Piecewise-Linear Motion Planning amidst Static, Moving, or Morphing Obstacles

TL;DR

This paper introduces a moment optimization-based method for planning shortest piecewise-linear paths in environments with static, moving, or morphing obstacles, outperforming existing methods in efficiency and scalability.

Contribution

It presents a novel hierarchy of semidefinite programs for globally optimizing motion paths without time discretization, enhancing scalability and performance.

Findings

Outperforms sampling-based and nonlinear optimization baselines

Handles continuous time constraints directly

Scales better with higher dimensions

Abstract

We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of semidefinite programs that yield increasingly refined lower bounds converging monotonically to the optimal path length. For computational tractability, our global moment optimization approach motivates an iterative motion planner that outperforms competing sampling-based and nonlinear optimization baselines. Our method natively handles continuous time constraints without any need for time discretization, and has the potential to scale better with dimensions compared to popular sampling-based methods.