Abstract
This paper presents a framework to deal with geometric uncertainties in motion planning for the robots in the vicinity of or in contact with obstacles in their environments. Although geometric uncertainties influence the safeness of the trajectories of the robots in close proximity of obstacles, little attention has been paid to the studies of systematic formalization of geometric uncertainties. Proposed framework utilizes a hierarchical representation: an augmented octree. Octree represents 3-dimensional space by the hierarchy of recursively divided cubes. In order to represent the geometric uncertainties in the object boundaries from the probabilistic point of view, a new concept, occupation probability, is introduced. The occupation probability is defined as the probability that the cube is completely occupied or completely vacant; the spatial uncertainties are expressed by occupation probability values in each octree cube element. Robot trajectories are evaluated by their probability of collision with obstacles. A path planning algorithm to search trajectories by calculating the collision probability is also presented for the purpose of showing the applicability of the proposed framework to motion planning problems.
