TY - JOUR
T1 - Optimal multivehicle motion planning using bernstein approximants
AU - Cichella, Venanzio
AU - Kaminer, Isaac
AU - Walton, Claire
AU - Hovakimyan, Naira
AU - Pascoal, Antonio M.
N1 - Manuscript received January 29, 2020; revised April 11, 2020; accepted May 14, 2020. Date of publication June 1, 2020; date of current version March 29, 2021.This work was supported in part by ONR under Grant N00014-19-1-2106 and Grant N00014-19-WX0-0155, in part by AFOSR under Grant FA9550-15-1-0518, and the H2020 EUMR Research Infrastructure Network under Grant GA 731103. Recommended by Associate Editor Leonid B. Freidovich. (Corresponding author: Ve-nanzio Cichella.) Venanzio Cichella is with the Department of Mechanical Engineering, University of Iowa, Iowa City, IA 52240 USA (e-mail: [email protected]).
PY - 2021/4
Y1 - 2021/4
N2 - 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.
AB - 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.
KW - Bernstein polynomial
KW - Bezier curve
KW - Multiple vehicles
KW - Optimal motion planning
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U2 - 10.1109/TAC.2020.2999329
DO - 10.1109/TAC.2020.2999329
M3 - Article
AN - SCOPUS:85103433905
SN - 0018-9286
VL - 66
SP - 1453
EP - 1467
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
M1 - 9105082
ER -