HAPTIC TELE-OPERATION OF A MOBILE ROBOT. Nicola Diolaiti, Claudio Melchiorri

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1 HAPTIC TELE-OPERATION OF A MOBILE ROBOT Nicola Diolaiti, Claudio Melchiorri DEIS-Dept. of Electronics, Computer Science and Systems University of Bologna - Italy {ndiolaiti, cmelchiorri}@deis.unibo.it Abstract: Teleoperation systems have been developed in order to allow a human operator to perform complex tasks in remote environments. Mobile robots can be considered as a particular example of telemanipulation systems, since they can be operated remotely to perform particular tasks. As an example, the inspection of underwater structures and the removal of mines are performed by mobile platforms controlled by a remote operator, which generally takes advantage only of the visual feedback provided by vision systems. In this paper, the use of a haptic interface is proposed in order to increase the user s perception of the workspace of the mobile robot. In particular, a virtual interaction force is computed on the basis of obstacles surrounding the mobile vehicle in order to prevent dangerous contacts. The passivity of the overall system is preserved, so that stability of the virtual interaction is guaranteed. Copyright c 2003 IFAC Keywords: Haptic feedback, mobile robot, passive control, vehicle teleoperation 1. INTRODUCTION Teleoperated mobile robots are widely used in order to carry out complex tasks in hazardous environments: well known examples are e.g. the inspection of underwater structures (Lin and Kuo, 1997), demining operations (Smith et al., 1992), or cleaning nuclear plants (K. Kim and Yang, 2002). Moreover, it is generally expected that this type of apparatus will be used in the next future in more and more applications, such as in space operations. Often, visual information provided to the remote operator are not sufficient because of the limited visual fields of cameras and more generally they do not allow to perceive the interaction between the robot and the surrounding environment. It is generally believed that if more sophisticated interfaces are adopted, by augmenting the number and quality of data feedback from the remote environment, the performances of the overall system could be noticeably increased, with a reduction of operator s stress and of task errors (Fong et al., 2000). Concerning mobile robots, a few researches are known in the literature to design proper control systems including force feedback from the robot to the human operator (Roth et al., 2002; Fong et al., 2000). In (S. Lee and Park, 2002), the distance from obstacles, measured by a laser scanner mounted on a mobile robot, is used to compute a repulsive force that is rendered to the human operator by means of a haptic interface. The haptic device is also used to control the robot motion. In addition, authors present some experimental results, confirming that the augmented perception of the environment surrounding the vehicle reduces the number of collisions with obstacles. In this paper, the problem of safely controlling a remote mobile platform is addressed. Several important aspects are considered: the nonholonomic constraint

2 LAN Haptic interface Haptic control loop Map-Building and Robot Control Mobile robot Fig. 1. Overview of the teleoperation system: the virtual interaction force computed on the basis of the local map is sent to the haptic interface, whose position is used to compute motion commands sent to the mobile platform. of the mobile robot, the stability of the overall system, the possible presence of communication time delays. For these reasons, passivity is considered a fundamental aspect in the proposed control strategy. In particular, an IPC (Intrinsically Passive Control) scheme is introduced in order to provide passivity also during interaction with unknown environments (Stramigioli, 2001; Melchiorri et al., 1999). The structure of this paper is the following. In Sec. 2 the teleoperation system is briefly described, then in Sec. 3 the mobile vehicle is modelled as a virtual mass subject to forces exerted by the operator and by the environment. These interaction forces are described in details in Sec. 4, where also a model of the complete system is discussed. Simulations and initial experimental tests are presented in Sec. 5, while Sec. 6 concludes with final remarks. 2. OVERVIEW OF THE SYSTEM The teleoperation system considered in this paper is schematically illustrated in Fig. 1. Data acquired by proper sensors (i.e. sonars) mounted on a Pioneer mobile robot are processed in order to build a local map of the surrounding obstacles. This map is represented by a grid of cells that can be either empty or occupied by an obstacle. Each occupied cell located near the vehicle exerts a virtual interaction force F e, emulating a physical contact by means of a virtual (repulsive) spring K e and a virtual damper b e, is computed as shown in Fig. 2. Virtual Interaction Force Mobile Robot F e K e b e obstacle Fig. 2. Virtual interaction with obstacles. The user can then perceive if the vehicle is close to an obstacle by means of a PHANToM haptic interface, that renders the total virtual interaction force F E, given by the superposition of forces exerted by each occupied cell. Conversely, position of the haptic device is used to generate velocity set-points that are transmitted to the mobile robot controller. As shown in Fig. 1, PCs controlling the haptic device and the mobile robot are connected by an UDP local network, while a radio link is used to exchange data with the Pioneer robot. In the current implementation, time delays affecting the communication between the two PCs are negligible. 3. MODEL OF THE MOBILE ROBOT The Pioneer mobile platform used in this paper belongs to the class of two-wheeled robots, because it has two actuated wheels whose velocity difference generates the steering motion. A third wheel, called castor, is not actuated and is used to provide stability to the vehicle. Therefore, the kinematic model is expressed by: ẋ v ẏ v θ v = cos θ v 0 sinθ v [ ] v(t) ω(t) (1) where [x v,y v,θ v ] T represents the position and the orientation of the vehicle with respect to a fixed reference frame, and [v(t),ω(t)] T represents the translational and rotational velocities. As well known, the constraint of rolling without slipping is nonholonomic and implies that the translational velocity v(t) of the mobile robot is always orthogonal to the axis of the actuated wheels. Actually, this constraint does not reduce the set of possible configurations of the vehicle, which is R 2 [0,2π], but only the feasible trajectories, that have to be tangent to the motion axis. Therefore, the nonholonomic constraint has to be considered when modelling the virtual interaction with the environment, because obstacles located in front of the robot are more dangerous than the lateral ones. In order to guarantee stability of the overall system and to consider the nonholonomic constraint of the mobile 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

3 Haptic Interface LAN F ok ẋ o Interaction with operator Virtual Mass Control of the interaction F o m F E ẋ Virtual Interaction FE Conversion of velocities Map Building [v d,ω d] T Sonars Controller Mobile Robot Fig. 3. Scheme of the proposed control strategy: forces F E and F o exerted by the environment and the operator are supposed to act on a virtual mass m, whose velocity is converted into set-points [v d (t), ω d (t)] T for the mobile robot. scheme, this velocity vector is computed considering the planar velocity ẋ of a virtual mass m subject to two forces: the interaction force F o exerted by the human operator, and the virtual force F e computed on the basis of the distance of the robot from the environment (see Fig. 3). In this manner, a holonomic motion of the virtual mass m in a horizontal plane is defined. In a second step, the mass 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 mass expressed with respect to a fixed reference frame, then its component v t, along the translation axis of the robot, and the orthogonal component v r, see Fig. 4, are expressed by: [ ] [ ][ ] vt cos θv sinθ = v ẋ (2) v r sin θ v cos θ v ẏ As shown in Fig. 4, v t can be interpreted as a translation command, 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 ẋ v r ẋ v t operator x o b K o F ob F ok m F e K e environment Fig. 5. Model of the interaction between operator, virtual mass and environment 1 2 m( vt 2 + vr 2 ) 1 = 2 Mv2 d Jω2 d (4) where M is the mass of the vehicle and J its inertia about the z axis. Equations (3) and (4) lead to the following conditions on the conversion constants: m K t = M (5) m K r = J In addition, in order to allow the human operator to perceive the correct inertia of the robot, the virtual mass m is assumed equal to the real mass M; this leads to K t = 1 and K r = M/J. b e x e θ v m (M,J) Fig. 4. Conversion of the mass velocity ẋ to mobile robot velocity set-points [v d (t), ω d (t)] T are obtained as: { vd (t) = K t v t (t) ω d (t) = K r v r (t) (3) The virtual mass is a passive system, i.e. it cannot generate energy. Assuming that both the interactions with the operator and the environment are also passive, if the kinetic energy of the mobile robot is not greater than the kinetic energy of the virtual mass, it can be easily concluded (van der Schaft, 2000) that the overall system is passive and therefore stable. Therefore, the stability of the overall system can be guaranteed if passivity is preserved by (3), that expresses the interconnection between the virtual mass and the real robot. This goal can be achieved if the kinetic energy E r of the robot is equal to the kinetic energy E m of the mass m: 4. VIRTUAL INTERACTION On the basis of the previous discussion, interaction forces exerted by the environment and the human operator are assumed to be applied onto the virtual mass m. In particular, Fig. 5 illustrates the forces applied to the virtual mass when a single obstacle is located near the mobile robot: F e is the virtual interaction force generated by the obstacle, F ok is the force exerted by the human operator while F ob is a dissipative force used to inject damping into the overall system. 4.1 Virtual Force Generated by the Environment As described in Sec. 2, a repulsive potential is associated to each occupied cell surrounding the mobile robot. Let E be the set of all the occupied cells around the mobile 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

4 virtual interaction, see Fig. 5. Let x and x e be respectively the position of the virtual mass representing the mobile robot and of the occupied cell. The elastic potential energy associated to the cell is defined by: K e 2 (r e x x e ) 2, V e (x,x e ) = x x e < r e (6) 0 otherwise where K e is the stiffness of the virtual spring and r e has the meaning of maximum distance of influence, so that obstacles located at distances greater than r e from the robot do not exert any repulsion force and their presence is not perceived by the operator. Note that the virtual force F ek is quite different from what is normally used for mobile robot navigation and obstacle avoidance based on artificial potential fields (Khatib, 1986), where an infinite repulsive force is generated when the robot hits an obstacle. In this case, F ek is a linear function of the distance, and its maximum value is K e r e. In this way, when several occupied cells are located around the vehicle, the total elastic force F E is just the sum of the single forces F e. Therefore, the human operator can perceive not only the presence of an obstacle, but also its shape by means of smooth variations of the repulsive elastic force. On the other side, a damping element is necessary in order to stabilize the virtual interaction and to take into account the nonholonomic constraint. As mentioned in Sec. 3, the instantaneous velocity of the mobile robot is aligned with its translation axis, so that a larger amount of damping is needed to prevent contact with obstacles located in front of the robot. This means that the damping 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: ) cos α e ẋ, ( b e 1 x x e r e F eb (x,ẋ,x e )= x x e < r e 0 otherwise (7) where b e is the damping coefficient, modulated by a factor depending on the distance between the robot and the obstacle. Similarly 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 damping 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 means of the factor cos α e, a larger damping action is exerted by frontal obstacles. Notice that in (7) only ẋ, the velocity of the robot with respect to the obstacle, is considered, i.e. ẋ e is assumed to be zero. However, this does not imply that only objects fixed in the environment can be taken into account, since mobile obstacles may be considered by properly changing the occupancy status of the gridmap. In order to compute the total force F E exerted by the environment on the virtual mass, 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 damping coefficient B E ( B E := b e 1 x x ) e cos α e (8) r e e E that summarizes the dissipation provided by each occupied cell e E. In a similar way, the total elastic potential energy stored in virtual springs, is represented by: V E := K e V e (x,x e ) (9) e E In this way, the total force F E exerted by the environment on the virtual mass when x x e < r e is: F E = B E ẋ V e (10) e E 4.2 Interaction with the Human Operator In order to make the virtual mass follow a desired trajectory, the operator exerts a virtual force by means of a spring whose stiffness is K o (see Fig. 5). The elastic force F ok is computed as: F ok (x,x o ) = K o (x x o ) (11) Note that F ok represents the force exerted by the human operator onto the virtual mass m, while F ok is the force perceived by the operator, that renders the environment around the mobile robot. The point x o in Fig. 5 represents the desired position of the virtual mass, and hence of the robot. Note that the workspace of the mass (and of the robot) is a theoretically unlimited horizontal plane. On the other hand, the desired position x o is specified by the operator by means of the haptic interface, whose position x h is obviously limited by the geometric constraints of the device. Therefore, we consider displacements of the tip of the interface with respect to an initial configuration as proportional to the desired velocity ẋ o of the virtual mass, see Fig. 6: ẋ o = K h x h (12) where K h is determined as the ratio between the maximum velocity of the mobile robot and the maximum distance of the haptic device from the origin of its reference frame. In this way, a displacement of the haptic interface from the

5 haptic device mobile robot ẋ o Note that steps 2) and 3) are passive (the computations are made on the basis of physical passive elements) and that 5) is also passive, since eq. (4) holds. x h Fig. 6. Position of the haptic device and computation of ẋ o in the mobile robot reference frame origin indicates a motion request for the mobile robot in that particular direction. Note that ẋ o computed on the basis of (12) can be expressed either with respect to the fixed reference frame or with respect to the reference frame of the mobile robot. this case (illustrated in Fig. 6), the vector ẋ o has to be rotated of θ v because the motion of the virtual mass is expressed with respect to the fixed reference frame. Conversely, a rotation of θ v has to be performed on the vector F ok so that the user is induced to move the haptic device in the correct direction. Finally, it is necessary to inject an adequate damping in order to stabilize the motion of the virtual mass (Stramigioli, 2001). This is done by means of the dissipative force F ob exerted by the damper b: F ob (ẋ) = bẋ (13) x o 5. SIMULATIONS AND EXPERIMENTAL RESULTS The applicability of the proposed algorithm has been tested at a simulation level and by means of the experimental setup shown in Fig. 1. First of all, simulations have been performed in order to evaluate the behavior of the system in a free environment and to test the tracking properties with respect to a reference trajectory requested by the operator. In particular, Fig. 7 shows the case of a circular path in the fixed reference frame in a completely free environment (left) and when and obstacle is present (right). Arrows represent the force F ok perceived by the user, that is proportional to the position error with respect to the circular path. A small force is present also without obstacles because of the nonholonomic motion of the mobile robot. When an obstacle is present, the repulsive force F e increases and deviates the vehicle from the reference trajectory so that a greater force is also rendered to the operator. 4.3 Model of the Overall Interaction The equation of motion of the virtual mass is: mẍ + (b + B E )ẋ F ok + e E V e = 0 (14) Note that the overall system is passive because the virtual springs store conservative energy while the virtual dampers provide dissipation and the interconnection (3) does not inject additional energy in the mobile robot. In conclusion, the overall control strategy can be summarized as follows: 1) computation of the virtual interaction force F E on the basis of the map obtained from the sonars; 2) computation of the force generated by the operator and by damping injection F o = F ok + F ob ; 3) computation of the holonomic motion of the virtual mass m subject to the forces F E and F o (velocity ẋ); 4) transformation of ẋ in [v t,v r ] T ; 5) transformation of [v t,v r ] T in [v d,ω d ] T, in such a way that passivity is preserved; 6) transmission of [v d,ω d ] T to the low-level robot controller; 7) rendering of F ok to the operator by means of the haptic interface. Fig. 7. Path followed by the mobile robot in a free environment (left) and in case that an obstacle is near the desired path (right) when a circular path is followed. Motion is counter-clockwise As discussed in Sect. 4.2, the desired motion can be also specified with respect to the reference frame of the mobile robot. In this manner a constant value x h produces, if there are no obstacles, a uniform circular motion in the fixed reference frame, as shown in Fig. 8 (left). If an obstacle is located near the reference trajectory (right), the path followed in the fixed reference frame is distorted by the repulsive force F e because the operator does not move the haptic device in order to change velocity set-points. These results has been obtained by assuming a virtual mass of 9 Kg, equal to the mass of the Pioneer mobile robot, conversion constants K t = 1, K r = m 1 and K o = 8100 N/m, b = 30 Ns/m. The assumed distance of influence is r e = 1.2 m and takes into account the fact that the mobile robot has a radius

according to the IPC principle, and passivity is guaranteed also for the mobile robot, taking into account also the nonholonomic constraint of the platform.

Future activity will aim at evaluating the system behavior in more complex tasks and also in presence of significant time delays in the data transmission. Fig. 8.

6 according to the IPC principle, and passivity is guaranteed also for the mobile robot, taking into account also the nonholonomic constraint of the platform. Initial experiments confirm the validity of the approach. Future activity will aim at evaluating the system behavior in more complex tasks and also in presence of significant time delays in the data transmission. Fig. 8. Path followed by the mobile robot in a free environment (left) and in case that an obstacle is near the desired path (right) when constant translation and rotation velocities are required. Motion is counterclockwise Acknowledgements. This work has been done in the context of the European sponsored project GeoPlex with reference code IST Further information is available at REFERENCES Fig. 9. Trajectory of the mobile robot in a wall following task, without (left) and with (right) force feedback of about 0.2 m, while the constants of the virtual interaction are K e = 2700 N/m, b e = 30 Ns/m. Moreover, the experimental setup of Fig. 1 has been used to carry out some initial experiments. At the moment, transmission delays are negligible because data are exchanged over a local network. A simple wall-following task in a free room has been chosen in order to evaluate the improvement of performances provided by force feedback. Fig. 9 (left) shows how this task is carried out by taking advantage only of visual information provided by the map built with sonars: dimensions of the cells are 4 4 cm, free cells are white, while occupied cells are dark and unknown cells are gray; the trajectory followed by the mobile robot is drawn as a black line. Fig. 9 (right) shows how performances are improved when force feedback is provided to the operator. Note that a more regular trajectory also improves the quality of the map because sonars are less subject to multiple reflections. 6. CONCLUSIONS AND FUTURE WORK In this paper, a passivity-based control scheme for a mobile robot has been presented. In particular, a haptic interface with force feedback has been used for the remote control of the mobile base. The control is based on the motion of a virtual mass, Fong, T., F. Conti, S. Grange and C. Baur (2000). Novel interfaces for remote driving: gesture, haptic and pda. In: SPIE Telemanipulator and Telepresence VII. Boston, MA, USA. K. Kim, H. Lee, J. Park and M. Yang (2002). Robotic contamination cleaning system. In: IEEE Conference on Intelligent Robots ans Systems. Lausanne, Switzerland. Khatib, O. (1986). Real-time obstacle avoidance for manipulators and mobile robots. In: The International Journal of Robotics Research. Number 5(1). Lin, Q. and C. Kuo (1997). Virtual tele-operation of underwater robots. In: Proceedings of IEEE International Conference on Robotics and Automation. Albuquerque, NM, USA. Melchiorri, C., S. Stramigioli and S. Andreotti (1999). Using damping injection and passivity in robotics manipulation. In: Int. Conf. on Advanced Intelligent Mechatronics. Atlanta, GA, USA. Roth, H., K. Schilling and O.J. Rosch (2002). Haptic interfaces for remote control of mobile robots. In: Proceedings of 15th IFAC World Congress. Barcelona, Spain. S. Lee, G.S. Sukhatme, G.J. Kim and C. Park (2002). Haptic control of a mobile robot: A user study. In: IEEE Conference on Intelligent Robots ans Systems. Lausanne, Switzerland. Smith, F.M., D.K. Backman and S.C. Jacobsen (1992). Telerobotic manipulator for hazardous environments. In: Journ. of Rob. Syst.. Vol. 9, NO. 2. pp Stramigioli, S. (2001). Modeling and IPC Control of Interactive Mechanical Systems: a coordinate free approach. LNCIS Springer. London. van der Schaft, A. (2000). L2 - Gain and passivity techniques in nonlinear control. Springer. London.

CMPUT 412 Motion Control Wheeled robots. Csaba Szepesvári University of Alberta

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