A time-optimal isotropic Cartesian trajectory generator with limited acceleration magnitude

In this paper we present an algorithm to compute the time-optimal trajectory from one point in multi-dimensional Cartesian space to another with arbitrary start and target velocity vectors and with limited acceleration norm. Based on Pontryagin´s minimum principle, we devise the conditions that have to be fulfilled and formulate a cost function for the time-optimal solution. The resulting boundary value problem is an optimization problem, which is exemplarily solved using the Nelder-Mead method. Exemplary curves are compared against cubic polynomials and trajectories generated by the Reflexxes Motion Libraries.