Spong94

Spong94 - Partial Feedback Linearization of Underactuated...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Partial Feedback Linearization of Underactuated Mechanical Systems * Mark W. Spong Coordinated Science Labor at ory University of Illinois at Urbana-Champaign 1308 W. Main St., Urbana, IL 61801 Abstract things as actuator dynamics in the model description. In this paper we discuss .the partial feedback lin- earization control of underactuated mechanical sys- tems. We consider an n degree of freedom system having m actuated, or active, degrees of freedom and B = n - m unactuated, or passive, degrees of freedom. It is known that the portion of the dynamics corre- sponding to the active degrees of freedom may be lin- earized by nonlinear feedback. In this paper we show, alternatively, that the portion of the dynamics corre- sponding to the passive degrees of freedom may be lin- earized by nonlinear feedback under a condition that we call Strong Inertial Coupling. We derive and ana- lyze the resulting zero dynamics which are crucial to an understanding of the response of the overall system. Simulation results are presented showing the perfor- mance of two link underactuated robots under partial feedback linearization control. 1 Introduction Underactuated mechanical systems are mechanical systems with fewer actuators than degrees-of-freedom and arise in several ways, from intentional design in the brachiation robot of Fukuda [13] or the Acrobot [2], in mobile robot systems when a manipulator arm is attached to a mobile platform, a space platform, or an undersea vehicle, [8], or because of the mathematical model used for control design when joint flexibility is included in the model [14]. In the latter sense, then, all mechanical systems are underactuated if one wishes to control flexible modes that are not directly actuated (the noncollocation problem), or even to include such Our main interest in this paper is the control of gymnast type robots like the Acrobot [2], and the three-link gymnast robot in [17]. We will show that the method of partial feedback linearization [7] and the recent method of integrator backstepping [9] pro- vide effective design tools for controlling such robots to perform various motions. It has long been known [16] that fully actuated robots are feedback linearizable by nonlinear feedback. For underactuated robots it is known that the portion of the dynamics corresponding to the actuated (or ac- tive) degrees of freedom may be linearized by nonlinear feedback[5]. The remaining portion of the dynamics after such partial feedback linearization is nonlinear and represents internal dynamics. In this paper we show that, under a condition which we call Strong In- ertial Coupling, it is alternatively possible to linearize the portion of the dynamics corresponding to non- actuated (or passive) degrees of freedom. .This some- what surprising result is quite interesting and, roughly speaking, means for a system with m actuators, that m of the equations of motion may be linearized whether or not they are directly actuated. We will show how these results may be used to control underactuated robots performing gymnastic type motions.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

Spong94 - Partial Feedback Linearization of Underactuated...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online