A linear-time algorithm for computing collision-free path on reconfigurable mesh

The reconfigurable mesh (RMESH) is an array of mesh-connected processors equipped with a reconfigurable bus system, which can dynamically connect the processors in various patterns. A 2D reconfigurable mesh can be used to solve motion planning problems in robotics research, in which the 2D image of robot and obstacles are digitized and represented one pixel per processor. In this paper, we present an algorithm to compute a collision-free path between two points in an environment containing obstacles. The time complexity of the algorithm is O(k)O(k) for each pair of source/destination points, with O(log2N)O(log2N) preprocessing time, where k is the number of obstacles in the working environment, and N is the size of the reconfigurable mesh.