Optimal Multivehicle Motion Planning Using Bernstein Approximants

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.

Automated summary

This article introduces a computational framework to efficiently generate feasible and safe trajectories for multiple autonomous vehicles, using optimal control problems and approximation with Bernstein polynomials. The method can effectively compute and enforce constraints, making it suitable for real-time trajectory generation in complex environments and multiple vehicle missions. The proposed method's advantages are investigated through numerical examples, showing convergence to the solution of the continuous-time problem.