An interval algorithm for minimum-jerk trajectory planning of robot manipulators

We present an approach to finding the minimum-jerk cubic spline joint trajectory of a robot manipulator, using interval analysis. Minimum-jerk trajectories are desirable for their amenability to path tracking and to limit robot vibrations whilst cubic splines are used in order to ensure continuity of velocities and accelerations in the robot movement. The optimization problem, that can be seen as a constrained minimax problem, is solved through the use of interval analysis that guarantees that the global minimum is found with an arbitrary precision. We describe the employed algorithm and computational results are also presented.