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140 Robot Dynamics

d. The Robot Function Parameter Matrix W

The robot dynamics are linear in the parameters. For the purposes of adaptive
control, one should select the parameter vector ϕ in Table 3.3.1 so that it
contains the unknown parameters.
The dynamics, including friction, can be written as

The second mass m 2 includes the mass of the payload. This and the friction
coefficients are often unknown. Therefore, select

Then the matrix W(q, , ) of known robot functions becomes

with

Copyright © 2004 by Marcel Dekker, Inc.