Using Rigid Landmarks to Infer Inter-Temporal Spatial Relations in Spatio-Temporal Reasoning

Abstract: Spatio-temporal reasoning is the area of automated reasoning about space and time and is important in the field of robotics. It is desirable for an autonomous robot to have the ability to reason about both time and space. ST0 is a logic that allows for such reasoning by, among other things, defining a formalism used to describe the relationship between spatial regions and a calculus that allows for deducing further information regarding such spatial relations. An extension of ST0 is ST1 that can be used to describe the relationship between spatial entities across time-points (inter-temporal relations) while ST0 is constrained to doing so within a single time-point. This allows for a better ability of expressing how spatial entities change over time. A major obstacle in using ST1 in practise however, is the fact that any observations made regarding spatial relations between regions is constrained to the time-point in which the observation was made, so we are unable to observe inter-temporal relations. Further complicating things is the fact that deducing such inter-temporal relations is not possible without a frame of reference. This thesis examines one method of overcoming these problems by considering the concept of rigid regions which are assumed to always be unchanging and using them as the frame of reference, or as landmarks. The effectiveness of this method is studied by conducting experiments where a comparison is made between various landmark ratios with respect to the total number of regions under consideration. Results show that when a high degree of intra-temporal relations are fully or partially known, increasing the number of landmark regions will reduce the percentage of inter-temporal relations to be completely unknown. Despite this, very few inter-temporal relations can be fully determined even with a high ratio of landmark regions.