On the moving-obstacle path-planning algorithm of Shih, Lee, and Gruver

We analyze a motion planning algorithm proposed by Shih, Lee, and Gruver (1990). In particular, we discuss the case of motion planning among moving obstacles, for which an algorithm is presented by Shih, Lee, and Gruver (1990). The algorithm is claimed to always yield a collision-free path when one exists. We provide a specific counter-example to this claim, examine the possibility of repairing the algorithm, and discuss the computational complexity of a corrected algorithm.