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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
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Given starting and ending positions and velocities, L₂ 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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