Torque-Bounded Admittance Control With Implicit Euler Realization of Set-Valued Operators

When a robot collides with environments of unknown stiffness, the resultant torque saturation can cause the conventional admittance control to exhibit unsafe behaviors such as large resilience force, oscillation, and snapping back. To address this challenge, this article proposes a novel torque-bounded admittance control algorithm that can quickly stabilize the robot to maintain a safe and compliant contact force, while also guaranteeing position tracking accuracy in free space. The new controller consists of two set-valued loops, which can be mathematically described by a differential algebraic inclusion (DAI). The first loop is constructed using the proxy system of conventional admittance control, but it is subjected to a set-valued nonsmooth operator that constrains the output force. The second loop is realized by a set-valued sliding mode control (SMC), which serves as the internal position controller that interacts with unknown environments of different stiffness. To enable the DAI to be implementable in digital environments, this article also provides an implicit-Euler discretization method for the two set-valued operators. The proposed admittance controller is validated by numerical simulations and comparative experiments with the Kinova Gen3 manipulator equipped with a force/torque sensor.