Biomimetic Robotics - Engineered Biomimicry - page 90

robotic manipulators: (1) point-to-point motion
control, and (2) motion control with prescribed
path tracking. Kahn and Roth [23] were the
first to propose an optimal control for a robotic
manipulator that belonged to the point-to-point
control category and was based on the local lin-
earization of the robot dynamics.
The motion-control problem with prescribed
path tracking requires a path to be specified and
is related to the general problem of path plan-
ning. Both motion-control approaches can be
implemented by the use of optimal control
methods, which could also be classified into two
broad groups: (1) methods based on the solution
of the Hamilton-Jacobi-Bellman equation or
nonlinear programming, and (2) methods based
on reduction of the solution to a two-point
boundary value problem. The latter class of
optimal controllers can yet again be classified
into two groups based on the nature of the con-
trol: (2a) on-off or bang-bang control or time-
optimal control, or (2b) continuous feedback
quadratic cost-optimal control.
Time-optimal control methods were initiated
in the mid-1980s by Bobrow et al . [24] and Shin
and McKay [25] , and efficient algorithms for
bang-bang (time-optimal) control were pro-
posed by Pfeiffer and Johanni [26] and Shiller
[27] . Chen and Desrochers [28] were able to
prove that that the time-optimal control prob-
lem is really a bang-bang solution. Bobrow et al .
[29] , Bien and Lee [30] , and Chen [31] dealt with
multiple manipulator arms. More recent efforts
have been focused on the application of state
and control constraints.
The application of evolutionary optimal
methods and learning and adaptive strategies
to time-optimal control have also been exten-
sively pursued. For example, Arimoto et al . [32]
introduced the concept of iterative learning
control; Berlin and Frank [33] applied the con-
cept of model predictive control to a robotic
manipulator. There are also several other evo-
lutionary techniques based on the use of fuzzy
sets, genetic algorithms, and neural networks

that seek control laws that ensure optimal per-
formance. The application of dynamic program-
ming methods to robotic manipulators was also
initiated in the 1980s, although the design of
optimal trajectories was done in the 1970s.
One of the most well-known robot control
schemes that emerged in the 1980s is the computed-
torque control method, which involves the
computation of the appropriate control torques
and forces based on the robot dynamics, using (1)
the sensed and estimated values of the generalized
coordinates and velocities, and (2) the estimated
values of the generalized accelerations. When the
robotic manipulator dynamics and the loads are
precisely known and if the sensors and actuators
are error-free and the environment is noise-free,
the computed-torque control method assures
that the trajectory error goes to zero. Gilbert and
Ha [34] have shown that the computed-torque
control method is robust to a small modeling
error. Moreover, the control law has the structure
of a nonlinear-feedback control law.
The computed-torque control method natu-
rally led to the use of quadratic cost-optimal con-
trol coupled with sensor-based estimation to
generate the feedback control torques, with or
without the use of a prescribed trajectory. This
also led to the development of independent sen-
sor-based quadratic cost-optimal control algo-
rithms for robot manipulators [35] .
The influence of flexibility on robot dynamics
was first considered in the late 1970s and early
1980s (see, e.g., topic [36] ). The inclusion of the
effects of the dynamics of flexibility into the con-
troller design process began shortly thereafter.
The paper by Spong [37] is a good example.
Many control schemes that are extensions of the
control schemes for rigid manipulators, such as
the computed-torque control method [38] , opti-
mal feedback control [39] , and optimal and robust
control [40] , have been successfully proposed to
tackle the modeling and control problems of flex-
ible manipulators. Several new approaches to
modeling [41-44] as well as a number of control-
ler synthesis techniques tailored to flexible robots