Cusp-Free,Time-Invariant,3D Feedback Control Law for a Nonholonomic Floating Robot

Abstract

In this paper, the feedback control of a nonholonomic 3D vehicle is considered; namely, the problem of steering an underactuated rigid body to a target position along a desired direction is addressed. A simple time-invariant strategy is determined on the basis of standard vector kinematics and a Lyapunov-like stability analysis. The resulting control law guarantees almost global exponential convergence of the configuration error to zero with paths that do not exhibit any cusps, thus satisfying a major requirement for the application of such results on real systems that are not allowed or desired to move in both the forward and backward directions.

Get full access to this article

View all access options for this article.

References

Aicardi, M., Casalino, G., Bicchi, A., and Balestrino, A. 1995. Closed loop steering of unicycle-like vehicles via Lyapunov techniques . IEEE Robotics and Automation Magazine, March, 27–35 .

Astolfi, A. 1994. On the stabilization of nonholonomic systems . Proceedings of the 33rd IEEE Conference on Decision and Control, Buena Vista, FL, December 14-16, pp. 3481–3486 .

Astolfi, A. 1996. Discontinuous control of a nonholonomic system . Systems & Control Letters 27: 37–45 .

Astolfi, A. 1999. Exponential stabilization of a wheeled mobile robot via discontinuous control . ASME Journal of Dynamic Systems, Measurement and Control 121: 121–125 .

Badreddin, E., and Mansour, M. 1993. Fuzzy-tuned state feedback control of a nonholonomic mobile robot . Proceedings of the 12th World Congress of the IFAC, Sydney, Australia.

Brockett, R. W. 1983. Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, ed. R. W. Brockett, R. S. Milman, and H. J. Sussmann, 181–193. Boston: Birkhauser .

Casalino, G., Aicardi, M., Bicchi, A., and Balestrino, A. 1994. Closed-loop steering for unicycle-like vehicles: A simple Lyapunov like approach . IFAC Symposium on Robot Control, Sy.Ro.Co’94, Capri, Italy, September, pp. 291–298 .

Egeland, O., Berglund, E., and Sørdalen, O. J. 1994. Exponential stabilization of a nonholonomic underwater vehicle with constant desired configuration . IEEE International Conference on Robotics and Automation, ICRA’94, San Diego, CA, pp. 20–25 .

Egeland, O., Dalsmo, M., and Sørdalen, O. J. 1996. Feedback control of a nonholonomic underwater vehicle with a constant desired configuration . International Journal of Robotics Research 15(1): 24–35 .

10.

Fossen, T. I. 1994. Guidance and Control of Ocean Vehicles. New York: John Wiley & Sons .

11.

Indiveri, G. (1999). Kinematic time-invariant control of a 2D nonholonomic vehicle . 38th IEEE Conference on Decision and Control CDC’99, Phoenix, AZ, December 7-10.

12.

Jiang, Z.-P. 2000. Robust exponential regulation of nonholonomic systems with uncertainties . Automatica 36: 189–209 .

13.

Khalil, H. K. 1996. Nonlinear Systems. 2d ed. Englewood Cliffs, NJ: Prentice Hall .

14.

Kolmanowsky, I., and McClamroch, N. H. 1995. Developments in nonholonomic control problems . IEEE Control Systems, December, 20–36 .

15.

Pettersen, K. Y., and Egeland, O. 1999. Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle . IEEE Transactions on Automatic Control 44: 112–115 .

16.

Slotine, J.-J.E., and Li, W. 1991. Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice Hall .