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4.3 Computer Simulation of Robotic Systems 181
4.3 Computer Simulation of Robotic Systems
It is very important to simulate on a digital computer a proposed manipulator
control scheme before actually implementing it on an arm. We show here
how to perform such computer simulations for robotic systems. Since most
robot controllers are actually implemented in a digital fashion (Section 4.5),
we also show how to simulate digital robot arm controllers.
Simulation of Robot Dynamics
There is a variety of software packages for the simulation of nonlinear
dynamical systems, including SIMNON [Åström and Wittenmark 1984],
MATLAB, and others. For convenience, we include in Appendix B some
simulation programs that are quite useful for continuous and digital control.
All simulation programs require the user to write similar subroutines. Time
response simulators that use integration routines such as Runge-Kutta all require
the computation of the state derivative given the current state. In Section 3.4
we saw how to represent the robot arm equation
(4.3.1)
in the nonlinear state-space form
(4.3.2)
with x(t) the state and u(t) the input.
.
T
Defining a state as x=[q q ] , we may write the implicit form
T T
(4.3.3)
with τ the arm control torque that is provided by the controller and τ d the
disturbance torque. We say that this is an implicit form since the coefficient
matrix of the left-hand side means that is not given
explicitly in terms of the right-hand side.
Given x(t), it is necessary to provide a subroutine for the integration program
that computes (t). One approach to solving for is to invert M(q). However,
due to potential numerical problems this is not recommended. Let us represent
(4.3.3) as
(4.3.4)
Note that in this case u(t) is the vector composed of the controls (t) and the
disturbances d(t).
Copyright © 2004 by Marcel Dekker, Inc.