Motion planning and feedback control for a unicycle in a way point following task: The VFO approach
This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of waypoints which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.
- Astolfi, A. (1996). Asymptotic Stabilization of Nonholonomic Systems with Discontinuous Control, Ph.D. thesis, Swiss Federal Institute of Technology, Zurich.
- Bhat, S. P. and Bernstein, D. S. (2000). Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization 38(3): 751-766.
- de Luca, A., Oriolo, G. and Samson, C. (1998). Feedback control of a nonholonomic car-like robot, in J. P. Laumond (Ed.), Robot Motion Planning and Control, Lecture Notes in Control and Information Sciences, Vol. 229, Springer, Berlin/Heidelberg, pp. 171-253.
- Fleury, S., Soueres, P., Laumond, J. and Chatila, R. (1995). Primitives for smoothing mobile robot trajectories, IEEE Transactions on Robotics and Automation 11(3) 441-448.
- Kozłowski, K. and Pazderski, D. (2004). Modeling and control of a 4-wheel skid-steering mobile robot, International Journal of Applied Mathematics Computer Science 14(4): 477-496.
- Lawrence, D. A., Frew, E. W. and Pisano, W. J. (2008). Lyapunov vector fields for autonomous UAV flight control, AIAA Journal of Guidance, Control, and Dynamics 31(5): 1220-1229.
- Madi, M. (2004). Closed-form expressions for the approximation of arclength parameterization for Bezier curves, International Journal of Applied Mathematics Computer Science 14(1): 33-41.
- Michałek, M. and Kozłowski, K. (2008). Motion planning and its realization using VFO stabilizer features for a differentially driven robot, in K. Tchoń and C. Zieliński (Eds.), Problemy robotyki, Prace naukowe, Elektronika, Vol. 166, II, Warsaw University of Technology Press, pp. 525-534, (in Polish)
- Michałek, M. and Kozłowski, K. (2009). Vector-field-orientation feedback control method for a differentially-driven vehicle, IEEE Transactions on Control Systems Technology, DOI: 10.1109/TCST.2008.2010406, (in print).
- Morin, P. and Samson, C. (2003). Practical stabilization of drifless systems on Lie groups: The transverse function approach, IEEE Transactions on Automatic Control 48(9): 1496-1508.
- Reeds, J. A. and Shepp, L. A. (1990). Optimal paths for a car that goes both forwards and backwards, Pacific Journal of Mathematics 145(2): 367-393.
- Samson, C. (1992). Path following and time-varying feedback stabilization of a wheeled mobile robot, Proceedings of the International Conference ICARCV'92, Singapore, pp. 13.1.1-13.1.5.
- Sasiadek, J. and Duleba, I. (1995). Local trajectory planner, Proceedings of the AIAA Guidance, Navigation and Control Conference, Baltimore, MD, USA, pp. 1474-1483.
- Scheuer, A. and Fraichard, T. (1997). Continuous-curvature path planning for car-like vehicles, Proceedings of the International Conference of Intelligent Robots and Systems, Grenoble, France, pp. 997-1003.
- Siegwart, R. and Nourbakhsh, I. R. (2004). Introduction to Autonomous Robots, The MIT Press, Cambridge, MA.
- Sordalen, O. J. and de Wit, C. C. (1993). Exponential control law for a mobile robot: extension to path following, IEEE Transactions on Robotics and Automation 9(6): 837-842.