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arXiv · 2403.04602

Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and $L_2$ Velocity and Acceleration Constraints

Victor M. Baez·Haoran Zhao·Nihal Abdurahiman·Nikhil V. Navkar·Aaron T. Becker
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Abstract

Given starting and ending positions and velocities, $L_2$ bounds on the acceleration and velocity, and the restriction to no more than two constant control inputs, this paper provides routines to compute the minimal-time path. Closed form solutions are provided for reaching a position in minimum time with and without a velocity bound, and for stopping at the goal position. A numeric solver is used to reach a goal position and velocity with no more than two constant control inputs. If a cruising phase at the terminal velocity is needed, this requires solving a non-linear equation with a single parameter. Code is provided on GitHub at https://github.com/RoboticSwarmControl/MinTimeL2pathsConstraints.

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Victor M. Baez, Haoran Zhao, Nihal Abdurahiman, Nikhil V. Navkar, Aaron T. Becker. 2024-03-07. Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and $L_2$ Velocity and Acceleration Constraints. https://arxiv.org/abs/2403.04602

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