Optimization-Based Collision Avoidance

This article presents a novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable using strong duality of convex optimization. We focus on controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation exact, does not introduce any approximations, and applies general objects that can be represented as the union sets. connect our results with notion signed distance, which widely used traditional trajectory generation algorithms. Our applied generic navigation planning tasks, smoothness property allows use general-purpose gradient- Hessian-based optimization Finally, case cannot avoided, framework us find “least-intrusive” trajectories, measured terms penetration. demonstrate efficacy automated parking problem, where numerical experiments suggest robust enables real-time optimization-based tight environments. Sample code example provided at https://github.com/XiaojingGeorgeZhang/OBCA.