  For motion planning in high dimensional configuration spaces, a significant
computational bottleneck is collision detection. Our aim is to reduce the
expected number of collision checks by creating a belief model of the
configuration space using results from collision tests. We assume the robot's
configuration space to be a continuous ambient space whereby neighbouring
points tend to share the same collision state. This enables us to formulate a
probabilistic model that assigns to unevaluated configurations a belief
estimate of being collision-free. We have presented a detailed comparative
analysis of various kNN methods and distance metrics used to evaluate C-space
belief. We have also proposed a weighting matrix in C-space to improve the
performance of kNN methods. Moreover, we have proposed a topological method
that exploits the higher order structure of the C-space to generate a belief
model. Our results indicate that our proposed topological method outperforms
kNN methods by achieving higher model accuracy while being computationally
efficient.
