2-Link Underactuated Robot with Flexible Elbow Joint

Abstract

This chapter concerns a set-point control problem for a 2-link underactuated robot moving in the vertical plane with a single actuator at the first joint and a spring between the two links (flexible elbow joint). First, it presents two new properties of such a flexible robot about the linear controllability at the upright equilibrium point (where two links are in the upright position) and about its equilibrium configuration. Second, it shows that for the robot with a certain range of spring constant, the PD control on the angle of the first joint can globally stabilize the robot at the upright equilibrium point. Third, for the robot not satisfying the above range of spring constant, it studies how to extend the energy-based control approach to design a swing-up controller. This chapter provides a necessary and sufficient condition for avoiding the singularity in the swing-up controller, and analyzes the motion of the robot under the presented controller by studying the convergence of the total mechanical energy and clarifying the structure and stability of the closed-loop equilibrium points. It presents numerical simulation results to validate the obtained theoretical results.