Operational Space Control Under Actuation Constraints Using Strictly Convex Optimization

Operational space feedback controllers can be used for tracking, motion coordination, stabilization, and a variety of other practical tasks. However, classical operational space controllers are only applicable to fully actuated robots and do not take into account fundamental physical limitations affecting the actuators in practical application. Here, we present an online computable operational space controller that extends to underactuated and overactuated systems, and which takes actuator limitations rigorously into account. In the proposed formulation, the control inputs are computed using constrained quadratic programs that have the minimal number of decision variables, and are strictly convex by construction. The resulting feedback controller is efficiently computable, and is applicable to fully actuated, underactuated, and overactuated systems. This is demonstrated via numerical simulations and experiments using two torque controlled robots.