IEEE Robotics & Automation Magazine - March 2014 - 78

ON THE SHELF

Underactuated Mechanical Systems

Analysis and Control of
Underactuated Mechanical
Systems
A. Choukchou-Braham, B. Cherki,
M. Djemai, and K. Busawon, Springer,
New York, 2014, 138 pages.
nalysis and Control of Underactuated Mechanical Systems is a
timely book. Currently, there
are several major research
projects in robotics aimed at creating
better solutions to the problem of locomotion. One of the major challenges is
the underactuated nature of locomotion
systems. Another challenge is the broad
and often seemingly unsystematic
nature of not only the problem but also
the literature. The authors attempt to
deal with these issues.
The book consists of five chapters
and four appendixes. Each chapter ends
with many excellent references. The first
chapter is an introduction and historical
literature review. There have been few
attempts like this to assemble the literature and present a systematic framework
for the control of underactuated
mechanical systems (UMSs). Although
this chapter does not cover all of the vast
number of techniques that are available,
it does provide many references for
those not described. The focus is mainly
on unified frameworks that include
nonlinear deterministic approaches.
The second chapter covers generalities and the state of the art on the control of UMSs. It discusses in depth the
concept of what it means to be underac-

Digital Object Identifier 10.1109/MRA.2014.2299502
Date of publication: 10 March 2014

IEEE ROBOTICS & AUTOMATION MAGAZINE

tuated (essentially a system possessing
more degrees of freedom to be controlled than there are control inputs),
and what the potential sources of
underactuation can be.
Typically UMSs not only render
many well-known results and properties for analysis and control invalid but
also exhibit undesirable properties such
as nonminimum phase behavior. The
authors do a good job of pointing out
known characteristics that are helpful,
such as the fact that UMSs do not satisfy
a known necessary condition for the
existence of smooth time-invariant
feedback stabilization.
After discussing how challenging
and interesting these types of systems
can be, the authors present an overview
of several methods of control, such as
energy based (swing the system up into
a linear region then switch to a linear
controller), passivity based (swing into a
desirable orbit then switch), outputfeedback, feedforward, small gains synthesis, and sliding mode control.
The authors state that since UMSs
are so varied in type, and are typically
addressed on a case-by-case basis,
this book attempts to present a means
by which to look for common patterns and determine what appropriate
control method should be applied
rather than outlining every possible
controller. The classification of the
problem is a key step, and this chapter introduces the two main classifications: the control flow diagram
(CFD) methods of Seto and John
Baillieul and the analytical methods
of Reza Olfati-Saber.

MARCH 2014

Before the classifications can be
presented in detail, UMSs must be
described carefully. The third chapter
presents UMSs from the Lagrangian
formalism. The authors state that two
major advantages of the Euler-
Lagrange formulation are 1) the resulting equations are invariant and 2) they
allow one to compute the evolution of
mechanical systems as a result of
applied forces. The equations are first
derived for fully actuated mechanical
systems, then for UMSs, and finally a
comparison with nonholonomic systems is drawn. The chapter then
describes the various forms of partial
linearization that are applicable to
UMSs and finishes with common cases
(the inverted cart-pendulum, acrobot,
and several others).
The fourth chapter details the two
main methods for classifying the
UMSs and explores the possibility of a
link between them. The key steps of
each method are laid out, and several
examples are provided, further aiding
in cementing the reader's understanding. For example, the CFD method
classifies every UMS into a combination of a tree structure, chain structure,
or isolated vertex. The authors provide
a balance of mathematical development with clear explanation so that the
reader is not overloaded. Ultimately,
the two classification systems are
determined to be independent but parallel tools.

(continued on p. 87)

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2014