Abstract
We present a hybrid systems solution to the problem of trajectory tracking for a four-wheel steered four-wheel driven mobile robot. The robot is modelled as a non-holonomic dynamic system subject to pure rolling, no-slip constraints. Under normal driving conditions, a nonlinear trajectory tracking feedback control law based on dynamic feedback linearization is sufficient to stabilize the system and ensure asymptotically stable tracking. Transitions to other modes are derived systematically from this model, whenever the configuration space of the controlled system has some fundamental singular points. The stability of the hybrid control scheme is finally analyzed using Lyapunov-like arguments.
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C. Altafini, A. Speranzon, K. H. Johansson. Hybrid Control of a Truck and Trailer Vehicle, In C. Tomlin, and M. R. Greenstreet, editors, Hybrid Systems: Computation and Control LNCS 2289, p. 21., Springer-Verlag, 2002.
M. S. Branicky. Analyzing and Synthesizing Hybrid Control Systems In G. Rozenberg, and F. Vaandrager, editors, Lectures on Embedded Systems, LNCS 1494, pp. 74–113, Springer-Verlag, 1998.
A. Balluchi, P. Souères, and A. Bicchi. Hybrid Feedback Control for Path Tracking by a Bounded-Curvature Vehicle In M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli, editors, Hybrid Systems: Computation and Control, LNCS 2034, pp. 133–146, Springer-Verlag, 2001.
G. Bastin, G. Campion. Feedback Control of Nonholonomic Mechanical Systems, Advances in Robot Control, 1991
B. D'Andrea-Novel, G. Campion, G. Bastin. Modeling and Control of Non Holonomic Wheeled Mobile Robots, in Proc. of the 1991 IEEE International Conference on Robotics and Automation, 1130–1135, 1991
G. Campion, G. Bastin, B. D'Andrea-Novel. Structural Properties and Classification of Kinematic and Dynamic Models of Wheeled Mobile Robots, IEEE Transactions on Robotics and Automation Vol. 12, 1:47–62, 1996
L. Caracciolo, A. de Luca, S. Iannitti. Trajectory Tracking of a Four-Wheel Differentially Driven Mobile Robot, in Proc. of the 1999 IEEE International Conference on Robotics and Automation, 2632–2838, 1999
J. D. Bendtsen, P. Andersen, T. S. Pedersen. Robust Feedback Linearization-based Control Design for a Wheeled Mobile Robot, in Proc. of the 6th International Symposium on Advanced Vehicle Contro, 2002
H. Goldstein. Classical Mechanics, Addison-Wesley, 2nd edition, 1980
T. A. Henzinger. The Theory of Hybrid Automata, In Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science (LICS 1996), pp. 278–292, 1996.
I. Kolmanovsky, N. H. McClamroch. Developments in Nonholonomic Control Problems, IEEE Control Systems Magazine Vol. 15, 6:20–36, 1995
D. Liberzon, A. S. Morse. Basic Problems in Stability and Design of Switched Systems, IEEE Control Systems Magazine Vol. 19, 5:59–70, 1999.
C. Samson. Feedback Stabilization of a Nonholonomic Car-like Mobile Robot, In Proceedings of IEEE Conference on Decision and Control, 1991.
B. Thuilot, B. D'Andrea-Novel, A. Micaelli. Modeling and Feedback Control of Mobile Robots Equipped with Several Steering Wheels, IEEE Transactions on Robotics and Automation Vol. 12, 2:375–391, 1996.
C. Tomlin, S. Sastry. Switching through Singularities, Systems and Control Letters Vol. 35, 3:145–154, 1998.
G. Walsh, D. Tilbury, S. Sastry, R. Murray, J. P. Laumond. Stabilization of Trajectories for Systems with Nonholonomic Constraints IEEE Trans. Automatic Control 39: (1) 216–222, 1994.
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Bak, T., Bendtsen, J., Ravn, A.P. (2003). Hybrid Control Design for a Wheeled Mobile Robot. In: Maler, O., Pnueli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2003. Lecture Notes in Computer Science, vol 2623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36580-X_7
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DOI: https://doi.org/10.1007/3-540-36580-X_7
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