Analysis of Indistinguishable Trajectories of a Nonholonomic Vehicle Subject to Range Measurements

TL;DR

This paper analyzes the conditions under which a nonholonomic vehicle's trajectory can be uniquely identified using range measurements and control inputs, providing a theoretical framework for localization in planar motion.

Contribution

It introduces a global constructibility analysis for vehicle trajectory localization using range measurements, applicable to various kinematic models including unicycle dynamics.

Findings

Conditions for unique trajectory identification depend on trajectory shape and sensor layout.

Provides local constructibility results for unicycle kinematics.

Framework applicable to a broad class of vehicle models.

Abstract

We propose a global constructibility analysis for a vehicle moving on a planar surface. Assuming that the vehicle follows a trajectory that can be uniquely identified by the sequence of control inputs and by some intermittent ranging measurements from known points in the environment, we can model the trajectory as a rigid body subject to rotation and translation in the plane. This way, the localisation problem can be reduced to finding the conditions for the existence of a unique roto-translation of the trajectory from a known reference frame to the world reference frame, given the collected measurements. As discussed in this paper, such conditions can be expressed in terms of the shape of the trajectory, of the layout of the ranging sensors, and of the numbers of measurements collected from each of them. The approach applies to a large class of kinematic models. Focusing on the special case of unicycle kinematics, we provide additional local constructibility results.