Piecewise-Linear Motion Planning amidst Static, Moving, or Morphing Obstacles
This addresses motion planning challenges in robotics or autonomous systems, offering a novel computational method with potential scalability improvements.
The paper tackles the problem of planning shortest piecewise-linear motions in environments with static, moving, or morphing obstacles, achieving this through a moment optimization approach that yields iterative lower bounds converging to optimal path length and outperforming existing baselines.
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.