Impedance control as an optimal control problem: a novel formulation of impedance controllers as a subcase of optimal control

A formulation of impedance control for redundant manipulators is presented here as a particular case of an optimal control problem. This allows the design of an impedance controller that benefits from the stability and efficiency of an optimal controller. To circumvent the high computational costs of finding optimal controllers, a suboptimal feedback controller based on state-dependent Riccati equations (SDRE) is developed. This approach is compared with the quadratic programming (QP) formulation, commonly used to solve redundancy of robotic manipulators. Numerical simulations of a redundant planar four-DOF serial-link manipulator show that the SDRE controller offers superior performance over the QP one in terms of stability, performance and required control effort.