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A global steering method for nonholonomic systems. (English) Zbl 1258.93056

Summary: In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in F. Jean, G. Oriolo, M. Vendittelli [”A globally convergent steering algorithm for regular nonholonomic systems,” 44th IEEE Conference on Decision and Control, Seville, pp. 7514-7519, (2005)] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in R. M. Murray S. S. Sastry [”Nonholonomic motion planning: Steering using sinusoids, IEEE Trans. Autom. Control 38, No.5, 700-716 (1993; Zbl 0800.93840)] for chained-form systems.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93C15 Control/observation systems governed by ordinary differential equations
93B27 Geometric methods

Citations:

Zbl 0800.93840
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