Robots can be characterised as systems which exist in a multidimensional
<i>configuration space</i>, whose structure is extremely complex, especially
since additional dimensions have to be introduced to allow for engineering
tolerances. We have adopted a 2-stage approach to the representation of
this spece (i) a nominal phase characterised by the topological structure
of the Euclidean group discussed above, which identifies <i> critical
points</i> in a planned action where an analysis of the consequences of
possible errors is required (ii) a capability for the analysis of the
local structure of configuration space around the critical points, which
allows us to predict what error-states can actually occur, and determine
strategies for achieving teleological transitions.