Discrete-Time Torque-Limited Set-Valued Admittance Control with Semi-Implicit Method

The conventional admittance control is used to regulate robotic systems and ensure they react safely against external contact forces. It does this by suppressing the hardware dynamics of the system during contact with soft environments. However, it has limitations in adapting to unknown environments and can exhibit unsafe behaviors such as snapping back or overshooting when there are changes in the environment. This paper proposes a new admittance controller that not only ensures safe behavior during actuator saturation but also enables safe contact with unknown environments based on stiffness. The new controller consists of two set-valued loops described mathematically by a differential algebraic inclusion (DAI). The first loop uses the proxy system of conventional admittance control but applies a set-valued nonsmooth operation to limit output force magnitude, while the second loop employs a set-valued sliding mode control (SMC) as an internal position controller for interacting with different-stiffness unknown environments. To make DAI implementable in digital environments, this paper provides an algorithm for implicit Euler discretization of DAI. Experimentation using an industrial motor equipped with a force sensor validate the proposed admittance controller compared to conventional admittance control algorithms.