Optimal Hypercube Algorithms for Robot Configuration Space Computation

Computing the configuration space is an important problem in spatial planning for robotics applications. In this paper, we present parallel algorithms for computing the configuration space by using hypercube multiprocessors. The digitized images of the obstacles and the robot are stored in an N×N image plane. In this paper, we develop optimal hypercube algorithms to compute the configuration space for circle and rectangle shaped robots. We also develop several new basic hypercube operations. The time complexity of all the algorithms is O (logN) and is asymptotically optimal for hypercube computers. The space complexity of each processor is O (1) which is again optimal