Before revision:  The trajectory function computes high-speed minimum-jerk arcing motions that are constrained to remain within joint limits and to travel through the 3D apex point by repeatedly solving quadratic programs for shorter time horizons to find the shortest and fastest feasible motion.
After revision:  The trajectory function computes high-speed minimum-jerk arcing motions that are constrained to remain within joint limits and to travel through the 3D apex point by repeatedly solving quadratic programs to find the shortest and fastest feasible motion.