Incorporating Compositions in Qualitative Approaches

Qualitative approaches to various tasks, ranging from localization and mapping to active planning, are gaining considerable momentum in recent years. These approaches represent the environment through spatial relationships between small sets of landmarks in independent local coordinate systems. An essential component in these approaches is the composition operator, enabling spatial information propagation between different sets to infer new ones. Integrating compositions within qualitative algorithms brings several difficulties. For instance, if the information required to perform a specific composition operation is unavailable, it must be inferred first, possibly via a preparatory composition operation. This recursive issue becomes more challenging as the amount of information grows. This letter addresses two main questions arising from the above, which remained open: 1. Given an initial set of qualitative spatial relationships, what new ones can be composed? 2. What is the optimal sequence of compositions operations to create a target set among all passible sequences? We provide a theoretical derivation to address the first question and a novel search algorithm to address the second.