Trajectory tracking control of three-DOF planar under-actuated manipulator
Liu Shengping1, Wu Licheng2, Lu Zhen1*
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. State Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China
The trajectory tracking control of a three-link planar under-actuated manipulator was presented. The third joint of the manipulator was passive. The dynamic constraint on the free link was shown to be second-order nonholonomic. Motion equations of the system were transformed into high order chained form using some global coordinate and input changes. A time-varying feedback controller was proposed to force the under-actuated manipulator to globally asymptotically track a reference trajectory. The control development was based on the current popular integrator backstepping technique. The method breaks down nonlinear system into low dimensional systems and simplifies the controller design using virtual control inputs and partial Lyapunov functions. Simulation results show the system can stably converge to a desired trajectory and demonstrate the effectiveness of the proposed control law.