Minimum jerk path generation

A simple method of trajectory generation of robot manipulators is presented. It is based on an optimal control problem formulation. The jerk, the third derivative of position, of the desired trajectory, adversely affect the efficiency of the control algorithms and therefore should be minimized. assuming joint position, velocity and acceleration to be constrained, a cost criterion containing jerk is considered. Initially, the simple environment without obstacles and constrained by the physical limitations of the joint angles only is examined. For practical reasons, the free execution time has been used to handle the velocity and acceleration constraints instead of the complete bounded state variable formulation. The problem of minimizing the jerk along an arbitrary Cartesian trajectory is formulated and given analytical solution, making this method useful for real-world environments containing obstacles