Estimating Configuration Space Belief from Collision Checks for Motion Planning

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.