Observability Conditions and Sensing Quality for Unicycle Systems with Constant External Forcing

TL;DR

This paper analyzes the observability conditions and sensing quality of unicycle systems under constant external forcing, providing analytical criteria and empirical methods for sensor selection and motion planning.

Contribution

It introduces analytical observability conditions for unicycle systems with external forcing and combines them with empirical Gramian analysis for sensor and motion optimization.

Findings

Derived necessary measurement conditions for observability.

Quantified sensing quality using empirical Gramian.

Provided guidelines for optimal sensor placement and motion modes.

Abstract

In certain systems which are subject to significant constant external forcing such as an airplane in wind or an underwater glider in ocean currents, the ability to detect the forcing depends on both the measurements available and whether appropriate control is being applied. Using analytical nonlinear observability techniques, we define the necessary characteristics required of a measurement function for systems with unicycle dynamics subject to constant forcing to be observable. We further consider the necessary associated motion characteristics required of this class of systems to enable the desired sensing capabilities. We then apply these results in combination with the empirical Gramian to quantify relative observability, optimal sensor selection, and sensing quality for different motion primitive modes for a Dubins path.