Robot Modeling and Control, 2nd Edition

CHAPTER 13UNDERACTUATED ROBOTS

13.1 Introduction

In this chapter we consider the control of an important class of robots known as underactuated robots. By an underactuated robot, or more generally an underactuated mechanical system, we mean one in which the number of independent control inputs is fewer than the number of generalized coordinates.

Underactuation arises in several ways, for example, from intentional design as in the so-called Acrobot and Pendubot described below, in which one or more of the joints are unactuated, or it may arise because of the mathematical model used for control design, such as when joint flexibility is included in the model. In the previous chapter we discussed the control of n-link flexible-joint robots, which have 2n degrees of freedom and n control inputs and hence fall into the class of underactuated robots.

Systems with unilateral constraints or nonholonomic constraints are also often underactuated. For example, in legged locomotion, the contact between the foot and the ground represents a unilateral constraint and is unactuated. Walking robots are therefore inherently underactuated. Wheeled robots, swimming robots, space robots, and flying robots are all examples of underactuated robots.

The class of underactuated robots is thus large and complex and the control problems are more difficult than for fully-actuated robots. As we saw in previous chapters, fully actuated robots possess a number of strong properties that facilitate control design. ...