On goal recognizability in motion planning with uncertainty

Motion planning with uncertainty in control and sensing raises two basic issues, goal reachability and goal recognizability, which subtly interact. A partial analysis of this interaction is presented here. It is shown that the capability of a motion command to recognize goal achievement is augmented by providing the termination condition of the motion command with the knowledge of the region in which the motion command is known to start (initial state) and the knowledge of the termination condition itself (final state). The increase in the recognition power of the termination condition is illustrated with a simple preimage construction example. The size of the preimage grows when one adds the initial and the final states in the knowledge of the termination condition. Although preliminary, these results are expected to eventually help design more powerful motion planners in the presence of uncertainty.