TOGGLE PRM: A SIMULTANEOUS MAPPING OF CFREE AND COBSTACLE FOR USE IN PROBABILISTIC ROADMAP METHODS

Motion planning for robotic applications is difficult. This is a widely studied problem in which the best known deterministic solution is doubly exponential in the dimensionality of the problem. A class of probabilistic planners, called sampling-based planners, have shown much success in this area, but still show weakness for planning in difficult parts of the space, namely narrow passages. The problem space is made of two subsets - free space and collision space, representing valid and invalid robot positions. A general method for probabilistic planners is the probabilistic roadmap method (PRM) which maps only free space to find a solution. This thesis proposes a new strategy, Toggle PRM, for probabilistic roadmap planners, which simultaneously maps both free space and collision space in order to guide the solution more efficiently. All sampled robotic configurations are kept in two separate maps. When the connection attempts between configurations in one roadmap fail, the witness to the failure is retained as a configuration in the opposing roadmap. By mapping both spaces, sampling density in narrow passages is greatly increased. A theoretical and experimental analysis of Toggle PRM shows the independence from the volume of a narrow passage and the volume of the obstacles surrounding the passage for sampling, overcoming a previous challenge of probabilistic planning. Additionally, Toggle PRM has increased efficiency as compared to other common sampling techniques in various motion planning problems because of this improved sampling in narrow passages