用凸化方法提升多机器人轨迹规划的收敛速度与安全性
Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs. Non-Convex
- 用缓冲沃罗诺伊图将非凸避障转为凸约束，提升优化效率
- 凸版C-ADMM比非凸基准少1000次迭代就收敛
- 非凸方法易导致不安全路径，适合追求稳定性的应用
C-ADMM是一种广受认可的分布式优化框架，因其在凸优化问题中具有收敛保证而被广泛应用。近年来，它已被用于多车目标追踪和协作操作等机器人任务。然而，由于缺乏理论保障，其在非凸问题中的表现研究较少。本项目旨在通过分布式多机器人轨迹规划场景，定量分析非凸C-ADMM的收敛行为。我们提出一种基于C-ADMM与缓冲沃罗诺伊图（BVCs）的凸轨迹规划方法，以规避非凸避障约束，并将其与采用非凸避障约束的非凸C-ADMM基线进行对比。实验表明，在多机器人航点导航场景中，凸版C-ADMM仅需1000次更少的迭代即可收敛。同时验证了非凸C-ADMM基线会生成次优解并违反安全约束。
原文摘要 · Abstract (English)
C-ADMM is a well-known distributed optimization framework due to its guaranteed convergence in convex optimization problems. Recently, C-ADMM has been studied in robotics applications such as multi-vehicle target tracking and collaborative manipulation tasks. However, few works have investigated the performance of C-ADMM applied to non-convex problems in robotics applications due to a lack of theoretical guarantees. For this project, we aim to quantitatively explore and examine the convergence behavior of non-convex C-ADMM through the scope of distributed multi-robot trajectory planning. We propose a convex trajectory planning problem by leveraging C-ADMM and Buffered Voronoi Cells (BVCs) to get around the non-convex collision avoidance constraint and compare this convex C-ADMM algorithm to a non-convex C-ADMM baseline with non-convex collision avoidance constraints. We show that the convex C-ADMM algorithm requires 1000 fewer iterations to achieve convergence in a multi-robot waypoint navigation scenario. We also confirm that the non-convex C-ADMM baseline leads to sub-optimal solutions and violation of safety constraints in trajectory generation.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。