Spatio-geometric impedance control of Gough-Stewart platforms

This paper looks at the control of mechanical impedance of the so-called Gough-Stewart class of parallel platforms. Two methods of compliance control are presented. One is based on global potential energy functions that have previously been applied to controlling serial manipulators and electrodynamically levitated platforms. The second method uses the exponential map to associate finite displacements of the platform from equilibrium with twist displacements. Compliant wrenches are then proportional to the twist displacements. Control of spatial damping is addressed as well, justifying the classification as impedance control. Control algorithms and simulation results are given.