Analysis of Obstacle based Probabilistic RoadMap Method using Geometric Probability
This work addresses a specific bottleneck in robot motion planning for narrow passages, but it is incremental as it focuses on evaluating an existing heuristic method.
The paper tackled the problem of probabilistic roadmap planners being ineffective in narrow passages by evaluating the success probability of the OBPRM heuristic using geometric probability theory, finding that the probability of generating free sample points around obstacles is directly proportional to their surface area.
Sampling based planners have been successful in robot motion planning, with many degrees of freedom, but still remain ineffective in the presence of narrow passages within the configuration space. There exist several heuristics, which generate samples in the critical regions and improve the efficiency of probabilistic roadmap planners. In this paper, we present an evaluation of success probability of one such heuristic method, called obstacle based probabilistic roadmap planners or OBPRM, using geometric probability theory. The result indicates that the probability of success of generating free sample points around the surface of the $n$ dimensional configuration space obstacle is directly proportional to the surface area of the obstacles.