Abstract
A framework is presented that uses the same strategy to solve both the learned navigation and terrain model acquisition. It is shown that any abstract graph structure that satisfies a set of four properties suffices as the underlying structure. It is also shown that any graph exploration algorithm can serve as the searching strategy. The methods provide paths that keep the robot as far from the obstacles as possible. In some cases, these methods are preferable to visibility graph methods that require the robot to navigate arbitrarily close to the obstacles, which is hard to implement if the robot motions are not precise.