This monograph provides readers with tools for the analysis, and control
of systems with fewer control inputs than degrees of freedom to be
controlled, i.e., underactuated systems. The text deals with the
consequences of a lack of a general theory that would allow methodical
treatment of such systems and the ad hoc approach to control design that
often results, imposing a level of organization whenever the latter is
lacking.
The authors take as their starting point the construction of a graphical
characterization or control flow diagram reflecting the transmission of
generalized forces through the degrees of freedom. Underactuated systems
are classified according to the three main structures by which this is
found to happen-chain, tree, and isolated vertex-and control design
procedures proposed. The procedure is applied to several well-known
examples of underactuated systems: acrobot; pendubot; Tora system; ball
and beam; inertia wheel; and robotic arm with elastic joint.
The text is illustrated with MATLAB(R)/Simulink(R)
simulations that demonstrate the effectiveness of the methods detailed.
Readers interested in aircraft, vehicle control or various forms of
walking robot will be able to learn from Underactuated Mechanical
Systems how to estimate the degree of complexity required in the
control design of several classes of underactuated systems and proceed
on to further generate more systematic control laws according to its
methods of analysis.
