— In this paper, we propose a novel path-planning and obstacle avoidance algorithm GODZILA for navigation in unknown environments. No prior knowledge of the environment is required. The path-planning algorithm follows a purely local approach using only the current range sensor measurements at each sampling instant and requiring only a small number of stored variables in memory. No map of the environment is built during navigation. This minimizes the memory and computational requirements for implementation of the algorithm, a feature that is especially attractive for small autonomous vehicles. The algorithm utilizes three components: an optimization algorithm, a local straight-line path planner to visible targets, and random navigation. It is proved, for navigation in any finite-dimensional space, that the pathplanning algorithm converges in finite time with probability