| Line-Integral Estimates And Motion Planning Using The Continuation Method (2007) | |||||||||||||||
Abstract | |||||||||||||||
| . For smooth driftless control-affine systems, the approach to the nonholonomic path planning problem based on the continuation method leads to an ordinary differential equation in the space of open-loop controls, known as the "path-lifting differential equation" (PLE). Global existence of the solutions of the PLE is known for systems that satisfy R. Strichartz' Strong Bracket Generating Condition (SBGC). We extend this existence result by proving an estimate for certain line integrals along trajectories, and showing that this estimate implies the global existence result for the case when the SBGC is satisfied, and also in some cases where it is not. In particular, we apply our results to a model of a front-wheel-driven car ---for which the SBGC does not hold--- and show that the continuation method solves the path-planning problem for this model. Key words. Nonholonomic path planning. Continuation method. Abnormal extremals. Sub-riemannian manifolds. Front-wheel-driven car. AMS(MOS)... | |||||||||||||||
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