On the gyroscopic force in mechanical manipulators and its artificial shaping for taskspace movement coordination

Abstract

In this paper, we try to draw attention to a particular type of force that has been somehow overlooked in the control of mechanical manipulators: gyroscopic force. At first, we broaden our understanding of gyroscopic effect intrinsic in mechanical systems by reformulating the Euler-Lagrange (EL) equation in terms of a gyroscopic part and the non-gyroscopic ones (or Rayleigh type). Then, we propose the use of artificial gyroscopic force to assist existing control laws. As a force that does not do any work, the gyroscopic force can be effectively used in combination with many existing control laws for mechanical systems without affecting their salient features such as the stability or the convergence to a target point. As a specific example, we look into the potential energy shaping parameterized by taskspace variables (also known as the Jacobian transpose method) as a base control law, and combine it with an artificial gyroscopic forcing term. We propose one specific way to design the gyroscopic force as a term quadratic in velocity that operates in reference to a desired velocity field shape (also parameterized in taskspace). The resulting control strategy enables us to shape the intermediate path profiles and thus realizes a taskspace control law that is free from any inverse transformations. We demonstrate the effectiveness of this method using simulation results with a three-link planar manipulator.