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0.2
0.15
0.1
0.05
0
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0.2 0.15 0.1 0.05
0
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(a)
(b)
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0.2 0.15 0.1 0.05
0
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(c)
(d)
Fig. 2.3 An analysis of the domain of attraction for good and bad kernel selection: (a) the
goal image and the contours of the good kernels; (b) the level curves of V for the good kernels.
The + symbols indicate locations at which V 0andthe symbols indicate locations where
V <
0; (c) the goal image and the contours of the bad kernels; and (d) the level curves of V
for the bad kernel with the associated marker for V
to the goal for all the initial condition within the invariant region. This illustrates the
need for a principled approach to kernel selection.
2.3.1.2
Depth
The domain of attraction for the depth motion was as large as the joint limits of
the robot allowed. That is, the Lyapunov function consisted of a convex quadratic
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