n-Link Planar Robot with Single Passive Joint

Abstract

This chapter concerns the swing-up control of an n-link revolute planar robot with any one of the joints being passive. The goal is to design and analyze a swing-up controller that can bring the robot into any arbitrarily small neighborhood of the upright equilibrium point, where all the links are in the upright position. This chapter presents a unified solution based on the notion of virtual composite link (VCL), which is a virtual link made up of one or more active links. By using the angles of two series of VCLs separated by the passive joint and using the total mechanical energy of the robot, this chapter designs a swing-up controller and analyzes the global motion of the robot under the controller. This chapter presents a lower bound for each control gain related to the angle of each VCL such that the closed-loop system has only one undesired equilibrium point in addition to the upright equilibrium point, and presents an original proof of the conditions on the control gains for a class of n-link underactuation-degree-one planar robots with an active first joint. This chapter provides a bigger control gain region for achieving the control objective than those of previous results on 3- and n-link robots with a passive first joint.