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132 Robot Dynamics

(3.3.35)

n
is skew symmetric, so that x Sx=0 for all x R Indeed, according to (3.3.13),
T
(3.3.27) we may define
(3.3.36)

for then the skew-symmetric matrix is nothing but

(3.3.37)

This V m is the standard one used in several modern adaptive and robust
control algorithms, and it is the definition we shall use in the remainder of the
book. Thus we shall write the arm equation either as

(3.3.38)

or

(3.3.39)

Note that it is possible to split V(q, ) into its Coriolis and centripetal
components as

(3.3.40)

where

(3.3.41)

and is (3.3.26) with all the square terms removed [Craig 1988] (see
the Problems).

Componentwise Analysis of . An alternative to the Kronecker product
analysis of the Coriolis/centripetal vector is an analysis in terms of the scalar
components of , which yields additional insight.
In terms of the components m kj(q) of the inertia matrix M(q) we may write
(3.2.38)–(3.2.40) componentwise as

Copyright © 2004 by Marcel Dekker, Inc.