Force-Position Exponential Tracking of Redundant Manipulators with Model-Free Sliding PD Control

A passivity-based model-free second order sliding mode controller is proposed for redundant manipulators under holonomic constraints. The closed-loop system enforces exponential tracking on the exerted contact force and the end-effector cartesian position trajectories as the primary task, while the controller reconfigures dynamically the whole kinematic chain in order to satisfy a secondary task through the redundant constrained degrees of freedom. To achieve this, the orthogonalization principle and the proposed redundancy resolution technique, are together synthesized for redundant constrained robots. This way, two pairs of orthogonal subspaces arises, the joint velocity and contact force orthogonal pair, and the end-effector velocity and null space orthogonal pair. Therefore, independent control on the end-effector cartesian position and the exerted contact force can be achieved, while proper control of the null space variables will allow to simultaneously carry out a secondary task, by locally optimizing a given cost function. Simulation results of the 7 degrees of freedom PA10 Mitsubishi robot manipulator performing tracking tasks on the cartesian, force, and null space (redundancy) subspaces are presented.