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170 Computed-Torque Control

problem is dealt with in Chapter 7. We will also assume in this chapter that
the robot is a well-known rigid system, thus designing controllers based on a
fairly well-known model. Control in the presence of uncertainties or unknown
parameters (e.g., friction, payload mass) requires refined approaches. This
problem is dealt with using robust control in Chapter 4 and adaptive control
in Chapter 5.
An actual robot manipulator may have flexibility in its links, or compliance
in its gearing (joint flexibility). In Chapter 6 we cover some aspects of control
with joint flexibility.
Before we can control a robot arm, it is necessary to know the desired path
for performing a task. There are many issues associated with the path planning
problem, such as avoiding obstacles and making sure that the planned path
does not require exceeding the voltage and torque limitations of the actuators.
To reduce the control problem to its basic components, in this chapter we
assume that the ultimate control objective is to move the robot along a
prescribed desired trajectory. We do not concern ourselves with the actual
trajectory-planning problem; we do, however, show how to reconstruct a
continuous desired path from a given table of desired points the end effector
should pass through. This continuous-path generation problem is covered in
Section 4.2.
In most practical situations robot controllers are implemented on
microprocessors, particularly in view of the complex nature of modern control
schemes. Therefore, in Section 4.5 we illustrate some notions of the digital
implementation of robot controllers.
Throughout, we demonstrate how to simulate robot controllers on a
computer. This should be done to verify the effectiveness of any proposed
control scheme prior to actual implementation on a real robot manipulator.

4.2 Path Generation

Throughout the book we assume that there is given a prescribed path q d(t) the
robot arm should follow. We design control schemes that make the manipulator
follow this desired path or trajectory. Trajectory planning involves finding
the prescribed path and is usually considered a separate design problem
involving collision avoidance, concerns about actuator saturation, and so on.
See [Lee et al. 1983].
We do not cover trajectory planning. However, we do cover two aspects of
trajectory generation. First, we show how to convert a given prescribed path
from Cartesian space to joint space. Then, given a table of desired points the
end effector should pass through, we show how to reconstruct a continuous
desired trajectory.

Copyright © 2004 by Marcel Dekker, Inc.