This paper presents a new parallel algorithm for collision-free path planning of a diamond-shaped robot among arbitrarily shaped obstacles, which are represented as a discrete image, and its implementation in VLSI. The proposed algorithm is based on a retraction of free space onto the Voronoi diagram, which is constructed through the time evolution of cellular automata, after an initial phase during which the boundaries of obstacles are identified and coded with respect to their orientation. The proposed algorithm is both space and time efficient, since it does not require the modeling of objects or distance and intersection calculations. Additionally, the proposed twodimensional multistate cellular automaton architecture achieves high frequency of operation and it is particularly suited for VLSI implementation due to its inherent parallelism, structural locality, regularity, and modularity.