Linear Quadratic Frequency-Shaped Implicit Force Control of Flexible Link Manipulators

Abstract

An implicit force control scheme for flexible link manipulators is considered in this article. The control output is composed of a feedforward and a feedback term. The feedforward torque component compensates the underlying rigid arm dynamics along the desired trajectory. The feedback component regulates the joint coordinate error perturbations. The minimization of a linear quadratic frequency-shaped cost functional yields the time-varying feedback controller gains. The frequency shaping dependence is included to eliminate undesirable effects associated with control and observation spillover. The proposed control scheme is employed in simulation studies on a two link rigid-flexible manipulator. Sufficient conditions for spatial tracking bounds and temporal gain switching bounds for the linearized rigid body error dynamics are provided. The effects of the linearized unmodelled error dynamics related to the flexible states on these bounds are also examined.