An Optimal Dynamic Control Method for Robots with Virtual Links

Abstract

Virtual links and virtual joints can be appended to the kinematic chain of a robot arm to assist in modelling and control of certain tasks. Activities such as spray painting, sand blasting, or scanning with a laser or camera can be enhanced by modelling the fluid stream, light beam, or field of view using a virtual link. Virtual joints can be used to allow movement in semi-redundant degrees of freedom of the task space. This can can be exploited to optimize the control of the real robot. A prudent choice is to minimize the effort required by the manipulator to execute the task. This often requires the inversion of the inertia matrix. However, virtual links have no inertia so the inverse does not exist. This paper first explores methods of adding virtual mass or modifying the inertia matrix to allow inversion and the consequences. Then an optimal control problem is proposed that minimizes kinetic energy in the real manipulator and maximizes use of the virtual joints. In doing so, we only need the real inertia matrix which is always invertible. The method is validated in a case study for high pressure water blasting. It is shown to reduce the dynamic torque norm compared to a minimum velocity controller.