Diego R Faria

Ricardo Martins
email: rmartins@isr.uc.pt

Jorge Dias

Grasp Exploration for 3D Object Shape Representation Using Probabilistic Map

Keywords: Grasp exploration, Probabilistic map, Object shape representation

In this work it is shown the representation of 3D object shape acquired from grasp exploration. Electromagnetic motion tracking sensors are used on the fingers for object contour following to acquire the 3D points to represent its shape using a probabilistic volumetric map. It is used the object referential for its representation. For that, it is found the center of mass of the 3D object through the moments to define its referential. The occupancy of each individual voxel in the map is assumed to be independent from the other voxels occupancy. The posteriori achieved from Bayes' rule is the probability distribution on the occupations percentage for each voxel. The probabilistic map in a Cartesian system is converted to the spherical coordinate system for visualization with more details on its surface.

Introduction

Applications of service robots will require advanced capabilities of grasping objects and skills that allow a robot to recognize the object also through the grasp exploration. Human uses the hand for recognizing some objects properties such as size, texture, etc. The skills of grasp exploration to acquire objects properties are important also in the robotic field to complement others sensors such as vision and laser to obtain more information of an object. The in-hand exploration strategies performed by humans motivated the development of analogous approaches to promote the exploration of surfaces of objects by robotic hands. These exploratory procedures are used to created internal representations of objects in order to proceed to its identification and integrating its 3D spatial and physical characteristics distribution to control the interaction with it.

In this work, it is generated the representation of the shape of a 3D object extracted from the data acquired during the human hand exploration of the object (by contour following). The representation of the object shape is built using a probabilistic volumetric map. The referential associated to the representation of the shape of the object is located in the estimated center of the mass of the object.

Contribution to Technological Innovation

Nowadays, there is a tendency to move the development of robotic manipulators from simple grippers towards more natural human inspired articulated robotic hands, with integrated multimodal sensing technologies. This new generation of autonomous dexterous robotic hands is playing an important contribution to the evolution of the robotic research paradigms. The field of robotics is moving to the development of new systems adapted to be introduced in new environments far from the traditional robotic applications in the industrial production lines. There is an emerging trend in the development of methods and strategies to endow these robotic platforms with the ability to autonomously explore these environments, proceed to the characterization of objects, use them as tools or interact with them. This work intends to contribute to the development of autonomous dexterous robotic hands by developing methods to extract a representation of the manipulated object in order to estimate the object shape and size. These methods are developed using contact points acquired from demonstrations performed by humans during the in-hand exploration. The developed methodology will be then transferred to robotic dexterous hands in order to estimate the shape and size of a manipulated object, from contact points acquired by a robotic hand through contour following. Achieving the 3D object shape estimation, it is possible to determine, through its geometrical properties, the best region of the object to perform the grasp. Using this knowledge (object representation) it is possible to endow a robot to grasp different types of objects including unknown objects.

Related Work

Researches about human perception concerning haptic exploration disclose that contour following is an ordinary way of "exploratory procedures" that people use for determining the geometry of an object [START_REF] Klatzky | Chapter 4 Intelligent exploration by the human hand[END_REF]. Many approaches have been proposed regarding robot haptic exploration for object recognition and object shape representation. In [START_REF] Allen | Haptic object recognition using a multi-fingered dextrous hand[END_REF] the authors present haptic object recognition using a dexterous robot hand with a manipulator arm. Through the hand contact by enclosing the objects at predefined positions was possible evaluate joint angles and force readings. The object shape recovery was performed using sparse contact points from hand. The point clouds were fitted to superquadric models defined by a set of parameters describing shape and pose. In [START_REF] Bierbaum | Haptic Exploration for 3D Shape Reconstruction using Five-Finger Hands[END_REF] the authors developed a framework for haptic exploration by contour following that can be used with robot or human hand. The object shape contour is acquired by a human hand using a data glove where the human operator visually guides the contact sensor along the contours of the object by the index fingertips. It is used an extended superquadric function for primitive modeling which can represent a variety of cubical and spherical geometries. They address modeling of basic superquadric shapes. The authors have used stereo vision for wrist tracking by particle filter. They have used a marker bracelet attached to the wrist of the subject with the data glove for its tracking. The proposed work in [START_REF] Bierbaum | Robust shape recovery for sparse contact location and normal data from haptic exploration[END_REF], the authors have used superquadric functions for shape recovery from haptic exploration with multi-fingered robot hands using fingertip tactile sensors. They have applied a hybrid minimization method utilizing a genetic algorithm by considering the contact normal information to recover superquadric primitives from synthetic exploration data. In a previous work [START_REF] Faria | Object shape retrieval through grasp exploration[END_REF] we developed a method to extract basic shapes (primitives) from data acquired from grasp exploration. Gaussian Mixture Models was used for points clustering and outlier removal. After a learning phase, the object shape was classified through Bayesian techniques. It was used least square minimization of a distance metric to find the shape orientation and scale for its representation.

Research Contribution and Innovation

In this section is described the methodology adopted for object representation using probabilistic map. Mapping techniques as occupancy grid [START_REF] Moravec | Sensor fusion in certainty grids for mobile robots[END_REF], [START_REF] Elfes | Using occupancy grids for mobile robot perception and navigation[END_REF] has been used tin robotics field to describe an environment of a mobile robot. Two-Dimensional grid has been very used for static indoor mapping [START_REF] Thrun | Robotic mapping: a survey[END_REF]. The idea is to verify the probability of each cell to be full or empty after the sensors observation. In [START_REF] Thrun | Robotic mapping: a survey[END_REF] is described the standard grid mapping algorithm that is a version of Bayes filter. This filter is used to calculate the posterior over occupancy of each cell. Probabilistic volumetric maps are also useful as presented in [START_REF] Ferreira | Active exploration using bayesian models for multimodal perception[END_REF] for data fusion (visual and auditory perception). The main idea of using the probabilistic map is due to: reach a simpler way of static object reconstruction and representation and the uncertainty of sensor noise due to real world (the sensor probability model depends on the characteristics of the sensor and the object being sensed). In the next subsections are presented the detailed content about the employed methodology for object representation through grasp exploration by contour following.

Probabilistic Volumetric Map for Object Representation

This work presents a model for grasp exploration, but it also can be used for data fusion. Our intention is to acquire the 3D shape of the object so that instead of work in an egocentric way, we will work with object-centric representation in a spherical coordinate system to reach more resolution on the object surface. The volumetric map is updated along the exploration in discrete intervals. The proposed methodology will be used for data fusion (multimodal perception) in a future work, e.g. using vision and touch. The occupancy of each individual voxel is assumed to be independent from the other voxels' occupancy and thus O C is a set of independent random variables: M C ∈ -index a cell on the Map; O C -probability value describing the occupancy of the cell C; Z grasp -grasp exploration measurement that influences the cell C. It represents 5 sensors which each one returns the 3D position of a movement; P(O C ) -Probability distribution of preliminary knowledge of coverage value describing the occupancy of the cell C, initially is an uniform distribution; P(Z grasp | O C ) -probability distribution corresponding to the set of measurement Z grasp that influences the cell C taken from the grasp exploration data. This distribution is taken from occupancy model. In case of data fusion from different sensors, it is necessary to declare the variables that represent the distribution of the measurement, e.g. working also with vision, then P(Z vision | O C ) represents the sensor model. In case of different sensors the joint distribution decomposition of the relevant variables shows the dependency assumptions according to Bayes' rule as follows:

) | ( ) | ( ) | ( ) ( Oc Z P Oc Z P C Oc P Z Z Oc P grasp vision grasp vision = ( 1
)
The posteriori is the probability distribution on the occupation's percentage

P(O C | Z vision Z grasp ) for each voxel: ) | ( ) | ( ) | ( grasp vision grasp vision Z Oc P Z Oc P Z Z Oc P α = (2)
Since this work is just for grasp sensor model, it is possible to simplify the estimation model of occupancy, so that the posteriori in this case is the probability distribution on the occupation's percentage P(O C | Z grasp ) for each voxel. The occupation's probability is given by:

)) ( 1 ( )) | ( 1 ( ) ( ) | ( ) ( ) | ( ) | ( C C grasp C C grasp C C grasp grasp C O P O Z P O P O Z P O P O Z P Z O P - - + = ( 3
)
where P(O C | Z grasp ) is the posteriori value; P(Z grasp | O C ) is acquired by the sensor measurement (likelihood); P(O C ) is the priori information (at the beginning it is a uniform distribution representing the state full or empty) and subsequently the last posteriori becomes the prior for the next computation.

Grasp Exploration Occupancy Model

For the data acquisition (grasp exploration), we are using the Polhemus Liberty system [START_REF]Polhemus Liberty Electromagnetic Motion Tracking System[END_REF]. It is used one magnetic sensor on the fingers (thumb, index and middle) to acquire the shape of an object by contour following. Each sensor return the 3D coordinates based on Polhemus Liberty referential. The frame rate of each sensor was configured to be up to 15Hz. During the data acquisition, it is defined a workspace (35x35x35cm 3 ) in the experimental area to place the object for mapping. This space is subdivided in 0.5x0.5x0.5cm 3 cells. During the displacement of each sensor in the workspace area, each one gives the information about its 3D position and it is possible to identify in which cell that the measurement is inserted. Due to the size of each cell relatively to the standard deviation of the magnetic tracking sensors measurements (until 0.2 cm for linear movements of 10cm), it is defined inside each cell a 3D isotropic Gaussian probability distribution, P( Z grasp | Oc), centred at the cell central point with standard deviation 0.2 and mean value equal to the cell central point coordinates of the cell. The probability of a measurement belongs to that cell is given by the equation ( 4). The values are normalized in order to consider that the probability value assigned to a point located at the centre of the cell is equal to 1.

      - ∑ - - ∑ Π = - ) ( ) ( 2 1 exp | | ) 2 ( 1 ) | ( 1 2 / 1 2 / 3 µ x µ x T C grasp O Z P (4)
In ( 4) | | ∑ represents the determinant of ∑ (sensor noise variation). It can also represent a scalar value. Due to the normalization used, the equation ( 4) takes the form:

                  - + - + - - = 2 2 2 2 2 ) ( ) ( ) ( exp ) | ( σ z y x C grasp u z u y u x O Z P (5)

Object Referential & Representation in Spherical Coordinate System

To have a better representation of the object and to reach more details on its surface we are working with object-centric representation. To find the object referential and represent it centred in a sphere, it is computed the center of mass of the object. As long as the center of mass of the object is determined, it is possible to define the object referential. The center of mass of the points' distributions that represents the object is found along the grasp exploration in the workspace. While the data is acquired during the exploration, the center of mass the object is changing due to the amount of data and the object surface growing (Fig. 1(a)). The axes of the tracker device referential are kept, so that we just need to translate the points in the tracker referential to the object referential. Through the centroid, it is possible to define the radius of a sphere is the center of mass of the object, thus it is possible to center the object inside a sphere for its volumetric representation as shown in Fig. 1 (b). To compute the center of mass of a 3D object shape we compute the discrete moments. The moments are a measure of the spatial distribution of the mass of a shape. The centroid is reached through some steps, computing the zero moment (summation of the voxels); first moments for x, y and z and then it is computed the centroid for each axis. The moments are computed in an iterative way, at some discrete intervals, after a new exploration the center of mass of the object is updated.

Experimental Results

The magnetic sensors were attached to a glove to perform the object contour following to acquire the contact points. For this experiment, it was decided to use just the thumb, index and middle fingers to explore the object surface due to be enough to cover the object shape through the movements around it. The setup for the experiments is composed of a wooden table, without any metallic parts, since the electromagnetic tracker is sensitive to nearby ferromagnetic materials. The rigid 3D object is fixed on the tabletop in a defined workspace for all experiments having the object in the same area. The magnetic tracker emitter unit that determines the frame of reference for the motion tracking system is placed on the tabletop at ~30cm near to the object. A workspace of 35x35x35cm 3 was defined on the table for the object mapping. The referential of the workspace was defined to be parallel to the sensor referential and then a simple translation is enough to convert the 3D points on the sensors referential to the workspace referential. Fig. 2 (a) shows the experimental setup area. Each voxel of the volumetric map was defined to represent an area 0.5x 0.5x0.5cm 3 due to the good precision of the sensor position resolution at 30cm range (less then 1mm). The chosen exploratory procedure is performed during 90 seconds. The volumetric map is updated with the new sensors measurements every 15 seconds. The contour following movements have no pattern, that is, it is not necessary to follow some pre-defined rules such as making movement just in one direction. The subject is allowed to do movements in any direction, but for better representation it is suggested to perform horizontal and vertical movements around the object until to contour all surface. The chosen object for this experiment was a bottle of wine. Fig. 3 shows other views of the object centered in the estimated center of mass.

Discussion of the Results

This approach for shape representation has a limitation: the rigid object need to be fixed in the specified workspace. If the object abruptly moves many times during the exploration, the reconstruction of the object can be less precise. The idea of this methodology is to do not represent the points with low probability so that the reachto-grasp movement before the object contour following starts are not represented because the hand trajectory reaching the object have very few points and that points are not repeated (i.e. do not pass in the same cell twice) to increase the probability of the cells that the movement has occupied. The application ignores all points outside of the workspace where the object is placed. The adopted method uses a unique global map, where all the fingertips data are represented e.g. if one or more sensors passed through the same cell the probability increases. Other method could be applied; instead of building a unique map for all sensors, it could be built a local map and then fusing them into a global map through a Bayesian filter. The exploration was done with the sensors on right hand. During the trials, the subject that was performing the exploration usually hold with the left hand the top of the object to guarantee that it does not move, thus it is possible to reach better results, but at least a small variation of the object position can happen. After analyzing the exploration performance of some subjects, it was possible to see that the object shape influences the exploratory procedure, e.g. the bottle of wine was more explored in the middle due to the cylindrical shape. The top and bottom of the explored object is poorer in the representation due to the subject explore less those parts. The retrieved object attributes such as shape and size were satisfactory. The raw data, i.e., fingers movements inside the workspace were 6169 points. We have considered all cells with probability higher than 0.7 to represents the object shape. After computing the probabilistic volumetric map, the object shape has occupied 723 cells (probability >= 0.7). The use of tactile sensors for contact points could facilitate and improve the results, e.g. using tactile sensor would be possible to know when the fingers are in contact to the object to initialize the tracker device points acquisition, avoiding to start the application with the hand on the object or to fill some voxel on the workspace during the reach-to-grasp. In this work we have introduced the idea of work with multimodal perception. Our future directions is also to use the visual perception to acquire more information of the object and then through sensors fusion we can reach better results for the probabilistic representation of the object to be used for features extraction for its characterization.

Conclusion and Future Work

In this work is shown the probabilistic representation of a 3D object model achieved by grasp exploration through probabilistic volumetric map due to the simplicity to recover, by this method, a shape given the sensors measurements. The center of mass of the object is computed to define the object referential for its representation in the spherical coordinate system. As future work, it will be used the extended model for sensor fusion using stereo vision and grasp exploration for better representation of the object. For that, it is necessary sensors calibration, and it is necessary a joint distribution decomposition of the relevant variables to show the dependency assumptions according to Bayes' rule for the data fusion. The experiments will be performed with non-fixed object (in-hand exploration using two hands). For that, it is necessary to have an initial position of the object to be used as reference, and then it will be computed a transformation between the object referential when it is moving to the initial position referential. This will be done every time that the object moves to be possible to map all points in the origin to have the object model representation.

After acquiring the representation of the object will be possible to recognize and characterize it.

Fig. 1 .

 1 Fig. 1. (a) The center of mass of the object changes along the grasp exploration; (b) Illustration of the object representation in spherical coordinate system.

Fig. 2 .

 2 Fig. 2.(a) Experimental area for the in-hand exploration; (b) raw data; (c) representation of the object shape (just voxels with probability higher than 0.7).

Fig. 3 .

 3 Fig. 3. Representation of the occupied cells with probability higher then 0.7 (object centered in the estimated center of mass).

Acknowledgments. This work is partially supported by the European project HANDLE (23-16-40). Diego Faria is supported by the Portuguese Foundation for Science and Technology (FCT).


Mihai Stoica
email: mihai-v.stoica@romania

Gabriela Andreea Calangiu
email: gabriela.calangiu@romania

Francisc Sisak
email: sisak@unitbv.ro@romania

Movement Speed Models of Natural Grasp and Release Used for an Industrial Robot Equipped with a Gripper

Keywords: Speed, Models, Robot, Grasp, Gripper

In this paper, movement speed models of a robotic manipulator are presented according to the mode of operation of the human hand, when it wants to grasp and release an object. In order to develop the models, measurements on a human agent were required regarding the movement coordinates of his hand. The movement patterns have been approximated on the intervals, using first and second degree functions. The speeds were obtained by deriving these functions. The models obtained are generally presented; for their implementation in models applied for a certain robot, specific changes from case to case have to be made.

Introduction

Robots became more powerful and more intelligent in the last decade and they are developing in the direction of services. Being used by people without technical knowledge, it's important for them to be easily operated using a flexible programming system. A great importance, concerning the robotics, is the way the robots catch and manipulate objects. The research is in the direction of the development of models for natural grasp of objects, like the human model.

In its functioning, the human hand has a completely natural movement with the sensorial ability for a subtle manipulation. Biological subtleties can be ignored since they contribute little to natural hand modeling [START_REF] Bando | A simple method for modeling wrinkles on human skin[END_REF][START_REF] Rhee | Human hand modeling from surface anatomy[END_REF]. In [START_REF] Van Nierop | A natural human hand model[END_REF] van Nierop et al. a model of the human hand is presented, which has natural movement and constraints due to the biomechanical joints of the skeleton and the skin of the hand. They present their research in modeling and provide a description of anatomic nomenclature. For the evaluation of the model, they realize the taxonomy of elementary tasks which describe the movements of the hands into a 2-dimensional parametric space.

Many papers have focused on the construction of a firm grasp [START_REF] Faverjon | On computing two-finger force-closure grasps of curved 2D objects[END_REF]. In [START_REF] Abu-Zitar | A Neural Network Approach to the Frictionless Grasping Problem[END_REF] R. Abu-Zitar and A.M. Al-Fahed Nuseirat present a heuristic technique used for solving the linear complementary problems (LCP). Their research consists in the determination of minimal force required for the grasp an object with a multi-finger gripper. The contact is assumed to be frictionless. A numerical algorithm, Lemke, can be used for solving the problem. Lemke is a direct method, deterministic, used for finding precise solutions using a few constraints. The authors propose the neural network technique for obtaining the largest number of precise solutions, in positions that can be solved and good solutions for position in which Lemke method fails. Using inequality theory, the problem is composed like a LCP. The research of the authors had to convert the problem into a heuristic search problem, using the architecture and learning capabilities of a single two layered neural network.

In their research, Alexandra Constantin et al. present a method for quality assessment in terms of arm movement imitation. They propose a segmentation and comparison algorithm based on the angle rotation of the joint [START_REF] Constantin | Evaluating Arm Movement Imitatio[END_REF]. Here, they describe an empirical study designed to validate the algorithm, comparing it with human assessment of imitation. The results show that automatic metric evaluation does not differ significantly from the human evaluation.

The work on automatic grasp synthesis and planning is a relevant idea [START_REF] Miller | Automatic grasp planning using shape primitives[END_REF][START_REF] Morales | Using Experience for assessing grasp reliability[END_REF][START_REF] Platt | Extending fingertip grasping to whole body grasping[END_REF]. In [START_REF] Tegin | Demonstration-based learning and control for automatic grasping[END_REF] is presented a method for automatic grasp based on shape primitives of an object, using a programming by demonstration platform. Initially, the system recognizes the grasp from a demonstrator and then generates the grasping strategies for the robot. The authors of this paper began by presenting how the grasp is modeled and learned and how it is mapped at the robot hand. They continued with the accomplishment of a dynamic simulation of the grasp execution, with focus on objects that must be grabbed whose position is not completely known.

Humanoid robotic requires new programming tools. The programming by demonstration method is good for simple movements, but until now the adaption for subtle moves is very difficult for it. The mathematical models have been realized only for simple hands or objects. In [START_REF] Folgheraiter | Teaching Grasping to a Humanoid Hand as a Generalization of Human Grasping Data[END_REF] Michele Folgheraiter et al. tried to use the information obtained directly by a human teacher. They have developed a glove which they used for collecting the information from the different experiments and generalized it into a neuronal network.

In this paper several elements derived from a research regarding natural grasp of an object by man, will be presented. In our research, we made some measurements on a human agent regarding the movement coordination of the hand and his finger when he wants to grasp and release an object. The basic idea was to translate these measurements into a model of movement speeds which can be used by an industrial robot equipped with a gripper.

Contribution to Technological Innovation

Humanoid and mobile robots development is heading in the direction of imitating the human behavior attempt. The objects grasp and manipulation is a significant domain even in the industrial robots field. In nowadays, industrial robots work with constant speeds when they have to grasp and release objects. This paper presents theoretical models of movement speed of an industrial robot manipulator simulating the human hand model. The usage of the proposed models for the movement speed of an industrial robot gripper improves the grasping quality, respectively the releasing quality of an object and minimizes the accomplishment time. Currently, the gripper of an industrial robot passes through three distinctive steps when a grasp or a release has to be done: the first step in which the gripper is positioned in the grasp point, respectively the release point; the second step in which the gripper closes, respectively it opens; and the third step in which the robots continues his movement with or without object. The proposed models determine that the three steps above defined to intertwine: thus they improve the quality of grasping and releasing and the time in which these are accomplished is minimized. Both the gripper speed movement model and the closing/opening speed model have relatively large periods of time for opening and closing of the gripper. This shows that the models approach to human hand model and reduce the force shocks, caused by the inertial force, as it happens when the industrial robots currently used manipulate objects.

Therefore, in this paper speed models of an industrial robot gripper are proposed, in order to improve the object grasping and releasing, using human hand model simulation.

Measurement Procedures

The measurements have been made using the OptiTrack system, using the camera displacement like in Fig. 1 a). For improving the precision, the work volume was reduced to approximately 1 cubic meter. The measurements were made on the object presented in Fig. 1 b). On this object there were attached four markers, which were selected for achieving a "rigid body", named "body" using the ARENA software.

The object is placed in the XOZ plane, like in Fig. 1 b). In this figure, the object is placed on worktable. If the object is lifted from the table, then OY coordinate of the four markers will increase; if it will be put down then it will decrease. In the measurement made the object is considered to be dot-like, being represented only by the coordinates of the rightmost marker.

The measurement operation consisted in capturing the human hand and the object coordinates when a human agent grasps an object from the workbench, lifts this object to a certain height, puts down the object on the workbench and releases it, lifts once again the hand without the object (open hand), than puts down the hand to grab again the object and starts again a new cycle.

For tracking the human hand those three markers disposed like in Fig. 2 were used. The markers are attached to a rigid support, as is it shown in the below picture. The arrangement of the markers on the hand surface has been tried. Due to the fact the four fingers do not constitute a rigid body a problem was encountered in which the software did not recognize the three markers as "rigid body", this is the reason for using the rigid support. As in the case of the object, the hand is considered dot-like by the coordinate's point of view. The coordinates of the hand are represented by the right-bottom marker coordinates in the Fig. 2.a. According to figures 1.b) and 2 when the hand opens, the distance on the OZ coordinate between the hand and the object will increase, and when it closes this will be reduced.

Obtained Results

In the figure 3 the coordinates of the human agent's hand and of the object on the OY direction, in a complete grab-release object cycle, are represented with green (A, B). The area where the object is lifted from the workbench is enclosed in a red rectangle (X), and the area where it is standing still on the workbench is enclosed in a blue rectangle (Y). It can be observed that the time which is needed in order to lift the object from workbench is smaller than the time which is needed for it to be still. The human agent, in the phase of placing the object back on the workbench, is more careful and the motion has a much higher precision.

The green lines (A, B) represent the coordinates at equal moments in time. The slope of the lines in every point is the speed in the corresponding point.

It can be observed that the speed of rise and descent isn't constant in either cases, not for the free hand and neither for the hand with an object. With other words the human agent's hand doesn't moves with a constant speed, which is usually the case in robotics, but according to a curve like the one presented in figure 3.

In figure 4 the blue lines (A, B) represent the OZ coordinates of the human hand, and also the object which has to be handled (coordinates through which the grabbing and releasing motions can be highlighted). The green ones (C) represent the OY coordinates of the hand and of the object. Just like it was the case with the horizontal movement, in the case of the closing and opening motion of the hand of the human agent, we have to deal with a motion which has a variable speed. The area inside the red rectangle (X) represents the release zone of the object. The area inside the black rectangles (Y1, Y2) represents the grabbing zone of the object. As it can be observed the time for grabbing the object is longer than time needed for releasing it.

Its grabbing starts in a moment before the moment in which the hand is at the level of the workbench. In the first black rectangle (Y1) the proper grasp of the object is presented. The second rectangle of the same color (Y2) follows an area of postgrabbing, an area where the human agents tests the grip. In this moment he checks whether the grip is stable and he ensures that it's the correct one. Only after realizing this, he begins to lift the object.

The Established Models

The results obtained in the previous chapter are used for constructing models of the movement speed on the vertical axis (in the direction of grabbing the object) and of the speed of closing-opening of the industrial robot's gripper. These models are obtained based on the actions of the human hand.

In the graphics from the previous figure the coordinates for vertical movement and for the closing-opening of the human hand are presented, at equal moments in time.

By deriving these curves the movement speeds for the corresponding directions can be obtained. In figure 5, on the upper graph, the vertical coordinate of the human agent's hand (A) is presented, when he lifts and lowers the object. In the interval t0 -t1 the curve can be approximated with a 2nd grade curve. By deriving the 2nd grade function a 1st grade function is obtained, thus the speed on this section can be approximated by a straight line segment. In the interval t1 -t2 the curve can be approximated with a straight line segment. For this reason the speed in this interval is constant. In the same way the other intervals are analyzed and in the end the speed's graph is obtained which is presented in the lower part of figure 5.

The graph at the lower part of figure 5 can represent an approximately model of the movement speed on the vertical (in the direction of the grabbing) of the gripper of an industrial robot. In this model the intervals t0-t1, t2-t3 and t3-t4 can be considered equal to T. In the t5-t6 interval (the interval for placing the object back to the workbench) is big. It can be considered as being equal to 3T. The intervals t1-t2 and t4-t5 depend on the distance between the coordinates in which the robot has to act. In conclusion the model presented above can be used on another scale, in a real system, considering the shape and some proportions of the speed-graph.

In figure 6, on the top graph the coordinates of the human hand and of the object are presented, when the object is released, the hand is raised without the object, the hand is lowered and the object is grabbed. The area in the yellow frame (X) is not used for establishing this model. When the object is released, the hand can have a relative motion on the OZ direction towards the object and because of this the coordinate difference on the OZ between hand and object is not the same as when the hand was opened. In the interval t4-t5 it is considered that the opening of the hand is constant. In the vicinity of the moment when the hand begins to rise and the moment in which it reaches the surface of the workbench, the difference on the direction OZ between the hand and the object, is approximately equal to the displacement of the thumb towards the other four fingers of the human hand (the opening of the hand). The vertical movement coordinates are presented in green (B), while the movement coordinates in the direction of the opening of the hand are blue (A). In the lower graph, the approximate model of the vertical movement speed of the robot's gripper is represented in red (C). The brown line (D) is the model which is used for closing and opening the gripper of the robot. These models were used in the same way as the one in figure 5. The interval t1-t4 is the interval in which the object is released. The robot's gripper opens with a growing speed until the moment t2. In this moment the robot begins to move the gripper on the vertical. For a brief period of time, t2-t3 the gripper opens with a constant speed, and in a very short time-period the gripper's speed reaches 0. In the periods of time: t1-t2 and t2-t3, in order to establish the model they can be considered to be T1. The deceleration period t3-t4 can be considered to be T1/3. The interval t5-t8 is the interval in which the object is grabbed. The gripper begins to close with an accelerating speed before it moves the proper grabbing position of the object. When it reaches the corresponding position, it closes with a constant velocity, and after a while the speed begins to drop until it reaches 0. This last phase is the period in which the robot tests whether the grip is stable.

An exact relationship between the intervals t5-t6, t6-t7 and t7-t8 can't be established, but they can be considered approximately equal to 2-3 times T1.

Conclusions

The obtained models are only approximations. They are not general, but they can be used for specific type of actions. In the shown models, the magnitude of acting speeds is intuitively chosen; it is important in which way this can be modeled. The speeds have been modeled with line segments: oblique and horizontal. Linear models have been used for simulating the human hand model in order to obtain simple and easy to use models. Others functions and techniques of measured data synthesis for the models improvement might be used, but those involve larger processing time.

In the models that have been presented only proportions between the time interval in which the speed is described by an oblique line segment, and in the time intervals with constant speed the time depends on distance between the point's coordinates in which the manipulator has to act are established.

These models have been realized for a two finger gripper, but they can be used also for manipulators with more than two fingers. In the future we want to implement and test these models on an industrial robot equipped with a three finger gripper.

Fig. 1 .

 1 Fig. 1. a) The displacement of the camera; b) The object used to accomplish the measurements.

Fig. 2

 2 Fig. 2 Markers arrangement on the human agent.

Fig. 3 .

 3 Fig. 3. The difference between the grip and the release of the object.

Fig. 4 .

 4 Fig.4. The OZ and OY coordinates of the hand and object for an entire cycle.

Fig. 5 .

 5 Fig. 5. Modeling of the vertical speed (in the direction of grabbing the object) of the gripper.

Fig. 6 .

 6 Fig. 6. Modeling the vertical speed of the robot's gripper and the closing-opening speed of the gripper.

Acknowledgements. This paper is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and by the Romanian Government under the contract number POSDRU/6/1.5/S/6.


Roberto Da Piedade
email: roberto.piedade@fe.up.pt

João Bastos
email: joao.bastos@fe.up.pt

Américo Azevedo

Using the Life-Cycle Paradigm to Support Factory Planning Approaches

Keywords: Factory Planning, Virtual Factory Framework, Life-Cycle Paradigm

In order to fulfill all challenges related to design, management, evaluation and reconfiguration of new or existing facilities, the development of a new, integrated and holistic factory framework is required. In this context, a new requirements model is proposed in the context of the innovative framework called Virtual Factory Framework. Using this approach in factory planning it is expected to improve the ability to generate better and more sustainable solutions over the entire factory life-cycle. This paper underlines the use of the life cycle paradigm in order to enable the future factory planning approaches.

Introduction

The Virtual Factory Framework is a new foresight to the Next Generation Factory, viewing the factory as a new and complex type of product. It is appropriate to consider factories as long life and complex products, since they have to follow the same steps in its origin as products. They also have to be permanently adapted to the needs and requirements of markets and economic efficiency, applying the life cycle paradigm to the factory as a product [START_REF] Vff | Holistic, extensible, scalable and standard Virtual Factory Framework[END_REF].

The new line of thought in manufacturing management is directed to the optimization and value creation of products, processes and technologies throughout the factory life cycle. The main objectives are to improve the effective use of the decreasing time available to reach the market and the increasing need to reduce design, implementation and production costs.

The present work addresses state of the art concepts and research issues in the context of an RTD European project entitled "Holistic, extensible, scalable and standard Virtual Factory Framework", namely in the topic of factory planning and the concept of "factory as a product".

This document is organized as follows: the second section presents the next generation factory concepts; the third section presents two contemporary factory planning approaches; the fourth section addresses the virtual factory framework and the supporting requirements model; and finally, the conclusions and further works are presented in the last section.

Next Generation Factory Concepts

In a factory development project, the factory can be seen as a product that requires a complex life cycle and the use of techniques already used for product development. This new paradigm can be introduced to support manufacturers in the creation of value through new solutions (products, processes and technology) that improve quality, reduce ramp-up and product delivery time, and also reduce production costs in order to achieve greater competitiveness. Some initiatives have been developed in order to reach these objectives. One of the most recent and robust is ManuFuture [START_REF] Jovane | The ManuFuture Road: Towards Competitive and Sustainable High-Adding-Value[END_REF]. This initiative aims to promote investments in innovation that will ensure the future of European industry in a knowledge-based economy. At the same time, its aim is to speed up the rate of industrial transformation in Europe, providing High-Adding-Value employment and reaching a major share of the world's manufacturing output in the future knowledge-driven economy, seeking to achieve Competitive Sustainable Manufacturing [START_REF] Jovane | The ManuFuture Road: Towards Competitive and Sustainable High-Adding-Value[END_REF].

Every factory and production facility is a distinctive entity. Each factory is different in terms of its products, processes, layout, structure, human resources and corporate philosophy. However, the common denominator for them to guarantee their survival is to make production facilities adaptable. The adaptability is becoming a top priority for modern enterprises and is a continuous task for management.

Modern factories have to be modular, scalable, flexible, open, agile and knowledge-based in order to be able to adapt, in real time, to the continuously changing market demands, technology options and government regulations.

In a manufacturing company, the job of a production facility is to perform competitively on the market, with high levels of adaptability, by producing (material) goods as products in line, as much as possible, with the market demand. In order to achieve this adaptability, its companies need to have an integrated perspective. The interrelationship between the products, processes and factory thus requires that the different actors are highly involved and interdependent (Figure 1). The product required by the market determines the process characteristics and configuration, such as equipment, organization and product volume and mix. The process determines the plant with the equipment, support facilities and services that individuals operate, control and supervise. And finally the factory determines the product volume, mix and cadence. Changing one component causes other components to change as well. This cannot only be applied to production facilities, but also to an entire factory [START_REF] Schenk | Factory Planning Manual[END_REF]. One of the factors that have a profound impact on adaptability is flexibility. Hence the constant need to strengthen and improve flexibility in the design of production processes and factory planning. Thus, the need for new methodologies that support the design of the factory as a product is increasingly obvious. But since this is a highly complex task, it is necessary to study and analyze the approaches followed by experts and experienced implementers in the field.

A first notion that must be present at this stage is the fact that the design of the factory cannot be separated from the planning process and product design, particularly due functional interdependencies and due to the similarity and parallelism observed in their life cycle, as represented in Figure 2.

Fig. 2. Factory, process and product life cycle

Indeed, the benefits of applying this concept are feasible and desirable if a factory planning can be carried out using knowledge on life cycle paradigm, process planning, factory planning and new product development (NPD).

The product life cycle is the time period between the moment that the product is conceived (concept, plan, design, idea, notion, or thought) and when its production is no longer profitable [START_REF] Mital | Product Development: A Structured Approach to Consumer Product Development, Design and Manufacture[END_REF]. This is a paradigm that can properly conduct the phases of product management through the concepts and tools applied in product development. Then, when taking the concept of the factory as a product, it can also extend the paradigm to this new perspective.

The product life cycle phases can be studied in different organizational areas such as: marketing, product management, manufacturing and computer systems. For instance, the concept of PLM (Product Lifecycle Management) has to do with the management of activities and product requirements from the viewpoint of processes development, manufacturing and product utilization in the context of data management, while the traditional concept of product life cycle applies to product marketing and service life [START_REF] Saaksvuori | Product Lifecycle Management[END_REF]. Although the PLM is currently presented as software, in fact, it is a methodology supported in an integrated set of software tools oriented to life cycle management that is used to manage specific tasks and to plan the entire process of product management.

In fact, the life-cycle paradigm can be applied in order to harmonize and integrate the life cycle of the product and factory (manufacturing view) simultaneously, providing the idealization of its phases, as shown in Figure 3. [START_REF] Pedrazzoli | High Value Adding VR Tools for Networked Customer-Driven Factory[END_REF] This approach intends to set up a foundation for factory planning in order to establish the phases that can be standardized in the context of design. This harmonization approach of the converging life-cycles makes it possible to use simulations in the design of an object-oriented collaborative product, starting at the vision of the virtual factory to the real factory at the intersection so-called "Crossinglife cycles point" [START_REF] Pedrazzoli | High Value Adding VR Tools for Networked Customer-Driven Factory[END_REF].

Fig. 3. Factory life cycle crossing product life cycle

According to this idea, we will now present some methodologies followed in Factory Planning and Product Life Cycle mentioned in the literature.

Factory Planning Approaches

In the context of the project research, it was possible to identify several factory planning approaches. The next paragraphs present a brief overview of two of them which have presented relevant contributions for the Virtual Factory Framework requirements definition on the factory design phase.

Systematic and Situation-driven Planning Methods [3] -Planning production facilities means envisioning several aspects that includes the products that are going to be produced, the processes required to produce them and the physical infrastructure required to the production. This approach requires the use of methodologies that efficiently design the planning process. According to Schenk [START_REF] Schenk | Factory Planning Manual[END_REF], a planning project can be developed systematically and/or situation-driven on the basis of various planning process and procedural model views.

A systematic, methodical approach is influenced by situation-driven decisions. It serves the development of a planning project through internal and external planning activities on the basis of various planning process and procedural model views. These production facility and factory lifecycle design planning phases and stages are represented in figure 4.

Fig. 4. Production facility and factory lifecycle design planning phases [3]

The planning activities span a production facility's entire life cycle from development/planning through setup, execution and operation to phase-out [START_REF] Schenk | Factory Planning Manual[END_REF].

Therefore, the Systematic Planning Processes have the following steps: 1. Rough sequence of processes and manufacturing plants planning 2. The project design takes place with the following sequence: a) Main process (parts manufacturing or assembly) b) Main process storage; main process transports system; production process control; quality assurance; fixtures tools and testing equipment; c) Manufacturing equipment engineering; maintenance; auxiliary materials storage; power conversion equipment; waste treatment facilities, d) Management; power generation; social, medical and sanitary facilities.

Complex planning model -this consists of the following planning complexes:

a) Project definition b) Project development c) Project implementation An enhancement of the systematic approach is the situation-driven method for factory planning also presented by Schenk et al. [START_REF] Schenk | Factory Planning Manual[END_REF]. The situation-driven planning differs from the systematic planning in that, as a result of operational decisions (e.g. changes in target, data, product, technology, requirement, time, profitability or quality specifications), all or part of the planning process and sequences have to be changed.

According to this situation-driven approach the planning model acquires reactivity and is adaptable to operational changes. Its redevelopment is based on the current situation and uses selected systematic planning components and activities to ensure the accomplishment of the goals.

Factory planning supported in simulation tools -Simulation tools are popular in various industrial fields as decision support systems. Since factory planning is one of the most complex tasks, the need of decision support tools was especially comprehensible. Several commercial solutions have been appearing in the last decade to the market as appropriate to deal with the problem of factory planning.

Mertins et al. [START_REF] Mertins | Integration of Factory Planning and ERP/MES Systems: Adaptive Simulation Models[END_REF] presents a scalable, flexible and adaptive simulation model used in factory planning based on existing ERP (Enterprise Resource Planning) and MES (Manufacturing Execution System) data. The objective of this work is to enable an industrial engineer without simulation expertise to perform the simulations that are necessary to support several tasks including process planning and factory planning. Moreover, the simulation model facilitates an analysis of the results for different scenarios, using the actual data from the ERP and MES systems.

In their research, Wenbin et al. [START_REF] Wenbin | Production engineering-oriented virtual factory: a planning cell-based approach to manufacturing systems design[END_REF] report a development in a production engineering-oriented virtual factory -a planning cell-based manufacturing systems design approach. This manufacturing systems design process is based on a planning cell reengineered according to the concept of concurrent engineering. The process modeling of a production engineering-oriented virtual factory is proposed at both generic and detailed levels. With logic level simulation (discrete event simulation, etc.) and physical level simulation (ergonomics simulation, immersed virtual reality, etc.), a distributed, layered and integrated simulation model can be used to build a virtual factory environment for concurrent manufacturing systems design during the whole lifecycle of production engineering, including production system configuration, factory layout, and so on. Therefore, the designed manufacturing systems can be evaluated and optimized before their implementation.

Once the planning methodologies and the life-cycle paradigm are presented, the next step is based on the development of a conceptual model to support the design of the new generation factories -the Virtual Factory Framework.

Virtual Factory Framework

Framework Overview

In the virtual factory context, the manufacturing attributes are migrating to other forms which include concerns on how to solve highly complex tasks under increasing demand for adaptability, cost, efficiency, durability, reliability, scalability and security [START_REF] Pedrazzoli | High Value Adding VR Tools for Networked Customer-Driven Factory[END_REF]. Thus, the aim of designing the future factories is accomplished if the process planning in a virtual factory can be synchronized with the real factory through basic components that can be simulated by aligning the factory design and decisionmaking process during the factory life-cycle.

A virtual factory can build designs of manufactured components (geometric models) and their respective process plans to make it possible for any manufacturing process to be defined, modeled and implemented.

So, this work is being developed within the authors' contribution for the Project VFF -"Holistic, extensible, scalable and standard Virtual Factory Framework", a European collaborative project supported by the European Commission that includes about thirty partners from several European companies, universities and research centers. The project's goal is to define the next generation of Virtual Factory Framework, encouraging the European industry to improve its knowledge in terms of design, management, evaluation and reconfiguration of new or existing facilities. At the same time, it seeks to promote major time and costs savings, supporting the capability to simulate the dynamic complex behavior over the entire life cycle factory interpreted as a complex long living product that synchronize the Virtual Factory with the Real Factory.

VFF Requirement Analysis for Factory Design

The first task to building up a framework that supports virtual factory relies on extensive requirements analysis of the real factory environment model. The present work have identified four main requirements blocks for the entire factory life-cycle characterization: Strategic Planning, Facility Planning, Process Planning and Factory Operation (Figure 5).

On each requirement's blocks there are subsets of requirements which deal with the main functionalities required in the design, management, evaluation and reconfiguration of new or existing facilities. As an example: the building requirements in the Facility Planning block comprises: Economic requirements (operation and maintenance costs; low energy costs, flexibility, operating supply materials, etc.); Sustainability Requirements (emissions, reusability, reutilization, etc.); Location requirements (building plot, logistic connections, accessibilities, etc); Layout requirements (optimal room geometry, utilities integration, modifiable structure configuration, etc.); Technological requirements (technological, changeability, capacity feasibility, ergonomics, etc.); Protection requirements (health and safety norms, supply protection, materials handling, etc.); General requirements (structural integration, optimal infrastructure, architecture, etc).

With this approach, it can be considered that the requirements blocks are iteratively adapted during the factory life-cycle in order to cope with the real changing environment. On each block construction, for each factory instantiation, there are constraints which are propagated to the next block of requirements. In fact, it intends to achieve a "continuous performance improvement" through a reference model finetuning for each cycle of iteration.

Conclusions and Further Work

This paper addresses the problem of factory planning during the entire factory lifecycle through a holistic, extensible, scalable and standardized virtual factory framework. It presents also some of the available methodologies for factory planning and how it can be integrated with the paradigm of product life-cycle.

The challenge of factory design derives from the interdependence between the factory planning, process planning and product development. Since this is a complex task with implications in a large number of functions and stakeholders, as well as time constraints, there is a need for a support framework. This need impelled a new area of research, with the involvement of academic and industry partners, aiming to develop a new generation virtual factory framework that will meet the challenges of integration, flexibility and sustainability of designing the next generation factories.

Finally, this paper addressed the requirements conceptual model within the Virtual Factory Framework project by presenting a set of requirements obtained in a short example.

The ongoing VFF project aims to provide the industrial managers with a more powerful toolset to support the decision making during the entire factory life-cycle. Any future work foreseen in this project involves development and implementation of the VFF framework with factories templates on several industrial scenarios.

Fig. 1 .

 1 Fig. 1. Interdependence between product, production process and factory plant.

Fig. 5 .

 5 Fig. 5. VFF main requirements blocks


Paulo Santos
email: pjsantos@ualg.pt

Paulo Felisberto

Sérgio M Jesus
email: sjesus@ualg.pt

Vector Sensor Arrays in Underwater Acoustic Applications

Keywords: Vector sensor array, Direction of arrival estimation, Bottom properties estimation

Traditionally, ocean acoustic signals have been acquired using hydrophones, which measure the pressure field and are typically omnidirectional. A vector sensor measures both the acoustic pressure and the three components of particle velocity. Assembled into an array, a vector sensor array (VSA) improves spatial filtering capabilities when compared with arrays of same length and same number of hydrophones. The objective of this work is to show the advantage of the use of vector sensors in underwater acoustic applications such as direction of arrival (DOA) estimation and geoacoustic inversion. Beyond the improvements in DOA estimation, it will be shown the advantages of using the VSA in bottom parameters estimation. Additionally, is tested the possibility of using high frequency signals (say 8-14 kHz band), acquired during the MakaiEx 2005, to allow a small aperture array, reducing the cost of actual sub-bottom profilers and providing a compact and easy-to-deploy system.

Introduction

Acoustic vector sensors measure both the acoustic pressure and the three components of particle velocity. Thus a single device has spatial filtering capabilities not available with pressure hydrophone. A Vector Sensor array (VSA) has the ability to provide information in both vertical and azimuthal directions allowing for a high directivity not possible with arrays of traditional hydrophone with same length and the same number of sensors. These characteristics have been explored during the last decade but most of the studies are related to direction of arrival (DOA) estimation. However, due to the VSA ability to provide directional information, this device can be used with advantage in other applications such as geoacoustic inversion. In this work it is shown that a reliable estimation of ocean bottom parameters can be obtained using a small aperture VSA and high-frequency signals.

This paper is organized as follows: in Section 2 is made a description of the contribution of this work to technological innovation. The state of the art and the related literature is presented in Section 3. Section 4 describes the vector sensor measurement model and the theory related to the Bartlett estimator based on particle velocity for generic parameter estimation, enhancing the advantages of the VSA. In Section 5, the discussion of the results is made, showing that the VSA remarkably reduces the ambiguities presents in DOA estimation obtained with a hydrophone array and provide information both in vertical and azimuthal direction. Also, it is shown that VSA improves the resolution of bottom parameters estimation, such as sediment compressional speed, density and compressional attenuation based in matched-field inversion (MFI) techniques. The data herein considered was acquired by a four element vertical VSA in the 8-14 kHz band, during the Makai experiment 2005 sea trial, off Kauai I., Hawaii (USA) [START_REF] Porter | The Makai experiment: High-frequency acoustic[END_REF]. Finally Section 6 concludes this work.

Contribution to Technological Innovation

Vector sensors are long time used in underwater acoustic surveillance systems, mainly for DOA estimation. Only from the last decade the interest in VSA rose exponentially, influenced by electromagnetic vector sensor applications and developments in sensor technology that allowed building compact arrays for acoustic applications in the air. It is expected that in a near future will be also commercially available vector sensor devices well suited to develop compact underwater VSA at a reasonable costs. Beyond DOA estimation, it is likely that these new compact systems can be used with advantage over traditional hydrophone arrays in other underwater application fields, thanks to inherent spatial filtering capabilities of vector sensors. The advantage of use a VSA in DOA estimation is considered in this work to show the enhanced spatial filtering capabilities of a short aperture (4 elements) VSA. However, the main contribution is on using the short aperture VSA to improve inversion problems found in underwater acoustics, in particular geoacoustic inversion. The proposed geoacoustic inversion method based on MFI techniques shows the advantage of including particle velocity information that contributes to a better resolution of the estimated parameters, some of them with difficult estimation with traditional hydrophone arrays, even with larger aperture arrays. These methods were tested with field data acquired during Makai Ex 2005 [START_REF] Porter | The Makai experiment: High-frequency acoustic[END_REF], where probe signals in the 8-14 kHz band were used. The bottom estimates obtained are in line with the bottom characteristics known for the area. The band of the probe signal used is well above the band traditionally used in geoacoustic inversion (bellow 1 kHz), thus a systems based on a few elements VSA operating at such frequency band can be very compact, easyto-deploy or to install in a light mobile platform like AUV, becoming a good alternative to actual profilers.

State of the Art

During the last decade, several authors have been conducting research on vector sensors processing, most of them theoretical works, suggesting that this type of device has advantage in DOA estimation and giving rise to an improved resolution. Nehorai and Paldi [START_REF] Nehorai | Acoustic vector-sensor array processing[END_REF] developed an analytical model, initially for electromagnetic sources extending then to the acoustic case, to compare the DOA estimation performance of a VSA to that of an array that measures only scalar acoustic pressure. At the beginning of 2000's, Cray and Nuttall [START_REF] Cray | Directivity factors for linear arrays of velocity sensors[END_REF], performed comparisons of directivity gains of VSA to conventional pressure arrays. Source bearing estimation was explored in [START_REF] Santos | Source localization with vector sensor array during Makai experiment[END_REF], where the plane wave beamformer was applied to real data acquired by a four element VSA in the 8-14 kHz band, during Makai Experiment 2005, off Kauai I., Hawaii (USA). Increased spatial filtering capabilities gave rise to new applications where the VSA could be used with advantage over hydrophone arrays. Due to these characteristics the VSA is appearing in different fields like port and waterway security [START_REF] Shipps | The use of vector sensors for underwater port and waterway security[END_REF], underwater communications [START_REF] Abdi | A new vector sensor receiver for underwater acoustic communication[END_REF], underwater acoustic tomography and geoacoustic inversion [START_REF] Peng | Geoacoustic inversion based on a vector hydrophone array[END_REF][START_REF] Lindwall | Marine seismic surveys with vector acoustic sensors[END_REF]. The bottom parameter estimation results [START_REF] Santos | Estimating bottom properties with a vector sensor array during MakaiEx[END_REF][START_REF] Santos | Geoacoustic Matched-field inversion using a vertical vector sensor array[END_REF] using high-frequency signals acquired by the VSA during the Makai Ex 2005 are of considerable interest due to their uniqueness in this research area. Recently, some theoretical works [START_REF] Miron | Quaternion-MUSIC for vector sensor array processing[END_REF][START_REF] Wang | Hypercomplex model of acoustic vector sensor array with its application for the high resolution two dimensional direction of arrival estimation[END_REF] were published using quaternion based algorithms in order to more effectively process VSA data. These works are concerned to DOA estimation but in [START_REF] Santos | Geoacoustic Matched-field inversion using a vertical vector sensor array[END_REF] it was suggested that quaternion based algorithms can be used with advantage also in geoacoustic inversions.

The Measurement Model

Particle Velocity Model Formulation

Solving inversion problems by MFI techniques, a propagation model to generate field replicas is required. Herein a ray tracing model -TRACE [START_REF] Rodríguez | The TRACE and TRACEO ray tracing programs[END_REF] -is considered to generate the particle velocity components, beyond the acoustic pressure.

Using the analytical approximation of the ray pressure [START_REF] Rodríguez | The TRACE and TRACEO ray tracing programs[END_REF], the particle velocity ) ( 0 Θ v for a generic set of environmental parameters ( 0 Θ ) can be written as [START_REF] Santos | Geoacoustic Inversion with a vector sensor array[END_REF]:

p ) ( ) ( 0 0 Θ = Θ u v , (1)
where the vector u is a unit vector related to the pressure gradient. The environmental parameter depends on the characteristics of the acoustic channel, including ocean bottom parameters.

Data Model

Assuming that the propagation channel is a linear time-invariant system, p is the pressure and v x , v y and v z are the three particle velocity components, a narrowband signal at frequency ω (omitting the frequency dependency in the following formulas) due to a source signal s, for a particular set of channel parameters 0 Θ , measured with an array of L vector sensors, can be written, for acoustic pressure as:

T pL p p y y )] ( ),..., ( [ ) ( 0 0 1 0 Θ Θ = Θ y , (2)
where ) ( 0 Θ pl y is the acoustic pressure at th l vector sensor. The linear data model for the acoustic pressure is:

p p p s n h y + Θ = Θ ) ( ) ( 0 0 , (3)
where

) ( 0 Θ p h
is the channel frequency response measured on L pressure sensors and p n is the additive noise. In the following formulation it is assumed that the additive noise is zero mean, white, both in time and space, with variance 2 n σ , uncorrelated between each sensor and uncorrelated with the signal s.

A similar definition has been adapted for the particle velocity:

T zL v z v yL v y v xL v x v v y y y y y y )] ( ),..., ( ), ( ),..., ( ), ( ),..., ( [ ) ( 0 0 1 0 0 1 0 0 1 0 Θ Θ Θ Θ Θ Θ = Θ y (4)
becoming the data model for the particle velocity components, taking in account (1):

v p v s n h u y + Θ ⊗ Θ = Θ ) ( ) ( ) ( 0 0 0 , ( 5
)
where ⊗ is the Kronecker product and v n is additive noise. Taking into account (3) and ( 5), the VSA data model defined for a signal measured on L elements can be written as:

      + Θ ⊗       Θ =       Θ Θ = Θ v p p v p pv s n n h u y y y ) ( ) ( 1 ) ( ) ( ) ( 0 0 0 0 0 . ( 6
)
Data model [START_REF] Abdi | A new vector sensor receiver for underwater acoustic communication[END_REF] expands data model for the particle velocity components with acoustic pressure.

Bartlett Estimator

The classical Bartlett estimator is possibly the most widely used estimator in MFI parameter identification, maximizing the output power for a given input signal [START_REF] Krim | Two decades of array signal processing research[END_REF].

The Bartlett parameter estimate 0 Θ is given as the argument of the maximum of the functional:

{ } ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 0 0 0 Θ Θ Θ = Θ Θ Θ Θ = Θ e R e e y y e H H H B E P ( 7
)
where the replica vector estimator ) ( ˆΘ e is determined as the vector ) (Θ e that maximizes the mean quadratic power:

)} ( ) ( ) ( { max arg ) ( ˆ0 Θ Θ Θ = Θ e R e e e H , (8)
where H represents the complex transposition conjugation operator, {} .

E denotes statistical expectation and

{ } ) ( ) ( 0 0 Θ Θ H E y y is the correlation matrix ) ( 0 Θ R
. The maximization problem is well described in [START_REF] Krim | Two decades of array signal processing research[END_REF], thus the Bartlett estimator when only pressure sensors are considered, can be written as:

= Θ) ( , p B P ) ( ) ( ) ( ) ( ) ( 0 Θ Θ Θ Θ Θ p H p p p H p h h h R h . ( 9
)
Appling the above formulation to the data model ( 5), it was shown in [START_REF] Santos | Geoacoustic Inversion with a vector sensor array[END_REF] that an estimator for particle velocity outputs is:

[ ] [ ] ) ( ) cos( ) ( ) ( ) ( ) ( ) ( ) ( , 2 , 2 0 , Θ ∆ ∝ Θ Θ Θ Θ Θ = Θ p B p B H H v B P P P θ u u u u . ( 10
)
where θ ∆ is the angle between the vector ) (Θ u from the replica and the vector ) ( 0 Θ u from the data. Based on this equation, one can conclude that the particle velocity Bartlett estimator response is proportional to the pressure Bartlett estimator response by a directivity factor (gave by the inner product

) ( ) ( 0 Θ Θ u u H
), which could provide an improved side lobe reduction or even suppression when compared with the pressure response.

For the data model ( 6), the VSA Bartlett estimator is given by [START_REF] Santos | Geoacoustic Inversion with a vector sensor array[END_REF]:

[ ] ( )
) ( 2 cos 2 ) ( ) cos( 1 ) ( , 2 , 2 , Θ       ∆ ∝ Θ ∆ + ∝ Θ p B p B v B P P P θ θ . ( 11
)
One can conclude that when the acoustic pressure is included a wider main lobe is obtained [START_REF] Miron | Quaternion-MUSIC for vector sensor array processing[END_REF], compared to the estimator with only particle velocity components [START_REF] Santos | Geoacoustic Matched-field inversion using a vertical vector sensor array[END_REF]. However, including the pressure on the estimator, can lead to reduce ambiguities when frequencies higher then the working frequency of the array are used.

Discussion of Results

DOA Estimation

One of the Bartlett estimator applications is the conventional beamformer for DOA estimation. The plane wave beamformer is applied to compare the performance of the VSA versus hydrophone arrays. In the case of plane wave DOA estimation, the search parameter Θ is the direction ) , ( S S φ θ and the replica vector is simple a combination of weights, which are direction cosines as weights for the particle velocity components and a unit weight for the pressure and is given by [START_REF] Santos | Source localization with vector sensor array during Makai experiment[END_REF]:

[ ] ) . exp( cos , sin sin , sin cos , 1 ) , ( r k i S T S S S S S S S r r ⊗ = φ φ θ φ θ φ θ e , ( 12
)
where r r is the position vector of the VSA elements (in this work the VSA used has four elements equally spaced with 10cm and located in the z-axis being the first one at the origin of the Cartesian coordinates system), S k r is the wavenumber vector corresponding to the chosen steered, or look direction ) , ( Fig. 2 presents the simulation results obtained for the working frequency of the array, 7500Hz, and for a DOA of (45º, 30º). Fig. 2 (a) shows that when the acoustic pressure sensors are considered [START_REF] Santos | Estimating bottom properties with a vector sensor array during MakaiEx[END_REF], only the elevation angle is obtained due to omnidirectionality of the sensors. On the other hand, Fig. 2 (b) shows that when the particle velocity components are introduced, the DOA is perfectly resolved due to the directivity factor obtained with the inner product in [START_REF] Santos | Geoacoustic Matched-field inversion using a vertical vector sensor array[END_REF]. Finally, when acoustic pressure is included, a wider main lobe is obtained, Fig. 2 (c), however the ambiguities are eliminated. This can be observed even when frequencies higher then the working frequency of the array are used. The main advantage of the VSA in the DOA estimation is that it resolves both vertical and azimuthal direction when compared with traditional hydrophones arrays. The results of the real data DOA estimation can be seen in [START_REF] Santos | Source localization with vector sensor array during Makai experiment[END_REF].

Bottom Parameters Estimation

The ocean bottom parameters estimation is another subject where the VSA can be used with advantage. Fig. 3 shows the sediment compressional speed estimation obtained with pressure data only (a), particle velocity only (b) and both pressure and particle velocity (c). The estimation results for density and compressional attenuation can be found in [START_REF] Santos | Geoacoustic Matched-field inversion using a vertical vector sensor array[END_REF]. The ambiguity surfaces illustrated in Fig. 3 were obtained for the maximum values of estimator functions during almost 2 hours of data acquisition, showing the stability of the results. Fig. 3 (a) shows a wider main lobe obtained when only pressure data is considered [START_REF] Santos | Estimating bottom properties with a vector sensor array during MakaiEx[END_REF], with poor resolution of the parameter estimation. Fig. 3 (b) and(c) were obtained considering the VSA Bartlett estimators [START_REF] Santos | Geoacoustic Matched-field inversion using a vertical vector sensor array[END_REF] and [START_REF] Miron | Quaternion-MUSIC for vector sensor array processing[END_REF], respectively without and with pressure. Comparing plots (b) and (c) clearly show that the estimate of sediment compressional speed is 1575 ± 5 m/s, but when the estimate function without pressure is considered, a narrower main lobe appears as well as some ambiguities, like in DOA estimation. The results obtained with the function that included all the vector sensor components are stable during the period of acquisition and show an increased resolution of the bottom parameters estimation, not possible with hydrophone arrays of same number of sensors.

Conclusion

This work shows the advantage of using a VSA for DOA and bottom parameters estimation. It was seen that the VSA reduces ambiguities in DOA estimation, when compared with hydrophone arrays, providing information in both vertical and azimuthal directions. Also, the VSA improves the resolution of the bottom parameters estimation allowing to access parameters, usually with difficult estimation using traditional hydrophone arrays.

One can remark that reliable estimates are obtained even with a small aperture array (4 elements only) and high frequency signals (say 8-14 kHz band). Thus the usage of VSA with high-frequencies can provide an alternative for a compact and easy-to-deploy system in various underwater acoustical applications.

  Fig. 1.

Fig. 1 .

 1 Fig. 1. The array coordinates and the geometry of acoustic plane wave propagation, with azimuth S θ and elevation S φ angles.

Fig. 2 .

 2 Fig. 2. DOA estimation simulation results at frequency 7500Hz with azimuth 45º and elevation 30º for Bartlett beamformer considering: only pressure sensors response (a), only particle velocity components response (b) and all elements of the VSA (p + v) (c).

Fig. 3 .

 3 Fig. 3. Real data ambiguity surfaces for sediment compressional speed during the period of acquisition considering: pressure only (a), particle velocity only (b) and both pressure and particle velocity (c).

Acknowledgments. The authors would like to thank Michael Porter, chief scientist for the Makai Experiment, Jerry Tarasek at Naval Surface Weapons Center for the use of the vector sensor array used in this work. The authors also thank Bruce Abraham at Applied Physical Sciences for providing assistance with the data acquisition and the team at HLS Research for their help with the data used in this analysis. This work was supported by project the FCT (ISR/IST plurianual funding U101/13) through the PIDDAC Program funds.


Rui Antunes
email: rui.mantunes@fct.unl.pt

Fernando V Coito

Hermínio Duarte-Ramos

Using Human Dynamics to Improve Operator Performance

Keywords: Human Dynamics, Man-Machine Interfaces, Human-in-the-Loop Control, Manual Tracking Systems

Traditionally Man-Machine Interfaces (MMI) are concerned with the ergonomic aspects of the operation, often disregarding other aspects on how humans learn and use machines. The explicit use of the operator dynamics characterization for the definition of the Human-in-the-Loop control system may allow an improved performance for manual control systems. The proposed human model depends on the activity to be performed and the mechanical Man-Machine Interface. As a first approach for model development, a number of 1-D manual tracking experiments were evaluated, using an analog Joystick. A simple linear human model was obtained and used to design an improved closed-loop control structure. This paper describes practical aspects of an ongoing PhD work on cognitive control in Human-Machine systems.

Introduction

Our life is enhanced by mechatronics products, comprising Man-Machine Interfaces. However, ordinary machines are not usually designed to assist human to improve one's skill, and in many cases much time and effort are needed for an operator to be trained. One of the main reasons is because machines usually don't change regardless of the human skill, often requiring a long operator training stage.

An important goal is to create and develop intelligent mechatronics systems, capable of adapting themselves to the level of the skill/dexterity of the operators who use them, considering not only the ergonomic aspects of the operation, but also the way humans learn and use machines 1 . This brings along a new concept for manual control engineering on Human-Machine systems that inevitably have to consider human in the closed-loop. Recent demands in many areas, for more precision, accuracy and safety (such as in medicine, biotechnology, robotics, transports, entertainment, space, nanotechnology, ocean, disaster site and factory), led to a new need for the development of HAM systems [START_REF] Harashima | Human Adaptive Mechatronics -Interaction and Intelligence[END_REF].

Contribution to Technological Innovation

The purpose of this paper is to present a contribution on human operator modeling for control applications purposes. The inclusion of the operator model on the development of Man-Machine interface devices leads to improved performance on manually controlled operations, as well as easier operation and a reduced training stage.

As a first approach for model development nonparametric system models are used. The models may be obtained from frequency, transient and spectral analysis. The scope of this document is centered on frequency analysis, which proved to be adequate for the development of operator models that, in spite of their simplicity, lead to a good performance. In the sequel, the modeling procedure will de described. The other approaches have also been evaluated but fall beyond the scope of this paper.

A real-time simulation experiment was developed for evaluating skill on predefined closed-loop Human-Machine systems, as a special tool to measure the overall performance. An effort performance measure is also proposed, based on human lazy strategies.

State-of-the-Art / Related Literature

It is a key idea that we need to model human behavior, and, so far, many models of the human controller have been proposed.

In 1940's Tustin tried to introduce a human control model using a transfer function to model human action, proposing a linear servo control. In the 1960's Ragazzini modeled a human as a PID controller and showed that humans are time-variant systems having randomness, stating also that the differences among individuals should be addressed. In 1970 Kleinman et al. studied the dynamics of pilots. The transfer function of a pilot was considered as the cascade of the reaction lags/delays attributed to the neuromuscular human system. A method to compensate the timedelay, using a Smith predictor, was described. Anil proposed in 1976 that the human controller could be described both as time-delay and a Kalman filter.

Kawato introduced later in the 1990's the feedback error learning model, which assumes that human has inverse and forward models of the dynamics of the movements, and that the brain, by learning, tends to change human's model from feedback to feedforward. More recently, Wolpert and Kawato improved the feedback error learning model to a module selection and identification control (MOSAIC), by expanding the inverse model into a controller and the forward model into a predictor.

HAM research [START_REF] Suzuki | Human skill elucidation based on gaze analysis for dynamic manipulation[END_REF], [START_REF] Suzuki | Skill analysis of human in machine operation[END_REF] is being promoted now in some countries, mainly at Japan and UK. Latest developments include studying the brain activity at particular Brodmann's areas using near-infrared spectroscopy [START_REF] Suzuki | Brain monitoring analysis of skill on voluntary motion[END_REF], and the manipulation of human behavior by distorted dynamics vision [START_REF] Kobayashi | Manipulation of Human Behavior by Distorted Dynamics Vision[END_REF].

Research Contribution and Innovation

Several methodologies can be carried out to obtain an LTI model. In this work, special focus is given on improved frequency analysis [START_REF] Söderström | System Identification[END_REF], for obtaining Human-Machine linear models from 1-D manual tracking experiences. However, two major points must be stressed over human operator modeling:

1) The operator behavior can not be fully captured through a simple dynamic model, or even a set of such models. Thus, the objective of the models developed is not to replicate human behavior, but only to capture enough information to compensate the drawbacks inherent to the human operator dynamics.

2) It is difficult, if not impossible, to experimentally obtain an open-loop operator model. In any experiment the operator closes the loop between sensing and acting. Hence, to obtain the operator "true" model it is necessary to extract it from the close loop data.

Frequency Analysis

Consider a one-dimensional input signal, to be tracked, x(t), built from a sum of N sinusoids at pre-defined multiple frequencies. Assume that the one-dimensional input normalized signal has duration T, and y(t) is the correspondent LTI system output. Such signals may be written as:

1 1 ( ) ( ) sin( ) N N k k k k k x t x t a t ω = = = = ∑ ∑ { } max ( ) 1 x t = , ( 0) 0 x t = = . (1) 1 1 ( ) ( ) sin(
)

N N k k k k k k y t y t b t ω ϕ = = = = + ∑ ∑ . ( 2
)
For each applied frequency, the I/O response may be obtained through the following scheme:

ω ϕ ω = + ∫ ( ) sin 2 k k C k b T y T ϕ = .
(3, 4)

0 ( ) sin( )sin k T S k k k k y T b t tdt ω ϕ ω = + ∫ ( ) cos 2 k k S k b T y T ϕ = .
(5, 6)

2 2 2 ( ) ( ) k k C S k b y T y T T = + and ( ) arctan ( ) k k C k S y T y T ϕ         = . (7, 8)
which corresponds to the operator closed-loop frequency response.

For each multiple input frequency, a corresponding magnitude was settled to build a human feasible manual tracking input signal. Figure 2 shows the magnitude Bode plot of the input signal x(t) created for the manual tracking experiments (made with a commercial Joystick).

Modeling Human Behavior

One hundred tracking time-trials, with T=120 seconds duration each, were obtained for the same participant with no history of neurological deficits. At least, a minimum 10 minute rest was given between trials, that all, lasted for 3 weeks. A sample of a trial for the input ( ) x t is presented below, in figure 4: One hundred open-loop linear models for the same individual were obtained, from the closed-loop time-trials, by inverse manipulation. The ±2σ limits were calculated (assuming a normal unimodal symmetrical distribution, approx. 95 of the models fits inside).

Controller Design Strategy

Three controllers are proposed to control an unstable P(s) dynamics. The first (C1) is a classical phase-shift compensator. The second (C2) considers human as a static gain only, and the third controller (C3) is obtained from the human model:

+ + + + = + + + + = . ( 12
)
Where H1(s) presents the same frequency behavior as (9), but includes an additional term (with unity static gain), in order to allow the implementation of C3(s). Manual step performance was measured on a double-integrator P(s) unstable process, considering the reference mean square error, for acuity, and the mean stabilized duration (related with human's lazy strategies, within ±0.0035 from input reference). From figures 7 and 8, C3 controller clearly took the best performance.

The simulation results from table 1 show that the C3 controller (obtained from the proposed linear human model and C1) widens the bandwidth of the Human-Machine system and raises the overall phase angle curve, improving the frequency response and the stability margins. C2 controller, assuming human model as a simple static gain (ko) gives also higher stability than C1 (which neglects H(s) in the closed-loop).

Conclusions and Further Work

In this paper, some HAM research topics that take human factor into account were introduced for the control of Man-Machine systems. To prove the effectiveness of the proposed modeling method, a 1-D Human-Machine experimental SISO system was implemented and tested. Further work is to improve the controller robustness and to develop multi-model design strategies, and also to move on to 2-D systems.

Fig. 1 .

 1 Fig. 1. Frequency analysis block diagram for each k-multiple frequency.

Fig. 2 .

 2 Fig. 2. Input signal magnitude based on the N=30 frequencies sum, ranging 0.0083Hz to 10Hz.

Fig. 3 .

 3 Fig. 3. LabVIEW developed application for the manual tracking experiences (left). Manual tracking time-trial using Logitech's Extreme 3D Pro. 8-bit analog Joystick (right).

Fig. 4 .

 4 Fig. 4. A 1-D manual tracking sample (first 20 seconds) at 100Hz sampling rate. The input signal is null at 0 and at 120 seconds (t=0, T).

Fig. 5 .

 5 Fig. 5. Proposed human model open-loop magnitude Bode plot, ranging between 0.02Hz and 7Hz, based on 100 1-D manual tracking experiments.

Fig. 6 .

 6 Fig.6. Block diagram for the closed-loop physical system to be controlled.

5Fig. 7 .

 7 Fig. 7. Human step response for two closed-loop control systems (without controller, and with C3 developed controller), with P(s) dynamics, at 300Hz sample rate. Input reference is 0.3925.

Fig. 8 .

 8 Fig. 8. Detailed human step response for two closed-loop control systems (with C1 and C2 controllers), with P(s) dynamics, at 300Hz sample rate. Input reference is 0.3925.

Table 1 .

 1 Step response manual performance (in 60 seconds) and stability margins, for P(s).

	Performance:	Controller C1	Controller C2	Controller C3
	Mean square error	0.0045634	0.0091764	0.0016567
	Mean stabilized duration (s)	1.5382	1.5542	5.5260
	Number of stabilized sequences 24	20	5
	Stability:	Controller C1	Controller C2	Controller C3
	Gain Margin Frequency (Hz)	1.0618	1.0618	4.6104
	Gain Margin (dB)	40.5313	50.1712	52.1004
	Phase Margin Frequency (Hz)	0.0494	0.0202	0.0202
	Phase Margin (°)	58.2328	45.9675	51.4105

A Human-Machine mechatronics system that has the function to assist the human operator is usually called Human Adaptive Mechatronics (HAM).