Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial

TL;DR

This paper introduces an efficient multi-agent trajectory planning algorithm that guarantees feasible, safe, and dynamically feasible paths in obstacle-dense environments by leveraging Bernstein polynomial properties and a sequential optimization approach.

Contribution

The paper proposes a novel algorithm combining Bernstein polynomial convexification with sequential dummy agents to improve scalability and guarantee feasibility in multi-agent trajectory planning.

Findings

Computes trajectories for 64 agents in about 6.36 seconds.

Reduces objective cost by over 50% compared to previous methods.

Validated through simulation and flight tests.

Abstract

This paper presents a new efficient algorithm which guarantees a solution for a class of multi-agent trajectory planning problems in obstacle-dense environments. Our algorithm combines the advantages of both grid-based and optimization-based approaches, and generates safe, dynamically feasible trajectories without suffering from an erroneous optimization setup such as imposing infeasible collision constraints. We adopt a sequential optimization method with \textit{dummy agents} to improve the scalability of the algorithm, and utilize the convex hull property of Bernstein and relative Bernstein polynomial to replace non-convex collision avoidance constraints to convex ones. The proposed method can compute the trajectory for 64 agents on average 6.36 seconds with Intel Core i7-7700 @ 3.60GHz CPU and 16G RAM, and it reduces more than $50\%$ of the objective cost compared to our previous work. We validate the proposed algorithm through simulation and flight tests.