Set-oriented optimal path planning of mobile robots by a polynomial rootfinder

In real applications, mobile robots are usually controlled to reach a “pose set” rather than a specific point to achieve mobile manipulation tasks. Motivated by this observation, this paper proposes a real-time set-oriented optimal path planning method based on a multi-precision polynomial rootfinder. Specifically, after giving a formal formulation of the proposed “set-oriented path planning problem”, a specific circular set-oriented planning problem, wherein the target pose is on a circle with the orientation directed to the origin, is considered in this paper. It is shown that the optimal path planning problem reduces to a constrained univariate signomial programming problem to minimize a performance index related to the path length, and an effective solution to this optimization problem can be obtained by a fast multi-precision polynomial rootfinder in a real-time manner. Extensive simulation results are provided to validate the proposed approach.