Minimum-Time Planar Paths with Up to Two Constant Acceleration Inputs and L2 Velocity and Acceleration Constraints
Victor M. Baez, Haoran Zhao, Nihal Abdurahiman, Nikhil V. Navkar, Aaron T. Becker · 2024
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 GitHub1, extended paper version at [1].