Control of nonholonomic systems using chained form. (English) Zbl 0788.70018

Enos, Michael J. (ed.), Dynamics and control of mechanical systems. The falling cat and related problems. Papers of the first Fields Institute Workshop held at Waterloo, Ontario (Canada), March 1992. Providence, RI: American Mathematical Society. Fields Inst. Commun. 1, 219-245 (1993).
This paper focuses on the problem of trajectory generation, stabilization, and tracking for mechanical systems with non-integrable (or nonholonomic) velocity constraints. Examples of nonholonomic control systems include multi-fingered robot hands with rolling contacts, space- based dynamical systems (where conservation of angular momentum plays the role of a constraint), and wheeled mobile robots. We make extensive use of a special nilpotent normal form, called chained form, and, in the two- input case, give necessary and sufficient conditions for the existence of a feedback transformation which puts the system into chained form.
For the entire collection see [Zbl 0777.00030].


70Q05 Control of mechanical systems
70F25 Nonholonomic systems related to the dynamics of a system of particles
70B15 Kinematics of mechanisms and robots
93C85 Automated systems (robots, etc.) in control theory