Minimum curvature path planning for a dual stage positioning system*

The use of two-stage positioning systems is becoming widespread in the manufacturing industry, as they allow shortening the completion of tasks while maintaining high positioning accuracy. This paper proposes a path planning algorithm which splits the movements to be executed by the two actuators, in such a way to obtain a beneficial effect on the Macro actuator motion, in terms of smoothness and limited vibration onset. The algorithm takes advantage of the spline properties to generate a smooth geometric path and to easily account for micro actuator limited range of motion. Compared to other methods described in literature, the proposed solution only needs a sequence of end-effector poses (not related by a time law) to generate a proper sequence of poses in the joint space. The proposed solution is carried out by solving a linearly constrained quadratic programming problem.