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.

翻译：给定起始和终止的位置与速度，以及加速度和速度的$L_2$范数约束，并限制不超过两个恒定控制输入，本文提供了计算最短时间路径的算法。当无速度约束和有速度约束时，分别给出了到达目标位置的最短时间闭式解，以及停在目标位置的最优解。采用数值求解器在不超过两个恒定控制输入的情况下实现目标位置和速度的到达。若需要在终端速度下进行巡航阶段，则需求解一个单参数非线性方程。代码已托管在GitHub上：https://github.com/RoboticSwarmControl/MinTimeL2pathsConstraints。