Barrier Lyapunov Function Based Control of a Flexible Link Co-Robot With Safety Constraints

In this paper, a control design for a flexible link co-robot with safety constraints is proposed. The safety constraints are converted to the constraints on the tip position and velocity. To handle this constrained control problem, a barrier Lyapunov function (BLF) is employed in the control design. The derivative of the logarithmic BLF is more complicated compared with the derivative of a quadratic Lyapunov function, which makes the problem of “explosion of terms” more serious. Thus, the dynamic surface control is used to deal with the problem. Furthermore, an extended state observer is adopted to estimate and compensate the uncertainty and disturbance in the system. The stability analysis via the singular perturbation theory shows the local practical exponential stability of the system. Simulation results indicate that the control performance is guaranteed without violation of the constraints.