Discrete-time practical robotic control for human–robot interaction with state constraint and sensorless force estimation

Employing a continuous-time control algorithm to control the practical system based on discrete-time digital computer will lead to the cost of performance degeneration. To address this issue, this paper proposes a discrete-time barrier Lyapunov function based controller for human–robot interaction in constrained task space to guarantee control performance. The Euler discrete-time stability of closed-loop system controlled by the proposed method is proved, and a feasible difference scheme to support the stability analysis is uncovered based on monotonic scaling. The parameter dependence of this study is well discussed, which involves sample interval and preset boundary of state constraints, and based on the architecture of barrier Lyapunov function, the dependence relationship is demonstrated by using analytical synthesis technique. With a certain sample interval, the proposal of controller parameters is qualified to guarantee that end-effector states are constrained with preset boundary. The discrete-time neural network estimation is designed to approximate the human being's behavior to rebuild the reference trajectory from the desired trajectory and impedance for smoothing the human–robot interaction. Controlled discrete-time states and estimated force are uniformly ultimately bounded, and the convergence vicinity around the origin is proven to be determined by sample interval, lumped uncertainty and preset boundary of state constraints. Numerical simulation and experimental results verify the effectiveness of proposed discrete-time barrier Lyapunov function based methods.