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• W2034190982 abstract "We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned singularities are the abnormal extremals associated to the dynamics of the control system and the Wazewski equation is an o.d.e. on the control space called the Path Lifting Equation (PLE). We first show elementary facts relative to the maximal solution of the PLE such as local existence and uniqueness. Then we prove two general results, a finite-dimensional reduction for the PLE on compact time intervals and a regularity preserving theorem. In a second part, if the Strong Bracket Generating Condition holds, we show, for several control spaces, the global existence of the solution of the PLE, extending a previous result of H.J. Sussmann." @default.
• W2034190982 created "2016-06-24" @default.
• W2034190982 creator A5000279658 @default.
• W2034190982 date "2005-12-15" @default.
• W2034190982 modified "2023-09-25" @default.
• W2034190982 title "A continuation method for motion-planning problems" @default.
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• W2034190982 doi "https://doi.org/10.1051/cocv:2005035" @default.
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