A geometric optimization method for the trajectory planning of flexible manipulators

Lightweight and flexible robots offer an interesting answer to industrial needs for safety and efficiency. The control of such systems should be able to deal properly with the flexible behavior in the links and the joints. In this paper, a feedforward control action is computed by solving the inverse dynamics of the system. Flexibility in the system is modeled using finite elements formulated in the local frame. The inverse problem is then solved using a constrained optimization formulation. This local frame representation reduces the nonlinearity in the equations of motion and improves the convergence of the numerical scheme. To illustrate the method, numerical examples of a serial and a parallel 3D robot are shown.