Regularized Continuation Method For Motion Planning
A regularized homotopy continuation method solves motion planning for control-affine systems with drift, converging to nonsingular solutions even near singular controls where classical methods fail.
Published Dec 16, 20241 citationPaper ↗
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Abstract
In this article, we investigate the motion planning problem for control-affine systems with nontrivial drifts using a regularized homotopy continuation method. We prove that when there exists a nonsingular solution of the original motion planning problem, the regularized solution converges to it almost everywhere, and the endpoints derived from the regularized solutions converge to the desired target point, may the solution of the classical continuation method is well defined or not. This provides a way to design the steering control in the presence of singular controls when the classical continuation method is not applicable. The effectiveness of the regularization is illustrated by numerical experiments on the rolling systems.