Motion Discontinuity-Robust Controller for Steerable Mobile Robots
Steerable wheeled mobile robots (SWMR) are able to perform arbitrary 3D planar trajectories, only after initializing the steer joint vector to the proper values. These robots employ fully steerable conventional wheels. Hence, they have higher load carrying capacity than their holonomic counterparts, and as such are preferable for industrial applications. Industrial setups nowadays are being prepared for the emerging field of humanrobot collaboration/cooperation. Such field is highly dynamic, due to fast moving human workers, sharing the operation space. This imposes the need for human safe trajectory generators, that can lead to frequent halts in motion, re-planning, and to sudden, discontinuous changes in the position of the robot’s instantaneous center of rotation (ICR). Indeed, this requires steer joint reconfiguration to the newly computed trajectory. This issue is almost ignored in the literature, and motivates this work. The authors propose a new ICR-based kinematic controller, that is capable of handling discontinuity in commanded velocity, while respecting the maximum joint performance limit. This is done by formulating a quadratic optimization problem with linear constraints in the 2D ICR space. The controller is also robust against representation and kinematic singularities. It has been tested successfully on the Neobotix-MPO700 industrial mobile robot.
Due to their wide use in the industry, many research efforts have been made to enhance their performance, against kinematic (ICR at the steering joint axis) and representation (from the mathematical model) singularities. The latter have been solved, in the case of SWMR with three or more wheels, by using the 3D Cartesian velocity in deriving the kinematic model . The former was addressed as a constraint to robot motion in , or by using repulsive potential fields in , , . However, reduction in robot maneuverability, by employing these methods, is not acceptable, and attempts were made to deal with kinematic singularity by handling the maximum joint limits  and by changing coordinate system . Steering mechanical limits were also studied in  and . Simulations in  do not indicate the behavior of the steer joints in terms of respecting the velocity limits at kinematic singularity, while in , it is shown that the steer rate will saturate and keep operating at the maximum limit. On the other hand, to the best of the authors knowledge, no thorough investigation has been conducted on the issue of reorienting the wheels, once discontinuity in the robot trajectory occurs. Usually, steer reconfiguration is performed in a manual fashion, depending on the test trajectory. This is found in the literature under various designations, e.g. ”initial phase” in , and ”open-loop starting procedure” in . Although an ICR-based controller is the most suited to handle such cases, the work in  and  is limited by the assumption of continuous and differentiable desired signal, whereas in  the singularities imposed by the ICR-based model are handled by reducing the robot maneuverability.
In this work, we propose a kinematic control framework that is: 1) robust against trajectory discontinuity, 2) capable of handling kinematic singularity, 3) compliant with the maximum steer joint limits in terms of velocity and acceleration (or jerk, seamlessly). The framework consists of two decoupled kinematic controllers: a Cartesian-velocity based controller, and an ICRbased one. The former is used to control the drive rate ”wheel speed”, employing a Cartesian space kinematic model. The latter controls the steering rate, while respecting the maximum steer joint limits, by using optimization to locate the ”next sample time” ICR coordinates. The developed 3D Cartesian space kinematic model is free from representational singularity, while the kinematic singularities are being handled in the 2D ICR space controller. The benefit of using separate kinematic controllers for the drive and steering rates, is that it does not require mapping the 2D ICR-coordinate space to the 3D Cartesian space, hence avoids associated singularities and inconveniences. Thanks to the formulated optimization problem, discontinuity in robot velocity trajectory is handled, while respecting the steer joint limits
A motion-discontinuity robust controller has been developed and successfully tested on an industrial mobile robot. A discontinuous benchmark test trajectory that excites representation and kinematic singularities has been performed by the proposed controller with success. Maximum steer joint performance limits are taken into account and shown to be well respected throughout the experiments. In future work, the drive joint maximum performance limits will be added to the proposed framework.
 P. R. Giordano, M. Fuchs, A. Albu-Schaffer, and G. Hirzinger, “On the kinematic modeling and control of a mobile platform equipped with steering wheels and movable legs,” in IEEE Int. Conf. on Robotics and Automation, 2009, pp. 4080–4087.
 B. Thuilot, B. d’Aandrea Novel, and A. Micaelli, “Modeling and feedback control of mobile robots equipped with several steering wheels,” IEEE Trans. on Robotics and Automation, vol. 12, no. 3, pp. 375–390, 1996.
 A. Dietrich, T. Wimbck, A. Albu-Schffer, and G. Hirzinger, “Singularity avoidance for nonholonomic, omnidirectional wheeled mobile platforms with variable footprint,” in IEEE Int. Conf. on Robotics and Automation, 2011, pp. 6136–6142.
 C. P. Connette, C. Parlitz, M. Hagele, and A. Verl, “Singularity avoidance for over-actuated, pseudo-omnidirectional, wheeled mobile robots,” in IEEE Int. Conf. on Robotics and Automation, 2009, pp. 4124–4130.
 U. Schwesinger, C. Pradalier, and R. Siegwart, “A novel approach for steering wheel synchronization with velocity/acceleration limits and mechanical constraints,” in IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2012, pp. 5360–5366.
 R. Oftadeh, R. Ghabcheloo, and J. Mattila, “A novel time optimal path following controller with bounded velocities for mobile robots with independently steerable wheels,” in IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2013, pp. 4845–4851.
 C. Connette, M. Hgele, and A. Verl, “Singularity-free state-space representation for non-holonomic, omnidirectional undercarriages by means of coordinate switching,” in IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2012, pp. 4959–4965.
 S. Chamberland, E. Beaudry, L. Clavien, F. Kabanza, F. Michaud, and M. Lauriay, “Motion planning for an omnidirectional robot with steering constraints,” in IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2010, pp. 4305–4310.
 R. Oftadeh, R. Ghabcheloo, and J. Mattila, “Time optimal path following with bounded velocities and accelerations for mobile robots with independently steerable wheels,” in IEEE Int. Conf. on Robotics and Automation (ICRA), 2014, pp. 2925–2931.
 M. Sorour, A. Cherubini, R. Passama, and P. Fraisse, “Kinematic modeling and singularity treatment of steerable wheeled mobile robots with joint acceleration limits,” in IEEE Int. Conf. on Robotics and Automation, 2016, pp. 2110–2115.