An effective technique to find a robot joint trajectory of minimum global jerk and distance

Minimum-jerk (MJ) trajectories introduce less robot vibrations and are desirable for their smooth movement, while Minimum-distance (MD) trajectories are required to limit both the expected and unexpected paths of robot manipulators. The combination of the MJ and MD trajectories provides an effective kinematic scheme for robotic applications. An approach based on time spacing optimization is developed to find the global minimum-jerk as well as minimum-distance trajectory of a robot manipulator within joint space using cubic splines, despite the fact that the manipulator dynamics as well as the obstacle avoidance are not taken into account. Cubic splines are used in a framework which guarantees the continuity of joint displacements, velocities and accelerations. Firstly, a minimax optimization problem is formulated by respecting the boundary conditions of the splines and the MJ and MD constraints. Then, the problem is solved by genetic algorithms based on time spacing analysis. After that, a global solution of the kinematic scheme is provided. Finally, a comparison is made between our results and that of an alternative MJ planner.