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

arXiv: https://arxiv.org/abs/2010.08167 · HTML: https://mlsanity.com/paper/2010.08167/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Convex Risk Bounded Continuous-Time Trajectory Planning and Tube Design in Uncertain Nonconvex Environments](https://mlsanity.com/paper/2305.17291/) (2023)

## Abstract (arXiv)

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.