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3.7 Summary 161

3.7 Summary

In this chapter we have laid the foundation for a study of robot control systems.
Using Lagrangian mechanics in Section 3.2, we derived the dynamics of some
robot arms that will be used for demonstration designs throughout the text.
We provided expressions for the general robot arm dynamics for any serial-
link arm.
In Section 3.3 we studied the properties of the robot dynamics such as
boundedness, linearity in the parameters, and skew symmetry that are needed
in controls design. Table 3.3.1 gives a summary of our findings. We used a
Kronecker product approach that yields great insight into the relations between
the terms in the robot equation.
A vital form in modern control systems design is the state-variable
formulation. In Section 3.4 we derived several state-space forms of the arm
dynamics, setting the stage for several design techniques to be provided in
subsequent chapters. The state formulation is also useful in computer simulation
of robot controllers, as we see in Section 3.3.
The dynamics in Cartesian form were given in Section 3.5. The dynamics
of the actuators that drive the robot manipulator links were analyzed and
included in Section 3.6.

Copyright © 2004 by Marcel Dekker, Inc.