Although robots have some kinematic and dynamic constraints such as the limits of the position, velocity, acceleration, jerk, and torque, they should move as fast as possible to increase the productivity. Researches on the minimum-time trajectory planning and control based on the dynamic constraints assume the availability of full dynamics of robots. However, the dynamic equation of robot may not often be exactly known. In this case, the kinematic approach for the minimum-time trajectory planning is more meaningful. We also have to construct a controller to track precisely the minimum-time trajectory. But, finding a proper controller is also difficult if we do not know the explicit dynamic equations of a robot.

This paper describes an optimization of trajectory planning based on a kinematic approach using the evolution strategy (ES), as well as an optimization of a sliding mode tracking controller using ES for a robot without dynamic equations.