Page 73 - Rapid Learning in Robotics

4.5 Basis Function Sets, Choice and Implementation Aspects 59

if i i
Q i
l i s A
Q i d i else
l if i i

i Q i S i

s Q i S i d i else

Q i S S i

l i i if i i
h i

s
Q i S i S i d i S i else

using: d i s a i

Y Y
C i a i a j const Q i d j
j i C i j i i

X X
S i
S i
j i i d j j i i d j
(4.24)
The interim quotients Q i and sums S i and S i are efficiently gener-
ated by defining the master product Q i (and sums S i respectively) and

working out the specific terms via “synthetic division” and “synthetic sub-
traction” for all i i

Q i
Q i , S i S i , and S i S i (4.25)
d i d i d i
Computing H a s and its derivatives is now a matter of collecting the
proper pre-computed terms.

H a s Q m l i s A

a s H l i s A if

Q m
s

s l i s A else

(4.26)

l i s A if

H a s
s

Q m l i s A if and

s
s

l i s A else

s