Torque-Bounded Admittance Control Realized by a Set-Valued Algebraic Feedback

Abstract

This paper proposes a new admittance controller that realizes safe behavior even under torque saturation. The new controller is analytically equivalent to a conventional admittance controller as long as the actuator torque is not saturated, but is free from unsafe behaviors such as snapping back, oscillation, or overshoots, which may happen with conventional admittance controllers after torque saturation. The new controller is described by a differential algebraic inclusion, and can be understood as a conventional admittance controller expanded with an additional algebraic loop through a normal-cone operator. Its continuous-time representation involves a nonsmooth, set-valued function, but its discrete-time implementation is free from set-valuedness and given as a closed-form algorithm as a result of the use of implicit (backward) Euler discretization. The controller is tested with one joint of an industrial manipulator equipped with a force sensor.