantee passivity of the teleoperation loop have been proposed in [START_REF] Kim | Robustly Stable Haptic Interaction Control using an Energy-bounding Algorithm[END_REF], [START_REF] Ryu | Sampled-and continuoustime passivity and stability of virtual environments[END_REF], [START_REF] Ryu | Time domain passivity control with reference energy following[END_REF]. Along the same line, in [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], a two-layer control scheme is proposed, in which a transparency layer computes the ideal {prattichizzo,barcelli,giannibi}@diism.unisi.it forces to be actuated at both the master and slave sides, while a passivity layer modulates such forces when necessary to avoid violations of the passivity condition, thus guaranteeing stability at the price of a temporary loss of transparency. More recently, in [START_REF] Ferraguti | An Energy Tank-Based Interactive Control Architecture for Autonomous and Teleoperated Robotic Surgery[END_REF] the authors introduced a passivity-based interactive control architecture based on the port-Hamiltonian framework. Most of the cited time-domain approaches employ the concept of energy tanks to enable the use of the (virtual) energy circulating in the controlled system in a flexible and passivity-preserving way.

This work builds upon the two-layer architecture proposed in [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF]. In that paper, the design of the passivity layer does not explicitly account for the amount of transparency that is lost due to the stabilizing effect. This issue is of fundamental importance especially in complex teleoperation tasks that involve multiple degrees of freedom (DoF). Indeed, for a particular configuration of a given task, it may be important to conserve transparency in terms of fidelity of the rendered force along some subset of the task space, while other components may be significantly altered in order to preserve passivity without compromising the overall task performance. The aim of this paper is to present an optimization-based design of the passivity layer which guarantees the maximum possible degree of transparency along subsets of the environment space that are preponderant for the given task at a given time, while preserving the energy bounds that are required to guarantee passivity. The optimal rendered force is computed via the solution of a convex quadratic program which is characterized by modest computational complexity and amenable to implementation in real time.

The paper is organized as follows. In Section II some preliminary concepts are recalled. The control architecture this work is based on is summarized in Section III. The proposed optimal control design is presented in Section IV. Experimental validation of the approach is performed in Section V. Finally, conclusions are drawn in Section VI.

A. Notation

We denote the continuous time index as t and the discrete time index as k. For a continuous-time signal q(t), we denote its sampling q(kT s ) with q(k) without ambiguity, being T s the sampling period. The interval from time k -1 to time k is indicated as k. H( k) denotes a signal H being held constant during k. For a vector or matrix v, v indicates its transpose. The notation v w is used to denote the component-bycomponent product of v and w. v is the Euclidean norm of v.

II. PRELIMINARIES

A. Transparency

Transparency is defined as the full display of the environment impedance to the human operator when he/she interacts with the robot [START_REF] Salisbury | Haptic rendering: Programming touch interaction with virtual objects[END_REF], [START_REF] Desai | Transparency enhancement of haptic interface using model matching approach[END_REF]. As defined in [START_REF] Franken | Bridging the gap between passivity and transparency[END_REF], ideal transparency is achieved when the generalized forces τ s and velocities qs at the slave side are equally reflected in the forces τ m and velocities qm at the master side, modulo a suitable scaling and an intrinsic time delay.

B. Passivity

Stability of the teleoperation chain is a key requirement in order to ensure a safe interaction at both the master and the slave sides. This property may be compromised by several factors such as relaxed user grasp, stiff contacts in the environment, and communication delays.

Passivity represents a viable solution to the stability preservation problem. Indeed, the interaction between passive systems is guaranteed to be stable, and properly combining passive systems results in a passive system [START_REF] Lozano | Dissipative systems analysis and control[END_REF]. Moreover,the human operator has been shown to preserve stability when interacting with a passive system [START_REF] Hogan | Controlling impedance at the man/machine interface[END_REF]. Hence, ensuring passivity of all components of the telemanipulation system is a convenient sufficient condition for stability of the interaction at all levels.

For a generic component R of a mechanical teleoperation system, let H R (t) denote its total internal energy. Passivity of R boils down to the condition that H R (t) never exceeds its initial value H R (0). Assuming without loss of generality a zero-energy initial condition, R is passive if

H R (t) = t 0 τ R (σ) q R (σ) dσ ≥ 0 ∀t ≥ 0 , (1)
where τ R (t) and q R (t) represent the applied external forces and generalized velocities, respectively. Following [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], the total energy H T (t) of the system can be decomposed as

H T (t) = H M (t) + H S (t) + H C (t),
where H M (t), H S (t) and H C (t) denote the energy levels pertaining to the master side, the slave side, and the communication channel, respectively. From (1), passivity of the overall system is therefore achieved if the controller is able to regulate the system in order to preserve the condition

H T (t) ≥ 0 ∀t ≥ 0. (2)

III. CONTROL ARCHITECTURE

The present work builds upon the energy monitoring control architecture presented in [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF]. With reference to Fig. 1, the overall system is made of several layers.

The physical layer represents the user/haptic device and robot/environment interactions. The generalized forces and displacements at the master [slave] side are denoted by τ m (k) [τ s (k)] and q m (k) [q s (k)], respectively. The transparency layer implements a position force controller (PFC) and interacts between the physical and passivity layer exchanging information on forces and positions.

A standard implementation of the PFC is as follows:

τ T Lm (k) = τ e (k -T ) (3) τ T Ls (k) = -K p (q m (k -T ) -q s (k)) -K d qs (k) (4)
where τ e (k) si the measured interaction force at the master side, while K p and K d are suitable proportional and derivative controller gains, and T is the master-slave communication delay (possibly time-varying). The force vectors τ T Lm (k) and τ T Ls (k), once actuated at the respective sides, ensure full transparency to the teleoperation system. Such transparency might not be always achieved in a passive manner. The role of the passivity layer is to suitably modulate the forces τ T L (k) generated by the PFCs at both sides in order to preserve passivity of the overall system, i.e., to ensure that (2) holds at all times. Due to the impossibility of monitoring the overall energy H T in real time due to the presence of delays, in [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF] the following paradigm is adopted. A virtual energy tank H characterized by an energy level H(k) is introduced at each side, Each tank can exchange virtual energy with its counterpart at the other side and functions as the energy budget available for performing the appropriate (master or slave) force control action. When the tank level at one side is detected as being low, a correction to the actuated force τ T L (k) is applied in order for the tank level not to drop below zero, therefore preserving passivity. The passivity layer also integrates an energy exchange protocol whose role is to transfer virtual energy packets between the master and slave tanks according to a suitable algorithm. The purpose of this protocol is to balance energy levels at both sides, so as to relax the conservative condition that both tank levels be positive in order to guarantee overall passivity. The details on the latter component are out of the scope of this work and the standard implementation of [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF] is used here. In this section, we describe the passivity layer without specific reference to the master or the slave side, as it can be implemented in either, and stick with the notation used in [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF].

Let q(k) be the sampled generalized device displacement, and denote with τ r ( k) the actuated force during k, which is held constant since a zero-order-hold is used. The energy loss in tank H during k is therefore given by

∆H(k) = τ r ( k)(q(k) -q(k -1)), (5)
Hence, the tank level after the control action has been performed amounts to

H(k) = H(k -1) -∆H(k). (6)
Taking into account a possible virtual energy exchange amounting to H ± (k), performed according to the exchange protocol, the energy tank level at the end of the time interval k becomes

H(k + 1) = H(k) + H ± (k). (7)
The tank level H(k + 1) in ( 7) represents the available amount of energy to perform the force actuation task during the time interval k + 1. In [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], the passivity layer is implemented as a curtailed version τ P L (k) of the force feedback τ T L (k), computed according to the value of H(k + 1). In particular, the following two strategies are considered. 1) Simply cut-off all forces if there's no energy left, i.e.,

τ P L (k) = 0 if H(k + 1) ≤ 0 τ T L (k) otherwise (8)
2) Provided the teleoperation system has only a single DoF, an estimate of the energy required for the control action in k + 1 is given by

Ĥ(k + 1) = τ r (k + 1) q(k)T s , (9)
where τ (k + 1) is the prospective actuated force. Based on this and on the available energy, a limitation on τ (k + 1) is as

τ max (k) = H(k + 1) | q(k)|T s .
The curtailed force τ P L (k) is then computed as

τ P L (k) = 0 if H(k + 1) ≤ 0 sgn(τ T L (k)) min(|τ T L (k)|, τ max (k)) otherwise.
Finally, a certain amount of virtual damping force τ d is added at the master side to prevent total tank depletion.

In [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], the problem of suitably shaping τ P L (k) in the multi-DoF case, depending on the task and in order to preserve transparency under the passivity constraint is left as an open question.

IV. OPTIMAL PASSIVITY LAYER DESIGN

In this paper, we propose an optimization-based design of the passivity layer which addresses the multi-DoF case and minimizes the loss of transparency on subsets of the task space which are relevant to the given task, while preserving passivity. Similarly to case 2) above, we consider the estimated energy loss as a function of the prospective actuated force τ r (k + 1)

as ∆ Ĥ(k + 1) = τ r (k + 1) q(k)T s . (10)
Therefore, an estimate of the tank level after the control action has been performed is given by

Ĥ(k + 1) = H(k + 1) -τ r (k + 1) q( k)T s . (11)
Let H min (k) > 0 be a possibly time-varying threshold level, chosen by the designer, corresponding to the amount of energy to be left in the tank after τ r (k + 1) has been applied during k + 1. In order for such a level to be guaranteed, according to the estimate in [START_REF] Schaft | L2 -Gain and Passivity Techniques in Nonlinear Control[END_REF], the following constraint must hold:

Ĥ(k+1) = H(k + 1)-τ r (k + 1) q( k)T s ≥ H min (k). ( 12
)
It is easily seen from ( 12)

that if H(k + 1) -τ T L (k) q(k)T s ≥ H min (k), then the unmodified τ T L (k) can be safely actuated (i.e., τ P L (k) = τ T L (k))
and therefore perfect transparency can be achieved. To address the situation in which this is not possible, τ P L (k) is computed as the solution of an optimization problem. To this purpose, we find it convenient to implement the effect of the passivity layer as a force correction in the form of a suitable amount of virtual damping. In particular, we define τ P L (k) as

τ P L (k) = τ T L (k) + τ T LC (k) (13)
where τ T LC (k) has the form

τ T LC (k) = -B(k) q(k) (14)
In [START_REF] Niemeyer | Telemanipulation with Time Delays[END_REF], B(k) is a symmetric matrix to be computed in an optimal fashion. To formulate the optimization problem, let S i (k), i = 1, . . . m be a suitable set of subspaces of the task space, depending on the given task and possibly also on the time index k. Let us assign a priority index p i (k) ≥ 0 to each subspace S i (k), also depending on the current task configuration. The idea of associating each subspace to a priority index is quite simple: the higher the priority p i (k), the stricter the requirement that the projection on S i (k) of the optimal rendered force τ P L (k) be as close as possible to the corresponding projection of τ T L (k). Let A i (k) be a matrix whose columns form a basis of S i (k). The projection of the force correction

τ T LC (k) = τ P L (k) -τ T L (k) on S i (k) is given by Π Si (τ T LC (k)) = T i (k)τ T LC (k),
where the projection matrix T i (k) reads

T i (k) = A i (k)[A i (k)A i (k)] -1 A i (k). (15)
Based on the arguments above, it is natural to define the following functional to be minimized:

J(B(k)) = m i=1 p i (k) T i (k)τ T LC (k) 2 , ( 16
)
where τ T LC (k) is as in ( 14) and the decision variables are represented by the entries of the damping matrix B(k). The minimization of ( 16) must be carried out under the constraint [START_REF] Ryu | Stable teleoperation with time-domain passivity control[END_REF]. Furthermore, it must be ensured that the sign of all components of τ P L (k) be the same as the corresponding components of τ T L (k) as a result of the force correction in ( 13)-( 14) corresponding to the minimum of J(B(k)). This constraint prevents the passivity layer from letting the tank gain energy from inverting the direction of rendered forces with respect to τ P L (k), thus resulting in an excessive loss of transparency. Said in another way, the maximum allowed correction along each direction must act so as to zero out the rendered force. To ensure the latter condition, the following constraint is required:

τ P L (k) τ T L (k) = (τ T L (k) -B(k) q(k)) τ T L (k) ≥ 0 ( 17
)
Motivated by the above observations, we propose the following algorithm as the implementation of the passivity layer.

Algorithm 1 Optimal passivity layer implementation 1: Given:

H(k + 1), τ T L (k), q(k), { p i (k), T i (k) }, H min (k) 2: if H(k + 1) -τ T L (k) q(k) ≥ H min (k) then 3: τ P L (k) = τ T L (k) 4: else 5:
Solve the optimization problem

B * (k) = arg min B J(B)
subject to

H(k + 1) -τ T L (k) q(k) + q (k)B q(k) ≥ H min (k) (τ T L (k) -B q(k)) τ T L (k) ≥ 0 (18) 6:
if Problem 5: is feasible then 7:

τ P L (k) = τ T L (k) -B * (k) q(k) 8:
else 9:

τ P L (k) = 0 10: end if 11: end if 12: Actuate τ r (k + 1) = τ P L (k)
The optimization problem ( 18) is a convex quadratic program. The global minimum can be efficiently computed using interior point methods. As it will be shown in the experimental section, the method can be implemented without problems on a 3-DoF teleoperation system operating at a sampling frequency of 1 kHz.

V. EXPERIMENTAL EVALUATION

A. Overview

To evaluate the feasibility and effectiveness of our Transparency-Optimal Passivity Layer (TOPL) approach, we carried out a palpation experiment. A user with previous experience on haptic devices was asked to palpate a virtual surface and locate an area stiffer than the rest. We evaluated the task performance considering different controller types and experimental conditions, i.e., the delay T in the loop. Fig. 2 shows the experimental setup. A detailed explanation of each experimental component follows. shows a contact area (the red surface) with a stiffness value lower than the virtual "bump" (the blue area). The end effector of the virtual environment is represented by the green sphere, and interacts with the surface, commanded by the master side. On the right side of the picture the Omega haptic device is shown. The virtual environment is an animated interface presented on the screen.

B. Experimental setup

As shown in Fig. 2, the master side is composed of a human user holding the end-effector of a grounded haptic device, whose position is linked to the one of a virtual end effector in the virtual environment. The user, by controlling the haptic interface, moves the virtual end effector and receives haptic feedback whenever it interacts with the virtual surface.

A stiff circular region of 1 cm radius is positioned randomly on this virtual surface. Differently from Fig. 2, during the experiment, the user was not provided with any visual information on the position of the stiffer region, and he had to rely only on force cues.

1) Haptic interface: The master side consists of a 6-DoF Omega haptic interface (Force Dimension, CH). It has 3 DoF for translations, which are actuated, and 3 DoF for rotations, which are not actuated. To reduce user's fatigue, the Omega haptic device provides gravity compensation.

This impedance haptic interface measures the positions of the end effector grasped by the human operator as an input, and renders forces on the end effector as an output. The haptic control loop operates at 1 kHz.

2) Communication Channel: The communication channel collects and distributes the signals between the master and slave sides. Those signals include the actions evaluated by transparency layer on the master side τ T Lm and the slave side τ T Ls . They also include the energy exchange information shared between master and slave. Finally, the communication channel introduces a time delay T (see ( 3)), which affects the forces and energy package distribution between sides. We carried out our palpation task simulating three communication delays T : 1 ms, 5 ms, and 10 ms. These delays were added up to the intrinsic delay of the system, which was measured to be, on average, 1.8 ms.

3) Virtual environment: The virtual environment runs on a GNU/Linux machine using the Robot Operative System (ROS) framework. It was rendered using the RVIZ visualization tool, as shown in Fig. 2. It is composed of the virtual surface, which is modeled as a spring with elastic constant K = 1 N/cm (red area in Fig. 2). As mentioned before, within this virtual surface, we placed a stiffer 1-cm-radius circular region (blue area in Fig. 2). This stiffer area was modeled as a spring having elastic constant K H = 2 N/cm. When the end-effector penetrates the virtual surface, the ideal force rendered on the z axis, normal to the surface, is

τ e (k) = -K H (h 0 (k) -q z (k))
if on the stiffer area -K(h 0 (k) -q z (k)) otherwise [START_REF] Ferraguti | An Energy Tank-Based Interactive Control Architecture for Autonomous and Teleoperated Robotic Surgery[END_REF] where h 0 (k) is the z position of the uncompressed surface and q z (k) the position of the virtual end effector along the z axis. When moving laterally across the surface, along axes x and y, the user is provided with force feedback about the friction of the surface, modeled using a standard Coulomb friction model with coefficient µ = 0.005.

C. Controllers 1) No Passivity Controller (NPC):

The first approach to be tested was a controller that directly transmits the forces and velocities between master and slave, without any concern for passivity.

2) Simple Tank Level Controller (STLC): This controller follows the two-layer energy-based approach, presented by Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], where the force is limited by the energy available in the tank according to [START_REF] Pacchierotti | Steering and Control of Miniaturized Untethered Soft Magnetic Grippers With Haptic Assistance[END_REF], and introduces a damping force on the master side. According to [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], the master side damping is implemented as

τ d (k) = -d(k) qm (k) d(k) = α(H d -H(k + 1)) if H(k + 1) < H d 0 otherwise (20)
where the damping gain α is set to 100, H d is set to 0.2, and the energy exchange factor β described on section V-B.2 of [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF] is set to 0.01.

3) Transparency-Optimal Passivity Layer (TOPL) : The approach described in IV was implemented using the architecture in Fig. 1. In this controller, a dynamic threshold level H min (k) is implemented as follows:

H min (k) = H(k + 1) + η(H 0 -H(k + 1)) q(k) 2 , ( 21
)
where H 0 represents a reference tank level to be maintained during transparent operation, and η > 0 is a tunable parameter which acts as a proportional controller gain. Equation [START_REF] Desai | Transparency enhancement of haptic interface using model matching approach[END_REF] allows the system to recover energy when the level of energy is below the reference level H 0 , as well as to limit the spending of energy when above. The norm of the current velocity also is weighted in the proportional controller gain in order to limit the damping forces generated by the passivity layer.

Given the aim of the experiment with respect to the virtual teleoperated environment, the subspaces S i , i = 1, 2, 3 have been defined as the three Cartesian axes x, y, z. The priorities p i (k) are taken to be constant. The highest priority was assigned to the projection on the z axis, since the perception of the stiffness perpendicular to the surface is fundamental for the scope of the experiment, while friction forces on the horizontal (x, y) plane are assigned lower priorities. The priority values were set as p 1 (k) = p 2 (k) = 0.1, p 3 (k) = 0.5.

D. Validation

Before running the palpation experiment, we carried out a simple validation of our setup. A human user was asked to move the virtual end effector across the surface, passing over the stiff circular area. Fig. 3 shows a representative trial, capturing the moment the user passes on the stiffer area of the environment. The forces computed by the transparency layer τ T L (k) and the ones computed by the passivity layer τ P L (k) along the z axis are shown in the upper part of Figs. 3a,3b, 3c. In the lower part of the same figures, we can see the same forces τ T L (k) and τ P L (k) for axes x and y. In this case, a delay of 1 ms was present between master and slave. When enforcing no passivity controller, the force measured in the virtual environment is directly provided to the user through the haptic interface, i.e., τ P L = τ T L regardless of passivity constraints (see Sec. V-C.1). When enforcing the STLC controller, a damping action is introduced along all directions when the energy tank level is below a predefined threshold. In the proposed TOPL approach, we give a higher priority/importance to vertical forces, which are the most informative for our palpation task, at the expense of losing transparency when rendering the horizontal (friction) forces. In this respect, we can see that in Fig. 3b (STLC) corrective actions are taken along all directions. On the other hand, Fig. 3c shows that the proposed approach takes significant corrective actions along the non-preferred directions (x and y), while it preserves transparency along the preferred direction z, which is the most useful for our palpation task.

E. Palpation experiment

In furtherance of testing the proposed approach, a human subject carried out 48 repetitions of our palpation task. The user was asked to find the location of a 3.14 cm 2 stiffer region placed on the virtual surface, as described in Sec. V-B. We compared the performance of the three controllers described in Sec. V-C, each tested when simulating three different communication delays between master and slave (1 ms, 5 ms, or 10 ms). To evaluate the effectiveness of our system in correctly rendering the stiffness of the environment, we registered the accuracy error in detecting the stiffer area within our virtual surface. Fig. 4 shows this result in the nine different experimental conditions. To compare this metric among the conditions, we ran a two-way repeated-measures ANOVA test on the data. Time delay in the communication (1 ms vs. 5 ms vs. 10 ms) and stability controller (no controller, NPC 3. Forces of the three experimental conditions with a pass over the bump. (a) shows the τ T L,z and τ P L,z forces when the end effector passes over the bump; as seen, τ T L,z follows τ P L,z presenting the most transparent scenario (NPC). (b) presents τ T L,z and τ P L,z forces when STLC controller is running, as well the τ T LC,y and τ T LC,z forces, that belong to the correction phase. (c) displays the τ T L,z and τ P L,z forces when TOPL controller is working, and the damping correction on τ T LC,y and τ T LC,z forces. vs. Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], STLC vs. our proposed approach, TOPL) were treated as within-subject factors. All data passed the Shapiro-Wilk normality test. Interaction effects between the factors were not statistically significant. Mauchly's Test of Sphericity indicated that the assumption of sphericity had been violated for both variables (delay, χ 2 (2) = 23.148, p < 0.001; controller, χ 2 (2) = 15.987, p < 0.001). The twoway repeated-measure ANOVA with a Greenhouse-Geisser correction revealed statistically significant difference between the time delays (F 1.005,6.029 = 6.815, p = 0.011, a = 0.05, partial η 2 = 0.533) and stability controllers (F 1.021,6.125 = 17.701, p < 0.001, a = 0.05, partial η 2 = 0.745). Post hoc analysis with Bonferroni adjustments revealed a statistically significant difference between having 1 ms vs. 5 ms delay (p = 0.019) and 1 ms vs. 10 ms delay (p = 0.047). Similarly, it revealed a statistically significant difference between enforcing NPC vs. STLC (p = 0.007), NPC vs. TOPL (p = 0.017), and STLC vs. TOPL (p = 0.044).

VI. DISCUSSION

To evaluate the feasibility and performance of our proposed passivity approach, we carried out an experiment in a simulated environment (see Sec. V-B). The user is asked to palpate a virtual surface and search for a circular area of 2 cm diameter which is stiffer than the rest. We tested the user's accuracy in finding such area considering (a) three different controllers (no controller, Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], our proposed passivity approach), and (b) three different communication delays between master and slave (1 ms, 5 ms, and 10 ms). Our hypotheses were that (i) as the communication delay increases, if no controller is implemented, the teleoperation system becomes unstable; conversely, the system remains always stable if one of the two considered passivity controllers are enforced. Moreover, as the communication delay increases, we also expect (ii) our TOPL approach to better preserve the transparency along prioritized directions with respect to the approach of Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF], which does not make any difference between directions.

Both hypotheses were confirmed by our palpation experiment. When a delay of 10 ms was introduced in the system, the experiment was very difficult to complete, as several oscillations arose during the palpation. This unstable behaviour lead to a significantly worse accuracy with respect to the other conditions (see Fig. 4) as well as to a very high task completion time (not reported in the figures). The subject repeatedly complained about this oscillation-prone behavior, and he was often forced to increase the grasping force on the haptic interface handle to prevent it from vibrating uncontrollably. On the other hand, the interaction was always safe and stable when any of the two passivity controllers were in place. Between the two controllers, our approach outperformed the one presented by Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF]. Of course, this result is not surprising, as our passivity controller makes use of additional information about the task, i.e., the importance of the different subspaces. This additional information is used by our TOPL controller to better distribute the energy available in the system, privileging forces rendered along the z axis with respect to those rendered along the other axes. Fig. 3 clearly shows this difference. Whenever it is needed to reduce transparency to preserve stability, Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF] corrects the forces along all axis in a very similar way. Conversely, our controller corrects very little along the privileged z axis, while it significantly corrects the forces along the other axes. This behavior resulted in a higher transparency along z at the cost of sacrificing transparency along x and y.

VII. CONCLUSIONS AND FUTURE WORK

In bilateral robotic telemanipulation, haptic feedback plays an important role in achieving high transparency and illusion of telepresence. Unfortunately, the stability and safety of teleoperation systems with force reflection can be significantly affected by communication latency in the loop, hard contacts, relaxed grasps, and many other timevarying destabilizing factors that dramatically reduce the effectiveness of haptics in this field. To prevent unstable behaviors, researchers have exploited passivity as one of the main tools for providing a sufficient condition for stable teleoperation. Within this context, we presented an innovative optimization-based passivity control algorithm for hapticenabled bilateral teleoperation systems with multiple degrees of freedom. Our contribution focused on implementing a novel passivity layer for the existing time-domain scheme of Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF]. While guaranteeing passivity, we ensure optimal transparency of the interaction along subsets of the environment space, designated as the most important ones for the given task. The involved optimization problem is convex and amenable to real-time implementation. We validated the feasibility and effectiveness of the proposed approach with a palpation experiment performed on a virtual environment. Results showed that our controller outperformed the timedomain scheme of Franken et al. [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF] while guaranteeing the stability and safety of the system.

In the future, we will focus on improving the performance of this proposed optimal correction approach as well as running a more extensive human subject evaluation. In this respect, we plan to study how we can automatically assign priority indexes to our subspaces given one (or more) representative runs of the considered task. Moreover, we plan to run real-world experiments using a robotic manipulator such as the 7-DoF KUKA LBR robot and a grounded haptic interface such as the 7-DoF Sigma.7 device.

Fig. 1 .

 1 Fig. 1. Controller architecture block diagram. The architecture of the controller is divided in three areas: A) the physical layer that defines forces as inputs and position as outputs for the devices. B) the transparency layer that computes position to force control. C) the passivity layer which computes the damping correction (only on the master side) and energy flow control.

Fig. 2 .

 2 Fig.2. Experimental set-up. On the left, the virtual environment (slave side) shows a contact area (the red surface) with a stiffness value lower than the virtual "bump" (the blue area). The end effector of the virtual environment is represented by the green sphere, and interacts with the surface, commanded by the master side. On the right side of the picture the Omega haptic device is shown. The virtual environment is an animated interface presented on the screen.

  Fig.3. Forces of the three experimental conditions with a pass over the bump. (a) shows the τ T L,z and τ P L,z forces when the end effector passes over the bump; as seen, τ T L,z follows τ P L,z presenting the most transparent scenario (NPC). (b) presents τ T L,z and τ P L,z forces when STLC controller is running, as well the τ T LC,y and τ T LC,z forces, that belong to the correction phase. (c) displays the τ T L,z and τ P L,z forces when TOPL controller is working, and the damping correction on τ T LC,y and τ T LC,z forces.

Fig. 4 .

 4 Fig.4. Experimental evaluation. Mean accuracy error (cm) in detecting the stiffer area within our virtual surface is plotted.


Firas Abi-Farraj

Claudio Pacchierotti

Paolo Robuffo Giordano

User Evaluation of a Haptic-enabled Shared-Control Approach for Robotic Telemanipulation

Robotic telemanipulators are already widely used in nuclear decommissioning sites for handling radioactive waste. However, currently employed systems are still extremely primitive, making the handling of these materials prohibitively slow and ineffective. As the estimated cost for the decommissioning and clean-up of nuclear sites keeps rising, it is clear that one would need faster and more effective approaches. Towards this goal, in this paper we present the user evaluation of a recently proposed haptic-enabled shared-control architecture for telemanipulation. An autonomous algorithm regulates a subset of the slave manipulator degrees of freedom (DoF) in order to help the human operator in grasping an object of interest. The human operator can then steer the manipulator along the remaining null-space directions with respect to the main task by acting on a grounded haptic interface. The haptic cues provided to the operator are designed in order to inform about the feasibility of the user's commands with respect to possible constraints of the robotic system. In this paper we compared this shared-control architecture against a classical 6-DOF teleoperation approach in a real scenario by running experiments with 10 subjects. The results clearly show that the proposed shared-control approach is a viable and effective solution for improving currently-available teleoperation systems in remote telemanipulation tasks.

I. INTRODUCTION

Remote telemanipulation has shown significant advancements over the last years and promising results have been achieved in several robotic tasks, such as space exploration [START_REF] Yoon | Model-based space robot teleoperation of ets-vii manipulator[END_REF], minimally invasive surgery [START_REF] Freschi | Technical review of the da vinci surgical telemanipulator[END_REF], sort and segregation of nuclear waste [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF]- [START_REF] Pedemonte | Visual-based shared control for remote telemanipulation with integral haptic feedback[END_REF], telemaintenance [START_REF] Aschenbrenner | Teleoperation of an Industrial Robot in an Active Production Line[END_REF], and micromanipulation [START_REF] Cecil | A review of micro-devices assembly techniques and technology[END_REF], [START_REF] Pacchierotti | Haptic feedback for microrobotics applications: a review[END_REF]. As teleoperation systems become more sophisticated and flexible, the environments and applications where they can be employed become less structured and predictable. In this respect, robotic telemanipulation in hazardous environments is attracting increasing attention for its potential in handling dangerous materials [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], [START_REF] Trevelyan | Robotics in hazardous applications[END_REF] and disaster response [START_REF] Stramigioli | A novel approach to haptic tele-operation of aerial robot vehicles[END_REF]- [START_REF] Murphy | Use of remotely operated marine vehicles at minamisanriku and rikuzentakata japan for disaster recovery[END_REF]. Indeed, being able to remotely, intuitively, and easily manipulate objects in such scenarios could significantly extend the application range of robotic teleoperation systems. For example, Jurmain et al. [START_REF] Jurmain | Hazbot: Development of a telemanipulator robot with haptics for emergency response[END_REF] designed a remotely operated robot for bio-event disaster response, called HazBot. It is composed of a mobile robot equipped with a 6-degrees-offreedom (6-DoF) manipulator. The manipulator incorporates a parallel jaw gripper with a 60 pound squeeze force and a gas detector to aid in material identification. Murphy et al. [START_REF] Murphy | Use of remotely operated marine vehicles at minamisanriku and rikuzentakata japan for disaster recovery[END_REF] evaluated the use of three Unmanned Marine Vehicles (UMV) in two areas damaged by the tsunami The authors are with the CNRS at Irisa and Inria Rennes Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes Cedex, France. e-mails: {firas.abi-farraj}{claudio.pacchierotti}{prg}@irisa.fr following the 2011 Tohoku Earthquake. The employed UMVs had a multi-beam imaging sonar, video, and a gripper. Stramigioli et al. [START_REF] Stramigioli | A novel approach to haptic tele-operation of aerial robot vehicles[END_REF] presented a framework for hapticenabled teleoperation of aerial robotic vehicles. The envisaged applications are inspection of piping and cabling in factories and mines, as they are often mounted inaccessibly on walls and ceilings. More recently, Abi-Farraj et al. [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF] proposed a shared-control architecture for remote manipulation of nuclear waste. A visual-based autonomous algorithm regulates a subset of the gripper's degrees of freedom (DoF) in order to ease the approach towards the object of interest. The operator, on the other hand, is allowed to control the remaining nullspace motions while receiving a force feedback informative of any constraint of interest of the robotic system (e.g., joint limits, collision avoidance, and so on).

The nuclear industry is, indeed, one of the most exciting fields of applications for robotic telemanipulation; and the management of nuclear waste is a prominent issue for several countries in the world [START_REF] Dittmar | Nuclear energy: Status and future limitations[END_REF], [START_REF] Agency | Radioactive Waste in Perspective[END_REF]. Sort and segregation of the stored nuclear waste is a first step needed for the decommissioning of the site. However, current robotic systems designed for such a task provide teleoperation capabilities through extremely primitive master consoles (e.g., passive joystick or teach pendants), making the task prohibitively slow for processing large amounts of material in a reasonable time. This need motivated the European H2020 "Robotic Manipulation for Nuclear Sort and Segregation" (RoMaNS) project whose aim is to improve the currently-available teleoperation systems in nuclear environments.

When addressing remote telemanipulation tasks, the interface provided to the human operator is one of the most important components and its design has historically followed two different philosophies. A first possibility is to provide a high-fidelity haptic feedback reflecting the actual physical contacts between manipulators and environment (with all the associated stability issues in case of non-idealities, communication delays, and so on [START_REF] Chopra | Bilateral teleoperation over unreliable communication networks[END_REF], [START_REF] Samur | Performance metrics for haptic interfaces[END_REF]). A second possibility is to rely on shared-control architectures that can assist the operator in manipulation tasks by conveying 'artificial' forces cues that result from more abstract requirements/constraints (e.g., following predefined paths possibly taught by expert operators, avoiding unfeasible robot configurations, avoiding self-or obstacle-collisions) [START_REF] Cecil | A review of micro-devices assembly techniques and technology[END_REF], [START_REF] Abi-Farraj | A learning-based shared control architecture for interactive task execution[END_REF]. The approach tested in this paper belongs to the latter category, where the focus is on achieving an efficient and fast task execution while minimizing the workload on the human operator. Therefore, the haptic interface, rather than reflecting the contact interactions of the slave, aims at guiding the operator to keep him away from undesired configurations of the robotic system.

As a step towards advancing the state-of-the-art in this field, we present here the evaluation of a haptic-enabled sharedcontrol architecture for telemanipulation. In our setup, an autonomous algorithm is in charge of regulating a subset of the manipulator DoF to help the human operator in approaching an object to be grasped. At the same time, the human operator steers the robotic end-effector along the remaining null-space directions with respect to the main task through a grounded haptic interface. Moreover, haptic feedback provides the human operator with information about the feasibility of the user's commands with respect to possible constraints of the robotic system, e.g., joint limits.

This shared-control algorithmic design has been preliminary presented by Abi-Farraj et al. in [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], but without providing any (even minor) user evaluation. With respect to [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], the goal of this paper is to then clearly assess the potential benefits (or cons) of a shared control architecture in remotely approaching an object to be grasped. Indeed, we note that while most of the literature concentrates on the manipulative task itself (e.g., assisted surgeries [START_REF] Okamura | Methods for haptic feedback in teleoperated robotassisted surgery[END_REF], or peg in hole [START_REF] Pacchierotti | Cutaneous haptic feedback in robotic teleoperation[END_REF]), the grasping and (in particular) the preceding approach-to-grasp phases are usually overlooked. On the other hand, the sole act of steering a remote manipulator towards a desired grasping pose (that may have been decided by the user) can be a time consuming and complex task for an operator controlling directly the 6-DoF pose of the manipulator (as in most classical setups). This is due to (i) the complexity of regulating at the same time both the position and the orientation and (ii) the typical presence of several constraints (e.g., joint limits, singularities) that further limit the operator's maneuvering dexterity (but of which the operator has no direct feeling). Therefore, the goal of this paper is to address this issue by assessing what is the best shared-control architecture for obtaining an easier, faster, and more effective robotic teleoperation for approaching an object of interest to be grasped.

The rest of the paper is organized as follows: Sect. II reviews the main algorithmic steps of the shared control architecture presented in [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], and introduces a velocityvelocity coupling as a new variation. Section III then describes the results of an experimental campaign aimed at comparing the two versions of the shared control [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF] (position-velocity or velocity-velocity) against a classical full 6-DoF teleoperation. Finally, Sect. IV provides an extensive discussion of the obtained results, and draws some possible future perspectives.

II. SHARED CONTROL ARCHITECTURE

This Section briefly summarizes the shared-control architecture presented in [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], and discusses how it has been adapted and extended for running the intended user evaluation.

A. Problem statement

The setup we considered consists of a 6-DoF serial manipulator equipped with a gripper. The task is the remote grasping of an object. The manipulator is controlled by an operator acting on a master device and interacting with the system through haptic and visual feedback. As shown in Fig. 1, three frames of reference are considered, F O :

{O O ; X O , Y O , Z O } attached to the object to be grasped, F G : {O G ; X G , Y G , Z G }
attached to the gripper and F B : {O B ; X B , Y B , Z B } attached to the base of the robot. For the grasp to be successful, we assume that Z G should be aligned with the gripper approaching direction. This geometric constraint is actively enforced by the autonomous part of the shared-control algorithm. For the purposes of this work, we assume the presence of an exteroceptive sensor (e.g., an external camera) able to retrieve the 3D pose of F O w.r.t. F B , represented by [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF]). On the other hand, the 3D pose of F G w.r.t. F B , namely

( B P O , B R O ) ∈ R 3 × SO(3) (see also
( B P G , B R G ) ∈ R 3 × SO(3)
, can be retrieved through forward kinematics.

Following this notation, and considering the position of the object to be fixed in the scene, the relative gripper/object pose in the gripper frame F G can be obtained as 6 , the linear and angular velocity of the gripper expressed in its own frame, to be the control inputs for the slave manipulator arm.

G R O = G R B B R O and G P O = G R B ( B P O -B P G ). Finally, we consider (v G , ω G ) ∈ R

B. Slave side

The proposed shared-control architecture aims at facilitating the pre-grasp approaching phase of the human operator, by enabling an autonomous algorithm to control a convenient subset s ∈ R m , m < 6 of the gripper/object relative pose as a "primary" task. The operator is then able to control the robot in the remaining null space directions. At the same time, the haptic interface provides force cues to avoid encountering potential constraints of the robotic system (e.g., joint limits). A convenient definition of the primary task for the pregrasp approach phase is to automatically orient the gripper towards the object. To this end, our control variable s is chosen to be

s = G P O G P O ∈ S 2 , (1)
as shown in Fig. 1. Since Z G should be aligned with the gripper approaching direction, the desired value of s would then be s d = Z G , and the resulting control law associated with the primary task is described by

v G ω G = k G L † s (s d -s), k G > 0, (2)
where k G is a control gain, and L † s represents the Moore-Penrose pseudo-inverse of the interaction matrix L s associated with s and defined by

L s = - 1 d P s [s] × ∈ R 3×6 , (3)
where P s = Iss T is the orthogonal projector onto the tangent space of the unit sphere S 2 at s, d = G P O , and [•] × is the skew-symmetric matrix operator, see also [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF]. Note that since s is the unit norm defined in (1), the rank of

L s ∈ R 3×6 is limited to 2. Let N B = [. . . n i .
. .] ∈ R 6×4 be a basis spanning the null space of L s . The human operator is given command over these 4 null-space motion directions, and the resulting control law governing the full motion of the gripper is

v G ω G = k G L † s (s d -s) + n i=1 λ i n i , k G > 0, (4)
where λ = [. . . λ i . . .] ∈ R 4 indicates the pseudo-velocity commands of the human operator. As described in [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], the null-space basis N B is chosen to be

n1 = s 0 , n2 = 0 s , n3 = -[s]×ey -P sey /d , n4 = [s]×ex P sex/d , (5)
with e x = [1 0 0] T and e y = [0 1 0] T . This provides the human operator with a clear and decoupled physical interpretation of the directions she/he is commanding. A visual illustration of the four null-space motion directions is illustrated in Fig. 2.

C. Master side

The human operator uses a grounded haptic interface to command the slave manipulator (i.e., the four aforementioned null-space motion directions). The haptic interface has 6 DoF, two of which are blocked when the shared control algorithm is actuated. Figure 2 shows the degrees of freedom the operator can command.

The master device is modeled as a generic, gravity precompensated, mechanical system,

M (x M )ẍ M + C(x M , ẋM ) ẋM = τ + τ h , (6)
where x M ∈ R 4 represents the device configuration vector, M (x M ) ∈ R 4×4 is the positive-definite and symmetric inertia matrix, C(x M , ẋM ) ∈ R 4×4 consists of the Coriolis/centrifugal terms, and τ , τ h ∈ R 4 are the control and human forces, respectively. Differently from [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF], we considered here two control modes:

• position-velocity: positions of the master handle are used to command the velocities of the slave robot (this is the same modality also employed in [START_REF] Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF]); • velocity-velocity: velocities of the master handle are coupled to the the velocities of the slave robot, modulo a constant roto-translation scaling factor. The details of both modes, along with the corresponding force cues, are illustrated below.

1) Position-velocity control: In the position-velocity control mode, the master/slave coupling is governed by

λ = K λ x M , (7)
where K λ ∈ R 4×4 is a diagonal matrix of positive scaling factors. The operator then needs to adjust the position of the master device to control the speed along the null-space directions n i . In this modality, force cues are designed with two goals in mind. First, we want to guide the user away from constraints in the robotic system (e.g., joint limits), and, second, we want the operator to easily find the "zero-velocity" position on the master side, i.e., x M = 0, for possibly sending a zero velocity command to the slave arm. Toward this objective, we define the feedback action as

τ = -B M ẋM -K M x M + f . ( 8
)
where K M ∈ R 4×4 and B M ∈ R 4×4 are positive definite matrices, indicating the stiffness and damping factors of a spring pushing the master handle toward x M = 0. In this way, whenever the user does not apply a force on the master handle, the latter moves back to x M = 0, causing the slave robot to stop (see [START_REF] Cecil | A review of micro-devices assembly techniques and technology[END_REF]). The damping B M is chosen so as to keep the teleoperation system stable.

The term f = [. . . f i . . .] T ∈ R 4 accounts for the force cues providing the user with information on the feasibility of her/his commands against possible constraints. Of course, the constraints will vary depending on the application, and they can be modeled as a positive cost function quantifying the proximity of the system to the corresponding constraint. Let H(q) ≥ 0 be a cost function where q ∈ R 6 is the joint configuration vector of the slave manipulator. Each force cue f i aims at informing the user of the impact of actuating the corresponding motion direction n i on the cost function H(q), i.e., (i) the direction (positive or negative) which would increase the cost function and drive the system closer to the constraint, and (ii) the magnitude, or the rate, by which moving along that direction would increase H(q). This is achieved by setting

f i = - ∂H(q) ∂q T J -1 G (q)n i , (9)
i.e., by projecting the joint motion caused by the i-th nullspace direction n i onto the negative gradient of H(q). Matrix J G (q) ∈ R 6×6 is the geometric Jacobian mapping the joint velocities q onto the gripper linear/angular velocities

(v G , ω G ).
In our experiments, proximity to joint limits was considered as a representative constraint of the slave system, and the cost function H(q) was designed as a quadratic penalty cost function:

H(q) = k H 6 i=1 h i (q), with h i (q) =     
(q i -(q i,maxq th )) 2 , if q i ≥ q i,maxq th (q i,min + q thq i ) 2 , if q i ≤ q i,min + q th 0, otherwise , where (q i,max , q i,min ) are the maximum/minimum range for the i-th joint, q th is a user-defined threshold defining the activation region inside which the user will receive a force feedback, and k H is a scaling factor. The main advantage of this position-velocity control mode is that the operator is not limited by the workspace of the master device, making it quite convenient when using a master interface with a small workspace w.r.t. the slave robot. However, mapping positions to velocities may be less intuitive than simply mapping velocities to velocities. For this reason, this shared control modality may increase the cognitive load on the operator performing the task, at least during the initial training phases.

2) Velocity-velocity control: In the velocity-velocity control mode, the master/slave coupling is governed by

λ = K λ,vel v M ω M , (10)
where, as before, K λ,vel ∈ R 4×6 is a diagonal matrix of positive scaling factors, while (v M , ω M ) is the linear/angular velocity of the master device. A button on the master handle works as a clutch. Clutching allows the user to pause the remote operation, move the haptic device to a more comfortable or suitable position, and then resume the control of the robot. This approach is commonly used to address issues of limited workspace on the master side. Force cues are then defined simply as

τ = -B M ẋM + f , (11)
with f having the same definition as [START_REF] Trevelyan | Robotics in hazardous applications[END_REF]. The clear advantage of this velocity-velocity control modality is the lower cognitive load required with respect to the position-velocity mode of Sec. II-C.1. In the velocityvelocity case, in fact, the user's commands are directly reflected to the slave (e.g., the robot stops when the operator stops, and it moves when the operator moves). On the other hand, in position-velocity mode, this relationship is not as evident for the operator, who needs to think a bit more about the impact of his actions on the slave manipulator. However, limitations in the workspace of the master device are more evident in velocity-velocity mode than in position-velocity mode, with the former requiring clutching. The amount of clutching required is directly dependent on the scaling factor between the master/slave workspaces. If the scaling is high, the user will not be required to clutch a lot. However, this may results in fast and abrupt movements of the slave robot. On the other hand, if the scaling is low, the user will be able to more precisely and smoothly control the motion of the slave robot. However, more clutching will be necessary.

III. EXPERIMENTAL EVALUATION

In order to demonstrate the feasibility and effectiveness of our method, we conducted a telemanipulation experiment in a real environment. We compared the proposed shared-control approach with a more classic teleoperation architecture, in which the human operator is in charge of controlling all the DoF of the slave manipulator. Moreover, we also compared two different approaches to control the motion of the robotic manipulator through the haptic interface (position-velocity vs. velocity-velocity).

A. Experimental setup

Figure 3 shows the experimental setup. The master system is composed of the Haption Virtuose 6D haptic device (Haption, France), a high performance force feedback device with three active translational DoF and three active rotational DoF. The maximum force/torque is about 30 N/3 Nm, the workspace has a spherical shape with an approximated radius of 0.9 m, and the device exchanges data over Ethernet with a computer at 1 kHz. The slave system is composed of a 6-DoF Viper S850 robotic arm carrying a pneumatic parallel gripper. A wooden object with dimensions 21 × 9 × 3 cm and weight 280 g is placed on a table in front of the robotic manipulator. The user had a direct view of the slave system and the object to be grasped.

B. Experimental conditions and task

Participants were required to control the motion of the robotic manipulator and gripper to grasp the wooden piece and lift it from the ground. The task started when the manipulator moved for the very first time and it was considered successfully completed when the object was lifted from the ground.

We considered two different ways of commanding the motion of the robot through the haptic interface (positionvelocity vs. velocity-velocity, see Sec. The shared-control architecture, employed in conditions S+PV and S+VV, is detailed in Sec. II.

In T+PV and T+VV conditions, the subject is in full control of the manipulator's 6 DoF. In this respect, the master/slave coupling in T+PV is

v G ω G = K P V x M , ( 12
)
where the configuration vector of the master device, x M , is now in R 6 and K P V ∈ R 6×6 is a matrix mapping x M to velocity commands on the slave side. Similarly to Sec. II-C.1, the force cues fed to the user are

τ = -B M ẋM -K M x M + f , ( 13
)
where B M ∈ R 6×6 and K M ∈ R 6×6 are the damping and stiffness matrices of a spring pushing the master handle back to the "zero velocity" position, and, from ( 9), f is defined as

f = - ∂H(q) ∂q T J -1 G (q), (14)
since now no primary task is present and, therefore, the null-space basis N B is just the identity matrix.

On the other hand, in the T+VV condition the coupling is

v G ω G = K V V v M ω M , (15)
where K V V ∈ R 6×6 is a diagonal scaling matrix. Haptic feedback is then designed similarly to Sec. II-C.2, with

τ = -B M ẋM + f , (16)
where f follows [START_REF] Agency | Radioactive Waste in Perspective[END_REF].

C. Participants

Ten right-handed subjects (average age 27.2) participated in the study. Three of them had previous experience with haptic interfaces. None of the participants reported any deficiencies in their visual or haptic perception abilities. The experimenter explained the procedures and spent about two minutes adjusting the setup to be comfortable before the subject began the experiment. Each subject then spent about three minutes practicing the control of the telemanipulation system before starting the experiment. Each subject carried out 8 randomized repetitions of the grasping task, 2 for each experimental condition. A video showing trials in all experimental conditions is available as supplemental material.

D. Results

To evaluate the effectiveness of our system in grasping the considered object, the usefulness of the proposed sharedcontrol approach, and the effectiveness of haptic stimuli to render robotic setup constraints, we recorded (i) the completion time, (ii) the linear trajectory followed by the robotic end-effector, (iii) the angular motion of the robotic end-effector, and (iv) the perceived effectiveness of the different conditions. To compare the different metrics, we ran both two-way and one-way repeated-measures ANOVA tests on the data. In the two-way analysis, motion control (positionvelocity vs. velocity-velocity) and human involvement in the control (shared control vs. teleoperation) were treated as within-subject factors. All data passed the Shapiro-Wilk normality test. Sphericity was assumed for variables with only two levels of repeated measures. The two-way analysis enables us to understand the role of each variable considered within-subject factor, while the one-way analysis provides us with an overview on the performances of the four conditions.

Figure 4a shows the average task completion time. The twoway ANOVA test revealed a statistically significant change in the task completion time for the human involvement in the control variable (shared control vs. teleoperation, F(1, 9) = 25.852, p = 0.001). The interaction effect between these two factors was not statistically significant. The one-way ANOVA test revealed a statistically significant change in the task completion time across the conditions (F(3, 27) = 9.312, p < 0.001). Post hoc analysis with Bonferroni adjustments revealed a statistically significant difference between S+VV vs. T+VV (p = 0.030), S+VV vs. T+PV (p = 0.035), S+PV vs. T+VV (p = 0.031), and S+PV vs. T+PV (p = 0.025). The Bonferroni correction is used to reduce the chances of obtaining false-positive results when multiple pair-wise tests are performed on a single set of data.

Figure 4b shows the average linear motion covered by the robotic gripper during the task. The two-way ANOVA test revealed a statistically significant change in the trajectory length for both the human involvement in the control (F(1, 9) = 30.968, p < 0.001) and the motion control type (velocity vs. position, F(1, 9) = 9.035, p = 0.015) variables. The interaction effect between these two factors was not statistically significant. The one-way ANOVA test revealed a statistically significant change in the trajectory length across the conditions (F(1.929, 17.360) = 14.072, p < 0.001). Post hoc analysis with Bonferroni adjustments revealed a statistically significant difference between S+VV vs. S+PV (p = 0.049), S+VV vs. T+VV (p = 0.043), S+VV vs. T+PV (p = 0.002), and S+PV vs. T+PV (p = 0.012).

Figure 4c shows the average angular motion covered by the robotic gripper during the task. The two-way ANOVA test revealed a statistically significant change in the angular motion for both the human involvement in the control (F(1, 9) = 39.350, p < 0.001) and the motion control type (positionvelocity vs. velocity-velocity, F(1, 9) = 8.202, p = 0.015) variables. The interaction effect between these two factors was not statistically significant. The one-way ANOVA test revealed a statistically significant change in the trajectory length across the conditions (F(3, 27) = 12.994, p < 0.001). Post hoc analysis with Bonferroni adjustments revealed a statistically significant difference between S+VV vs. S+PV (p = 0.025), S+VV vs. T+VV (p = 0.007), S+VV vs. T+PV (p = 0.001), S+PV vs. T+VV (p = 0.039), and S+PV vs. T+PV (p = 0.005).

Immediately after the experiment, subjects were also asked to report the effectiveness of each feedback condition in completing the given task using bipolar Likert-type ninepoint scales. Fig. 4d shows the perceived effectiveness for the four experimental conditions. A Friedman test showed a statistically significant difference between the means of the four feedback conditions (χ 2 (3) = 26.753, p < 0.001, a = 0.05). The Friedman test is the non-parametric equivalent of the more popular repeated-measures ANOVA. The latter is not appropriate here since the dependent variable was measured at the ordinal level. Post hoc analysis with Bonferroni adjustments revealed a statistically significant difference between S+VV vs. T+VV (p < 0.001), S+VV vs. T+PV (p = 0.026), S+PV vs. T+VV (p < 0.001), and S+PV vs. T+PV (p = 0.044).

Finally, all ten subjects found conditions using the sharedcontrol approach to be the most effective at completing the grasping task. Seven subjects out of ten chose the sharedcontrol condition employing velocity-velocity control to be the most effective.

IV. DISCUSSION, CONCLUSIONS, AND FUTURE WORK

This paper presents the evaluation of a generic sharedcontrol architecture for robotic telemanipulation, whose objective is to help a human operator in completing a predefined grasping task. While in the literature we can find several works presenting different shared-control architecture, very few evaluate their task performance and user's acceptance in principled human subjects experiments. In our work, we tested the proposed shared-control architecture in a real environment composed a 6-DoF robotic manipulator, equipped with a parallel gripper, whose motion is controlled through a 6-DoF grounded haptic interface. The autonomous algorithm is in charge of controlling 2 DoF of the robotic manipulator, keeping the gripper always oriented toward the object to grasp. The gripper is therefore constrained to move on the surface of a virtual sphere centered on the object. The human operator is able to move the gripper across the surface of the sphere and toward/away from the object (i.e., changing the radius of the sphere).

In order to demonstrate the feasibility and effectiveness of our method, we conducted a remote telemanipulation experiment where ten human subjects were asked to control the motion of the 6-DoF telemanipulator to grasp a wooden object. We tested the performance of the proposed sharedcontrol system against a more classic teleoperation approach, in which the human user was able to freely control all the degrees of freedom of the robotic manipulator. Moreover, we considered two ways of controlling the motion of the robot through the haptic interface -velocity-velocity and positionvelocity, -ending up with four experimental conditions. As a measure of performance, we considered the average completion time, trajectory length, angular motion, and perceived effectiveness.

We carried out a 2-way statistical analysis to be able to separately compare the different ways of commanding the motion of the robot through the haptic interface (velocityvelocity vs. position-velocity) and the different levels of human involvement in the control (shared-control vs. teleoperation). After that, we also carried out a 1-way statistical analysis to be able to compare all the four composite experimental conditions at the same time. Results showed that, in all the considered metrics, the shared-control approach significantly outperformed the more classic teleoperation architecture. Moreover, all the subjects preferred the sharedcontrol architecture with respect to teleoperation. This proves our hypothesis that shared-control can be a viable and very effective approach to improve currently-available teleoperation systems in remote manipulation tasks. However, it is important to notice that our subjects were not expert in using the experimental setup. In this respect, it may happen that the recorded significant difference in performance between shared control vs. teleoperation might become less significant in the presence of experienced users. This is something we plan to extensively study in the coming future, since it is particularly relevant for the context of our target project, RoMaNS, in which the operators in charge of sorting and segregating the nuclear waste can be skilled and experienced.

In addition to this first result, the 1-way statistical analysis gave us insights about the differences between the composite conditions. Results show a significant difference between S+PV vs. S+VV in the trajectory length and angular motion metrics, with the former condition outperforming the latter. This result came as a surprise, since it is in contrast with the results of the user experience evaluation. In fact, both the perceived effectiveness and the choice of the preferred condition clearly show that users preferred conditions employing velocity-velocity control with respect to position-velocity control. In this respect, all subjects complained that positionvelocity conditions required more attention and, in general, a higher cognitive load. Three subjects, who indicated S+VV as their preferred condition, asserted that they would have probably preferred condition S+PV if the task would have required more time to complete, since S+PV does not require clutching (see Sec. II-C).

Clutching is indeed another interesting point to discuss. Even in the velocity-velocity control approach, given a grounded haptic interface and a grounded slave manipulator, it is always possible to define an appropriate scaling factor between master and slave velocities such that the operator does not require clutching. However, as the difference between the master and slave workspaces increases, this mapping requires higher and higher gains, resulting in a telemanipulation system very hard to control, since the operator's accuracy/resolution in positioning the slave arm is degraded. The RoMaNS project presents us with the perfect example: the custom rig at the National Nuclear Laboratory is composed of (i) the same grounded haptic interface we are using in this paper, and (ii) a 500-kg-payload Kuka KR 500 manipulator. Although it is theoretically possible to map the workspace of the Virtuose 6D to the (much) larger workspace of the KUKA robot, this would result in very high motion gains (i.e., a small movement of the master interface would cause a big movement of the slave robot). For this reason, we decided to implement the velocity-velocity modality using the clutch. In this respect, we are also interested in understanding how to best tune the master-slave motion scaling factor, with the final objective of finding a good trade-off between high precision of movement and low need of clutching.

It is important to highlight that the proposed shared-control architecture is independent from the distribution of the DoF between the autonomous controller and the human operator. While having the autonomous controller keeping the gripper oriented toward the object seemed a natural choice for our task, the underlying shared-control architecture is agnostic to the task, the primary task variables, and the level of human involvement. In this respect, we are planning to study how the number of DoF controlled by the autonomous controller affects the task performance. For example, a system could use a highly-autonomous shared-control approach (i.e., many DoF managed by the autonomous controlled) when it is operated by novices, while it could implement a lowly-autonomous sharedcontrol approach (i.e., few DoF managed by the autonomous controlled) when it is operated by experts. This flexible approach could be also useful when teaching new operators.

Although our approach has shown promising result, it significantly limits the control capabilities of the human users, who are not able to freely move the robot wherever they prefer. This could be a serious problem if something unexpected happens in the environment. In order to address this point, we are studying new ways of providing guidance information to the operators using ungrounded tactile stimuli, with the objective of providing them with information about what the autonomous controller thinks they should do, but without reducing their capabilities to control the motion of the robot. This is particularly relevant in those scenarios where, for reasons of responsibility, safety, and public acceptance, it is beneficial to provide a human operator with full control of the motion of the robot, e.g., robot-assisted surgery. Another approach is to use a second robot holding a camera to track the position of the gripper and the object, adjusting the behavior of the autonomous controller if the object moves away from its original position.

Finally, all subjects appreciated the presence of haptic feedback to provide information about the manipulator's joint limits. This approach enabled them to always complete the task successfully, pushing them away from dangerous robot configurations in a very intuitive and non-obtrusive way. Subjects described the feeling due to the haptic feedback "as if the system was trying to nudge them towards a safer configuration of the robot."

Fig. 1 .

 1 Fig.1. An illustration of the manipulator with the gripper and the object to be grasped, along with explanatory notations and the attached frames of reference.

Fig. 2 .

 2 Fig. 2. A visualization of the four null-space directions defined in (5). (a): the four directions and the associated pseudo-velocity commands λ i projected on the slave and the master. (b-e): an illustration of the motion resulting from actuating each individual direction n i .

Fig. 3 .

 3 Fig.3. Experimental setup. The master system is composed of the Haption Virtuose 6D haptic device, while the the slave system is composed of a 6-DoF Viper S850 robotic arm carrying a pneumatic parallel gripper. A wooden object with dimensions 21 × 9 × 3 cm and weight 300 g is placed on a table in front of the robotic manipulator.

  II-C) and two different levels of human involvement in the control (shared control vs. teleoperation), ending up with four different experimental conditions: S+PV: shared-control with position-velocity motion control, where the subject controls only 4 DoF of the manipulator, and positions of the haptic device are mapped into velocities of the manipulator (see Sec. II-C.1); S+VV: shared-control with velocity-velocity motion control, where the subject controls only 4 DoF of the manipulator, and velocities of the haptic device are mapped into velocities of the manipulator (see Sec. II-C.2) T+PV: teleoperation with position-velocity motion control, where the subject controls all the 6 DoF of the manipulator, and positions of the haptic device are mapped into velocities of the manipulator; T+VV: teleoperation with velocity-velocity motion control, where the subject controls all the 6 DoF of the manipulator, and velocities of the haptic device are mapped into velocities of the manipulator.

Fig. 4 .

 4 Fig. 4. Experimental evaluation. Mean and 95% confidence interval of (a) completion time, (b) trajectory length, (c) angular motion, and (d) perceived effectiveness of the four feedback conditions are plotted.

ACKNOWLEDGMENTS

This work was supported by the EU H2020 RoMaNS project 645582.