Navigation with Probabilistic Safety Constraints: Convex Formulation

TL;DR

This paper introduces a convex optimization framework for navigation problems with probabilistic safety constraints, utilizing dual space density lifting and data-driven transfer operator approximations.

Contribution

It presents a novel convex formulation for probabilistic safety-constrained navigation using linear transfer operator theory and finite-dimensional approximations.

Findings

Convex formulation enables efficient safety verification and control design.

Dual space density lifting facilitates handling probabilistic safety constraints.

Data-driven approximation makes the approach practical for real-world applications.

Abstract

We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The deterministic unsafe set will arise as a particular case of the proposed probabilistic description of safety. We provide a convex formulation to the navigation problem with probabilistic safety constraints. The convex formulation is made possible by lifting the navigation problem in the dual space of density using linear transfer operator theory methods involving Perron-Frobenius and Koopman operators. The convex formulation leads to an infinite-dimensional feasibility problem for probabilistic safety verification and control design. The finite-dimensional approximation of the optimization problem relies on the data-driven approximation of the linear transfer operator.