Optimal Multivehicle Motion Planning Using Bernstein Approximants

• 成果类型: Article
• 署名作者: Cichella, Venanzio; Kaminer, Isaac; Walton, Claire; Hovakimyan, Naira; Pascoal, Antonio M.
• 署名单位: University of Iowa; United States Department of Defense; United States Navy; Naval Postgraduate School; University of Illinois System; University of Illinois Urbana-Champaign; Universidade de Lisboa
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2999329
• 发表日期: 2021
• 页码: 1453-1467
• 关键词: Optimal control; PLANNING; trajectory; CONVERGENCE; tools; Approximation methods; Autonomous Vehicles; Bernstein polynomial; Bezier curve; multiple vehicles; optimal motion planning

摘要

This article presents a computational framework to efficiently generate feasible and safe trajectories for multiple autonomous vehicle operations. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate its solutions in a discretized setting using Bernstein polynomials. The latter possess convenient properties that allow to efficiently compute and enforce constraints along the vehicles' trajectories, such as maximum speed and angular rates, minimum distance between trajectories and between the vehicles and known obstacles, etc. Thus, the proposed method is particularly suitable for generating trajectories in real-time for safe operations in complex environments and multiple vehicle missions. We show, using a rigorous mathematical framework, that the solution to the discretized optimal motion planning problem converges to that of the continuous-time one. The advantages of the proposed method are investigated through numerical examples.