Hybrid dynamical type theories for navigation
This work addresses safety verification for navigation algorithms, but it appears incremental as it builds on existing frameworks and methods.
The authors developed a hybrid dynamical type theory to organize and prove safety properties for navigational control algorithms, applying it to an obstacle-avoiding navigation algorithm as a case study.
We present a hybrid dynamical type theory equipped with useful primitives for organizing and proving safety of navigational control algorithms. This type theory combines the framework of Fu--Kishida--Selinger for constructing linear dependent type theories from state-parameter fibrations with previous work on categories of hybrid systems under sequential composition. We also define a conjectural embedding of a fragment of linear-time temporal logic within our type theory, with the goal of obtaining interoperability with existing state-of-the-art tools for automatic controller synthesis from formal task specifications. As a case study, we use the type theory to organize and prove safety properties for an obstacle-avoiding navigation algorithm of Arslan--Koditschek as implemented by Vasilopoulos. Finally, we speculate on extensions of the type theory to deal with conjugacies between model and physical spaces, as well as hierarchical template-anchor relationships.