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

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. Our global moment optimization approach natively handles continuous time constraints without any need for time discretization. For computational tractability, we derive an iterative motion planner which compares favorably with sampling-based and nonlinear optimization baselines.