Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial (1909.10219v2)

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.

• The paper proposes a novel algorithm using Relative Bernstein Polynomials to convert non-convex collision constraints into convex ones and ensure feasible trajectories.
• Simulation results demonstrate the algorithm’s capability to plan trajectories for 64 agents in 6.36 seconds, achieving over 50% improvement in objective cost.
• The approach integrates grid-based and optimization-based planning to balance computational efficiency and trajectory optimality, validated through simulations and flight tests.

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

The paper presents a sophisticated algorithm to address multi-agent trajectory planning within environments dense with obstacles, a common challenge in robotic systems using Unmanned Aerial Vehicles (UAVs). This work situates itself between grid-based and optimization-based methodologies, aiming to draw advantages from both to mitigate the pitfall of non-feasible constraints typical in pure optimization approaches.

A pivotal aspect of the proposed method involves the use of Relative Bernstein Polynomials to convert otherwise non-convex collision constraints into convex ones. By employing these, the algorithm ensures dynamically feasible trajectories void of erroneous collision avoidance constraints. This is achieved by leveraging the Bernstein polynomial's convex hull property to manage collision avoidance among multiple agents via sequential optimization, incorporating dummy agents to improve scalability.

Simulation results underscored the efficiency of this planning approach. Testing showed the algorithm capable of planning trajectories for 64 agents in approximately 6.36 seconds, which represents a significant enhancement in computational efficiency—exceeding 50% improvement in objective cost relative to prior work. Such results were validated in both simulation environments and actual flight tests, demonstrating applicability and robustness.

The algorithm promises several practical implications for fields engaging with multi-agent systems, particularly where safe and efficient trajectory planning in cluttered environments is crucial. The substantial improvement in computation speed and reliability over previous methods provides a robust basis for further technological and algorithmic implementations in autonomous vehicles and UAVs.

Theoretically, this work contributes a structured framework within which non-convex problems can be reformulated into solvable convex problems by using polynomial-based approximations. Practically, it elucidates significant potential for real-time applications while maintaining a balance between computational load and optimality of pathway, which is a critical constraint in the field of robotics and control systems.

Looking towards future developments, enhancements could consider broader environmental dynamics, including moving obstacles, and further optimizing initial trajectory paths for non-grid spaces. Such extensions will augment the algorithm's robustness and flexibility, ensuring adherence to dynamic constraints in a more comprehensive array of real-world scenarios.