Solving open polygonals in elastic correction of dead-reckoning errors

A major problem in map building is due to the imprecision of sensor measures. In a previous paper we proposed a technique, called elastic correction, for correcting the dead-reckoning errors made during the exploration of an unknown environment by a robot capable of identifying landmarks. Elastic correction is based on an analogy between the relational graph modelling the environment and a mechanical structure: the map is regarded as a truss where each route is an elastic bar and each landmark a node; errors are corrected as a result of the deformations induced from the forces arising within the structure as inconsistent measures are taken. The main weakness of this method lies in the way positional inconsistencies are solved when routes are covered for the first time. In this paper we improve first-sight elastic correction by replacing the heuristics previously adopted with a new approach which considers all the knowledge of the surrounding map acquired so far; this is achieved by calculating the minimum forces to be applied in order to restore metric consistency. The effectiveness of the new approach is demonstrated by presenting some experimental tests.