Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and $L_2$ Velocity and Acceleration Constraints
<|reference_start|>Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs and $L_2$ Velocity and Acceleration Constraints: 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.<|reference_end|>
@article{baez2024minimum-time,
    title={Minimum-Time Planar Paths with up to Two Constant Acceleration Inputs
  and $L_2$ Velocity and Acceleration Constraints},
    author={Victor M. Baez, Haoran Zhao, Nihal Abdurahiman, Nikhil V. Navkar,
  Aaron T. Becker},
    journal={arXiv preprint arXiv:2403.04602},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04602},
    primaryClass={cs.RO}
}