Tele-Operation of a Mobile Robot Through Haptic Feedback

Transcription

1 HAVE 00 IEEE Int. Workshop on Haptic Virtual Environents and Their Applications Ottawa, Ontario, Canada, 7-8 Noveber 00 Tele-Operation of a Mobile Robot Through Haptic Feedback Nicola Diolaiti, Claudio Melchiorri DEIS - Dept. of Electronics, Coputer Science and Systes University of Bologna - Italy Eail: {ndiolaiti, celchiorri}@deis.unibo.it Abstract Teleoperation systes have been developed in order to allow a huan operator to perfor coplex tasks in reote environents. Mobile robots can be considered as a particular exaple of teleanipulation systes, since they can be operated reotely to perfor particular tasks. As an exaple, the inspection of underwater structures and the reoval of ines are perfored by obile platfors controlled by a reote operator, which generally takes advantage only of the visual feedback provided by vision systes. In this sense, the nature and copleteness of the data provided to the operator about the state of the reote syste are of crucial iportance for proper task execution, and it is generally accepted that a ore efficient achieveent of the task can be obtained by increasing the nuber of data feedback and by using proper MMI. In this paper, the use of a haptic interface is proposed in order to increase the user s perception of the workspace of the obile robot. In particular, a virtual interaction force is coputed on the basis of obstacles surrounding the obile vehicle in order to prevent dangerous contacts, so that navigation tasks can be carried out with generally better perforances. In addition, passivity of the overall syste is taken into account, so that stability of the virtual interaction is guaranteed. I. INTRODUCTION Teleoperated obile robots are widely used in order to carry out coplex tasks in hazardous environents: well known exaples are e.g. the inspection of underwater structures [], deining operations [], or cleaning nuclear plants [3]. In this type of apparatus, often the reote operator can take advantage only of visual inforation about the environent and in the ajority of the cases they are not sufficient to carry out coplex tasks because of the liited visual fields of caeras. Therefore, besides the possibility of errors and failure of the task, reote teleoperations turn out to be tiring activities requiring a specific training to the huan operator. In [4] it is discussed how ore sophisticated an-achine interfaces can iprove the perforances of the overall syste by augenting the nuber and quality of data feedback fro the reote environent. In particular, a noticeable reduction of operator s stress and of task errors can be achieved by eans of a haptic device that allow the operator to perceive forces related to obstacles surrounding the obile robot. Another application of this concept can be found in [5], where a force sensor is ounted on a obile vehicle in order to easure the contact force with objects that have to be shifted fro a place to another. By eans of a suitable MMI, the user can perceive the easured force and therefore he can detect is the object is blocked by an obstacle. In [6], the distance fro obstacles, easured by a laser scanner ounted on a obile robot, is used to copute a repulsive force that is rendered to the huan operator by eans of a haptic interface. The haptic device is also used to control the robot otion. In addition, authors present soe experiental results, confiring that the augented perception of the environent surrounding the vehicle reduces the nuber of collisions with obstacles. In this paper, the proble of safely controlling a reote obile platfor is addressed. Several iportant aspects are considered: the nonholonoic constraint of the obile robot, the need to detect by eans of low-cost sensors the presence of obstacles, the stability of the overall syste, the possible presence of counication tie delays. For these reasons, passivity is considered a fundaental aspect in the proposed control strategy. In particular, an IPC (Intrinsically Passive Control) schee is introduced in order to provide passivity also during interaction with unknown environents [7], [8]. The structure of this paper is the following. In Sec. II the teleoperation syste is briefly described and soe details on the ap-building algorith are illustrated. In Sec. III the obile vehicle is odelled as a virtual ass subject to forces exerted by the operator and by the environent. These interaction forces are described in details in Sec. IV, where also a odel of the coplete syste is discussed. Siulations and initial experiental tests are presented in Sec. V, while Sec. VI concludes with final rearks. II. OVERVIEW OF THE SYSTEM The teleoperation syste considered in this paper is scheatically illustrated in Fig.. Data acquired by proper

2 LAN Haptic interface Haptic control loop Map-Building and Robot Control Mobile robot Fig.. Overview of the teleoperation syste: the virtual interaction force coputed on the basis of the local ap is sent to the haptic interface, whose position is used to copute otion coands sent to the obile platfor. sensors (i.e. sonars) ounted on a Pioneer obile robot are processed in order to build a local ap of the surrounding obstacles. On the basis of this ap and of the kineatic status of the vehicle, a virtual interaction force F e, eulating a physical contact by eans of a virtual (repulsive) spring K e and a virtual daper b e, is coputed as shown in Fig.. The PSfrag replaceents Fig.. Virtual Interaction Force Mobile Robot F e K e b e obstacle Virtual interaction with obstacles. virtual interaction force is sent, by eans of a local network using the UDP protocol, to a PHANToM haptic interface in order to render to the operator the feeling that the vehicle is close to an obstacle. Conversely, the huan operator, by eans of the haptic device, generates velocity set-points that are transitted to the obile robot controller. A. Map-building algorith Inforation about the environent surrounding the obile robot is acquired by eans of 6 ultrasonic sensors ounted on the Pioneer platfor. These sensors, even if widely used in obile robotics, are affected by several drawbacks. Indeed, the easure of the position of an obstacle is obtained with a poor angular resolution (i.e. about 5 degrees) and ultiple reflections of the acoustic wave can occur so that a distance greater than the real one is easured by the sensor. Moreover, the speed of sound liits the axiu sapling rate to about 50 s. According to these considerations, data provided by each sensor are filtered and then fused into a ap of the environent surrounding the vehicle. In particular, the ap is represented by a grid of cells, that can be either epty or occupied by an obstacle. In order to represent the occupancy status of each cell, an algorith based on the Transferable Belief Model [9] has been adopted because it is faster than standard probabilistic ethods in detecting changes in the environent. A vector s of basic belief asses is associated to each cell of the grid: s := [s, s O, s F, s U ] T () where s O and s F quantify, respectively, the belief that the cell is occupied or free, while s U quantifies the belief that the cell is unknown, and quantifies the lack of ore detailed inforation. Finally, s represents the aount of contradictory inforation accuulated fro sonars; indeed, when e.g. a previously occupied cell becoes free, a great aount of contradiction is generated by the cobination of the previously accuulated inforation with new easures coing fro sensors, and this fact can be used to quickly detect changes in the environent [0]. Note that the su of the eleents of the status vector has to be. Initially, all cells are unknown and their status is: s(0) := [0, 0, 0, ] T Whenever new easures are available fro sonars, they are filtered in order to reduce the influence of the poor angular resolution and of ultiple reflections and then they are fused into the gridap by eans of the Depster s rule of cobination [9]. By eans of the so called pignistic transforation it is possible to copute the occupancy probability p O of the cell: p O = ( s O + s ) U () s Finally, only cells whose occupancy probability is greater than a fixed threshold value are considered occupied and generate a virtual interaction force on the obile robot. III. CONTROL STRATEGY The Pioneer obile platfor used in this paper belongs to the class of two-wheeled robots, because it has two actuated wheels whose velocity difference generates the steering otion. A third wheel, called castor, is not actuated and is used to provide stability to the vehicle. Therefore, the kineatic odel is expressed by: ẋ v ẏ v θ v = cos θ v 0 sin θ v 0 0 [ v(t) ω(t) where [x v, y v, θ v ] T represents the position and the orientation of the vehicle with respect to a fixed reference frae, ] (3)

3 LAN F ok Interaction with operator F o F E Virtual Interaction F E Map Building Haptic Interface ẋ o Virtual Mass PSfrag replaceents ẋ Conversion of velocities [v d, ω d] T Sonars Controller Mobile Robot Fig. 3. and [v(t), ω(t)] T represents the translational and rotational velocities. In the hypothesis that the two actuated wheels are constrained to roll without slip over a horizontal plane, feasible trajectory for the obile robots have to be tangent with its translation axis. Indeed, the constraint of rolling without slipping is nonholonoic and iplies that the translational velocity v(t) of the obile robot is always orthogonal to the axis of the actuated wheels, without reducing the set of possible configurations of the vehicle, which is R [0, π]. In conclusion, the nonholonoic constraint has to be considered when odelling the virtual interaction with the environent, because obstacles located in front of the robot are ore dangerous than the lateral ones. In order to guarantee stability of the overall syste and to consider the nonholonoic constraint of the obile base, a passivity-based approach has been adopted in the design of the overall control strategy. The robot low-level control accepts as input a velocity vector [v d (t), ω d (t)] T, representing the translational and rotational velocity to be actuated by the robot. In the proposed control schee, this velocity vector is coputed considering the planar velocity ẋ of a virtual ass subject to two forces: the interaction force F o exerted by the huan operator, and the virtual force F E coputed on the basis of the distance of the robot fro the environent (see Fig. 3). In this anner, a holonoic otion of the virtual ass in a horizontal plane is defined. In a second step, the ass velocity ẋ is converted into the vector [v d (t), ω d (t)] T that is sent to the robot low-level controller. Let ẋ = [ẋ, ẏ] T be the velocity of the ass expressed with respect to a fixed reference frae, then its coponent v t, along the translation axis of the robot, and the orthogonal coponent v r, see Fig. 4, are expressed by: [ ] [ ] [ ] vt cos θv sin θ = v ẋ (4) v r sin θ v cos θ v ẏ As shown in Fig. 4, v t can be interpreted as a translation coand, while v r can be interpreted as a request of rotation in order to align the robot with the vector ẋ. Therefore, velocity set-points are obtained as: { vd (t) = K t v t (t) (5) ω d (t) = K r v r (t) Assuing that the syste is passive with respect to the virtual ass, if the interconnection between the virtual ass Virtual ass Real robot Schee of the proposed control strategy ( ω d ) ( v d ) ẋ v r (M, J) Fig. 4. Conversion of the ass velocity ẋ to obile robot velocity set-points [v d (t), ω d (t)] T and the obile robot is passive, i.e. it cannot generate energy, it can be easily concluded [] that the overall syste is passive and therefore stable. Therefore, the stability of the overall syste can be guaranteed if passivity is preserved by (5), that expresses the interconnection between the virtual ass and the real robot. This goal can be achieved if the power supplied to the virtual ass is equal to the power supplied to the obile robot. Therefore, by supposing that the initial velocities both of the robot and of the ass are null, the kinetic energy E r of the robot is equal to the kinetic energy E of the ass : ( vt + ) v r = Mv d + Jω d (6) where M is the ass of the vehicle and J its inertia about the z axis. Equations (5) and (6) lead to the following conditions on the conversion constants: M K t = (7) M K r = J In addition, in order to allow the huan operator to perceive the correct inertia of the robot, the virtual ass is assued equal to the real ass M; this leads to K t = and K r = M/J. ẋ IV. VIRTUAL INTERACTION On the basis of the previous discussion, interaction forces exerted by the environent and the huan operator are assued to be applied onto the virtual ass. In particular, Fig. 5 illustrates the forces applied to the virtual ass when a single obstacle is located near the obile robot: F e is the virtual interaction force generated by the obstacle, F ok is the θ v v t

4 PSfrag replaceents operator x o b K o F ob F ok F e K e obstacle Fig. 5. Model of the interaction between operator, virtual ass and environent force exerted by the huan operator while F ob is a dissipative force used to inject daping into the overall syste. A. Virtual Force Generated by the Environent As described in Sec. II, a repulsive potential is associated to each occupied cell surrounding the obile robot. Let E be the set of all the occupied cells around the obile robot. The virtual force F e, exerted by a single occupied cell e E, is generated by the superposition of an elastic repulsive force F ek and a viscous friction F eb that dissipates energy in order to stabilize the virtual interaction, see Fig. 5. Let x and x e be respectively the position of the virtual ass representing the obile robot and of the occupied cell. The elastic potential energy associated to the cell, shown in Fig. 6, is defined by: V e (x, x e ) = b e K e (r e x x e ), x x e < r e 0 otherwise where K e is the stiffness of the virtual spring and r e has the eaning of axiu distance of influence, so that obstacles located at distances greater than r e fro the robot do not exert any repulsion force and their presence is not perceived by the operator. Fig Elastic potential energy of an occupied cell On the other side, a daping eleent is necessary in order to stabilize the virtual interaction and to take into account the nonholonoic constraint. As entioned in Sec. III, the instantaneous velocity of the obile robot is aligned with its translation axis, so that a larger aount of daping is needed to prevent contact with obstacles located in front of the robot. 0 3 x e (8) This eans that the daping force F eb has to depend on the angular position of the obstacle with respect to the translation axis of the vehicle. According to these considerations, F eb is defined as: ( ) b e x xe r e cosα e ẋ, F eb (x, ẋ, x e )= x x e < r e (9) 0 otherwise where b e is the daping coefficient, odulated by a factor depending on the distance between the robot and the obstacle. Siilarly to what happens for the elastic potential, no influence is exerted by obstacles located at a distance greater than r e and the increase on daping force is a linear function of the distance x x e. In addition, α e represents the angle between the robot translation axis and the occupied cell so that, by eans of the factor cosα e, a larger daping action is exerted by frontal obstacles. In order to copute the total force F E exerted by the environent on the virtual ass, the superposition of forces produced by each cell e E has to be taken into account. First of all it is possible to define a total daping coefficient B E ( B E := b e x x ) e cosα e (0) r e e E that suarizes the dissipation provided by each occupied cell e E. In a siilar way, the total elastic potential energy stored in virtual springs, is represented by: V E := K e V e (x, x e ) () e E In this way, the total force F E exerted by the environent on the virtual ass when x x e < r e is: B. Interaction with the Operator F E = B E ẋ e E V e () The point x o in Fig. 5 represents the desired position of the virtual ass, and hence of the robot. Note that the workspace of the ass (and of the robot) is a plane, and therefore theoretically unliited. On the other hand, the desired position x o is specified by the operator by eans of the haptic interface, whose position x h is obviously liited by the geoetric constraints of the device. Therefore, we consider displaceents of the tip of the interface with respect to an initial configuration as proportional to the desired velocity ẋ o of the virtual ass, (see Fig. 7): ẋ o = K h x h (3) where K h is deterined as the ratio between the axiu velocity of the obile robot and the axiu distance of the haptic device fro the origin of its reference frae. In this way, a displaceent of the haptic interface fro the origin indicates a otion request for the obile robot in that

5 Sfrag replaceents haptic device Fig. 7. x h obile robot ẋ o x o Position of the haptic device and coputation of x o particular direction and the requested velocity is proportional to the size x h of the displaceent. Finally, the force F ok of interaction with the virtual ass, shown in Fig. 5, is coputed as: F ok (x, x o ) = K o (x x o ) (4) where K o is the stiffness of the linear spring. Note that F ok represents the force exerted by the huan operator onto the virtual ass, while F ok is the force perceived by the operator, that renders the environent around the obile robot. Finally, a dead zone around the origin of the reference frae of the haptic device is considered to filter treors of the hand of the user. In addition, it is necessary to inject an adequate daping in order to stabilize the otion of the virtual ass [7]. This is done by eans of the dissipative force F ob exerted by the daper b: F ob (ẋ) = bẋ (5) ) coputation of the force generated by the operator and by daping injection F o = F ok + F ob ; 3) coputation of the holonoic otion of the virtual ass subject to the forces F E and F o (velocity ẋ); 4) transforation of ẋ in [v t, v r ] T ; 5) transforation of [v t, v r ] T in [v d, ω d ] T, in such a way that passivity is preserved; 6) transission of [v d, ω d ] T to the low-level robot controller; 7) rendering of F ok to the operator by eans of the haptic interface. Note that steps ) and 3) are passive (the coputations are ade on the basis of physical passive eleents) and that 5) is also passive, since eq. (6) holds. V. SIMULATIONS AND EXPERIMENTAL RESULTS The applicability of the proposed algorith has been tested at a siulation level and by eans of the experiental setup shown in Fig.. First of all, siulations have been perfored in order to evaluate the behavior of the syste in a free environent and to test the tracking properties with respect to a reference trajectory requested by the operator. Fig. 8 reports C. Model of the Overall Interaction Note that the overall syste is passive because the virtual springs store conservative energy while the virtual dapers provide dissipation and the interconnection (5) does not inject additional energy in the obile robot. Finally, the equation of otion of the virtual ass is: ẍ + (b + B E )ẋ F ok + e E V e = 0 (6) (a) (b) Notice that the position and the velocity of the virtual ass are perfectly known because its otion is coputed inside the control loop by integrating (6). Therefore, there is no need to estiate the position and the velocity of the obile robot in order to calculate the virtual interaction with the environent, except for what concerns angles α e. However, since trajectories followed by the huan operator are necessarily continuous, it is clear that, after an initial transient, the translation axis of the obile robot tends to be aligned with the vector ẋ, so that it is possible to copute α e by considering the instantaneous velocity of the virtual ass. In conclusion, the overall control strategy, illustrated in Fig. 3, can be suarized as follows: ) coputation of the virtual interaction force F E on the basis of the ap obtained fro the sonars; PSfrag replaceents (c) Fig. 8. Circular reference trajectory and rendered force in a free environent (a), in case that an obstacle is on the desired path (b) or near the desired path (c,d). Motion is counter-clockwise. four situations in which the desired otion is circular path to be tracked with constant velocity of 0. /sec. The force F ok rendered to the operator is also shown. Initially, the vehicle is located in the origin with its translation axis horizontal. When the environent is copletely free (a), a sall force is perceived by the huan operator related to the tracking error due to the nonholonoic otion of the obile robot. When an obstacle is located on the reference path, the effect (d)

6 Fig. 9. Obstacle on the desired path, repulsive force at speed of 0.4 /sec (left) and of 0.8 /sec (right). Motion is counter-clockwise. of the repulsive force F e related to the obstacle is illustrated in (b). While the robot is approaching the obstacle, the repulsive force increases so that the operator is induced to deviate fro the initial trajectory in order to avoid contact. Note that the robot turns first to the right and then to the left because of the superposition of the attractive F o force related to path and the, initially weak, repulsive force F e related to obstacle. Fig. 8 (c) and (d) illustrate how the robot is deviated also by obstacles located near the desired path. Paraeters for the siulation are: = 9 Kg, equal to the ass of the Pioneer obile robot, K t =, K r = 9.03 and K o = 900 N/, b = 30 Ns/. The assued distance of influence is r e =. and takes into account the fact that the obile robot has a radius of about 0., while the constants of the virtual interaction are K e = 700 N/, b e = 30 Ns/. Fig. 9, shows that the iniu distance fro the obstacle is reduced if the requested velocity is increased. However, also the daping effect is increased and the contact can be still avoided by the huan operator. Moreover, the experiental setup of Fig. has been used to carry out soe initial experients. At the oent, transission delays are negligible because data are exchanged over a local network. A siple wall-following task in a free roo has been chosen in order to evaluate the iproveent of perforances provided by force feedback. Fig. 0 (left) shows how this task is carried out by taking advantage only of visual inforation provided by the ap built with sonars: diensions of the cells are 4 4 c, free cells are white, while occupied cells are dark and unknown cells are gray; the trajectory followed by the obile robot is drawn as a continuous line. Initially, the robot is located on the botto of the figure and its translation axis is perpendicular to the wall, so it has to steer on the left and then it has to keep constant the distance fro the wall located at its right. Fig. 0 (right) shows how perforances are iproved when force feedback is provided to the operator. Note that a ore regular trajectory also iproves the quality of the ap because sonars are less subject to ultiple reflections. VI. CONCLUSIONS AND FUTURE WORK In this paper, a passivity-based control schee for a obile robot has been presented. In particular, a haptic interface with force feedback has been used for the reote control of Fig. 0. Trajectory of the obile robot in a wall following task, without (left) and with (right) force feedback the obile base. The control is based on the otion of a virtual ass, according to the IPC principle, and passivity is guaranteed also for the obile robot, taking into account also the nonholonoic constraint of the platfor. Initial experients confir the validity of the approach. Future activity will ai at evaluating the syste behavior in ore coplex tasks and also in presence of significant tie delays in the data transission. Acknowledgeents. This work has been supported by the EU research progra Geoplex, n. IST REFERENCES [] Q. Lin and C. Kuo, Virtual tele-operation of underwater robots, in Proceedings of IEEE International Conference on Robotics and Autoation, Albuquerque, NM, USA, 997. [] F. Sith, D. Backan, and S. Jacobsen, Telerobotic anipulator for hazardous environents, in Journ. of Rob. Syst., 99, vol. 9, NO., pp [3] J. P. K. Ki, H. Lee and M. Yang, Robotic containation cleaning syste, in IEEE Conference on Intelligent Robots ans Systes, Lausanne, Switzerland, October 00. [4] T. Fong, F. Conti, S. Grange, and C. Baur, Novel interfaces for reote driving: gesture, haptic and pda, in SPIE Teleanipulator and Telepresence VII, Boston, MA, USA, Noveber 000. [5] H. Roth, K. Schilling, and O. Rosch, Haptic interfaces for reote control of obile robots, in Proceedings of 5th IFAC World Congress, Barcelona, Spain, July 00. [6] G. K. S. Lee, G.S. Sukhate and C. Park, Haptic control of a obile robot: A user study, in IEEE Conference on Intelligent Robots ans Systes, Lausanne, Switzerland, October 00. [7] S. Straigioli, Modeling and IPC Control of Interactive Mechanical Systes: a coordinate free approach. London: LNCIS Springer, 00. [8] C. Melchiorri, S. Straigioli, and S. Andreotti, Using daping injection and passivity in robotics anipulation, in Int. Conf. on Advanced Intelligent Mechatronics, Atlanta, GA, USA, Sept [9] P. Sets, The cobination of evidence in the transferable belief odel, in IEEE Transactions on Pattern Analysis and Machine Intelligence, May 990, vol., NO. 5, pp [0] G. Oriolo, G. Ulivi, and M. Vendittelli, Real-tie ap-building and navigation for autonoous robots in unknown environents, in IEEE Transactions on Systes, Man and Cybernetics, 999, no. Y, pp [] A. van der Schaft, L - Gain and passivity techniques in nonlinear control. London: Springer, 000.