Mutually visible agents in a discrete environment

As computer controlled entities are set to move and explore more complex environments they need to be able to perform navigation tasks, like finding mini-mal cost routes. Much work has been done on this problem with a single entity in a continuous environ-ment. However these entities may be in teams and their actions may be constrained by the need to con-sider the actions of other entities. We consider the case of two entities wishing to reach their destinations while travelling the minimum distance and remain-ing in sight of each other. A version of this problem in continuous space has been addressed previously; however, the problem of minimum length paths does not only exist in continuous space. Robots may have restricted orientations in movement. Also, domains such as circuit design and computer games require discrete movements and restricted orientation. The restricted orientation and the fact that (even in genus zero environments) minimal length paths may not be unique present some challenges. This paper investi-gates the problem of two entities in a discrete setting, moving to preserve visibility and provides algorithms for computing schedules that minimise the total dis-tance travelled.