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

paper

Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and $L_{2}$ Velocity and Acceleration Constraints

arXiv:2403.04602

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.

8 pages, 8 figures, accepted for presentation at ACC 2024, https://acc2024.a2c2.org/

Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and L2​ Velocity and Acceleration Constraints

Abstract

Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and $L_{2}$ Velocity and Acceleration Constraints