Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs Non-Convex
<|reference_start|>Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs Non-Convex: 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.<|reference_end|>
@article{chen2024multi-robot,
    title={Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs.
  Non-Convex},
    author={Jushan Chen},
    journal={arXiv preprint arXiv:2410.01728},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01728},
    primaryClass={cs.RO cs.SY eess.SY}
}