Abstract
The concept of feasible command strategies is introduced and its applicability is demonstrated by solving a guidance and control problem. This problem concerns the motion of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its endpoint, about the disk center. The motion of the disk-rod system is subjected to state and control constraints, and it serves as a model for the motion of a simple mobile robot. In addition, the concept of path controllability is introduced and a condition is derived for the system motion path controllability. The derivation of this condition enables one to design closed-loop control laws for the system motion.
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References
Whittaker, E. T.,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, Cambridge, United Kingdom, 1917.
Latombe, J. C.,Robot Motion Planning, Kluwer Academic Publishers, Boston, Massachusetts, 1991.
Laumond, J. P.,Controllability of a Multibody Mobile Robot, IEEE Transactions on Robotics and Automation, Vol. 9, pp. 755–763, 1993.
Micaelli, A., andSamson, C.,Trajectory Tracking for Unicycle-Type and Two-Steering-Wheels Mobile Robots, Research Report 2097, INRIA, Sophia-Antipolis, France, 1993.
Murray, R. M., andSastry, S. A.,Nonholonomic Motion Planning: Steering Using Sinusoids, IEEE Transactions on Automatic Control, Vol. 38, pp. 700–716, 1993.
Pomet, J. B., andSamson, C.,Time-Varying Exponential Stabilization of Nonholonomic Systems in Power Form, Research Report 2126, INRIA, Sophia-Antipolis, France, 1993.
Sordalen, O. J.,Feedback Control of Nonholonomic Mobile Robots, Dr. Ing. Thesis, Department of Engineering Cybernetics, Norwegian Institute of Technology, Trondheim, Norway, 1993.
Walsh, G., Tilbury, D., Sastry, S., Murray, R., andLaumond, J. P.,Stabilization of Trajectories for Systems with Nonholonomic Constraints, IEEE Transactions on Automatic Control, Vol. 39, pp. 216–222, 1994.
Goldstein, H.,Classical Mechanics, Addison-Wesley, Reading, Massachusetts, 1980.
Yavin, Y., andFrangos, C.,Computation of Feasible Control Trajectories for the Navigation of a Big Ship around an Obstacle in the Presence of a Sea Current, Mathematical and Computer Modelling, Vol. 21, pp. 99–117, 1995.
Snyman, J. A.,A New and Dynamic Method for Unconstrained Minimization, Applied Mathematical Modelling, Vol. 6, pp. 449–462, 1982.
Snyman, J. A.,An Improved Version of the Original Leap-Frog Dynamic Method for Unconstrained Minimization: LFOP(b), Applied Mathematical Modelling, Vol. 7, pp. 216–218, 1983.
Friedland, B.,Control System Design, McGraw-Hill, New York, New York, 1987.
Bazaraa, M. S., Sherali, H. D., andShetty, C. M.,Nonlinear Programming: Theory and Algorithms, John Wiley, New York, New York, 1993.
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Communicated by C. T. Leondes
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Yavin, Y., Frangos, C. Feasible command strategies for the control of motion of a simple mobile robot. J Optim Theory Appl 90, 671–692 (1996). https://doi.org/10.1007/BF02189801
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DOI: https://doi.org/10.1007/BF02189801