Minimization of Maximal Torque of a Flywheel Robot

Summary

This paper treats the optimization of the design and control of the Linkoping Flywheel Robot with respect to maximal torque. The robot consists of three links, where the inner rotates with constant angular velocity to handle major displacements and the two outer are used for local positioning. The objective is to minimize the maximal torque in the two outer joints, subject to the constraints that the Tool Center Point is still at the gripping and placing operations. The link lengths, the points of time for the pick-and-place operations, and the trajectory of the manipulator are variable. The link movements as functions of time are expressed by B-splines. Two different solution approaches are developed and tested in experiments. In the first, the maximal torque is approximated using an integral and the constraints are handled via a quadratic penalty function. In the second approach, an augmented Lagrangean reformulation is done; we use exponential and quadratic penalty functions, respectively. Our numerical results are better than those obtained earlier with less advanced methods.