A controller design for compliant manipulators modeled with elastic links and joints

A controller for general flexible robotic manipulators is developed. A flexible manipulator system´s dynamics is first transformed into error-driven dynamic equations by nonlinear feedforward and PID feedback loops. The solution is then stabilized asymptotically by using the second method of Lyapunov. Also, the special structure of the problem is exploited to find a closed-form solution to the Lyapunov matrix equation. This explicit solution is studied to assess the influence of Lyapunov function parameters on system response. Analytical results are then tested by numerical simulations which are carried out on a six-link spatial arm. In these simulations one flexible model considers six compliant joints, while another model contains three joint and four link compliance components. Simulation results show successful trajectory tracking and oscillation rejection properties