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arXiv · 2108.07625

Hybrid dynamical type theories for navigation

Paul Gustafson·Jared Culbertson·Daniel E. Koditschek
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Abstract

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.

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Paul Gustafson, Jared Culbertson, Daniel E. Koditschek. 2021-08-17. Hybrid dynamical type theories for navigation. https://arxiv.org/abs/2108.07625

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