Design and analysis of energy-based controller for 3-link robots with a single actuator

For a 3-link planar robot moving in the vertical plane with a single actuator, this paper studies the effect of its actuator configuration from the perspective of the energy-based control. For the control objective of simultaneous stabilization of the actuated variable and of the desired level of the total mechanical energy of the robot corresponding to those of the upright equilibrium point, where all three links of the robot are in the upright position, this paper presents an energy-based controller for three configurations of the single actuator in a unified way. Moreover, this paper carries out a global motion analysis of the robot with a single actuator at joint 1 or 2 under the presented controller. Specifically, this paper shows that the control objective is achievable for the robot with the actuator at joint 1 for almost all initial conditions of angular displacements and velocities without any condition on the mechanical parameters of the robot, and the control objective is achievable for the robot with the actuator at joint 2 for almost all initial conditions provided that another condition on the mechanical parameters of the robot is satisfied. The numerical simulation shows that the presented control can be applied to the swing-up and stabilizing control for a physical 3-link robot with a single actuator at joint 1 or 2.