Minimum-Time Planar Paths with Up to Two Constant Acceleration Inputs and L2 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
¹
, extended paper version at [1].