An Efficient Solution to Optimal Motion Planning With Provable Safety and Convergence

Abstract

An innovative solution to the optimal motion planning problem is presented in this work. A novel parametrized actor structure is proposed, which guarantees safe and convergent navigation by construction. Concurrently, an efficient scheme for optimizing a mixed state and energy cost function is formulated. The proposed method inherits the positive traits of continuous methods, while at the same time providing sub-optimal –but close to optimal– results significantly faster and in more complex workspaces than previous ones. The scheme is demonstrated to outperform established relevant methods, while at the same time being competitive w.r.t. execution time. Extensive simulations to validate the effectiveness of the method are presented, along with relevant technical proofs for safety and convergence.