Nonlinear observability of unicycle multi-robot teams subject to nonuniform environmental disturbances
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Nonlinear observability of unicycle multi-robot teams subject to nonuniform environmental disturbances Larkin Heintzman1
· Ryan K. Williams1
Received: 20 August 2019 / Accepted: 9 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this work, we consider the problem of localizing a team of robots, without access to direct pose measurements, under the influence of nonuniform environmental disturbances and measurement bias. Specifically, we are interested in the conditions under which teams remain range-only localizable when the environmental disturbances vary from robot to robot. We approach this problem through nonlinear observability and graph theory. After analyzing the system’s observability properties, we present theorems that identify the structural conditions under which the system maintains local weak observability. We demonstrate that rigid structures are important not only in defining multi-robot interactions, but also in characterizing the influence of nonuniform disturbances. We also give several example systems to cement intuition on the derived conditions. An observability-based planner is then presented that guides a subset of robots toward trajectories that are highly observable through finite-horizon optimization on robot headings. Simulations are then presented, along with an extended Kalman filter for state estimation, and a comparison to previous methods, to corroborate and demonstrate the results derived. Keywords Observability · Nonlinear observability · Estimation · Graph theoretic methods · Rigidity · Networked robotics
1 Introduction Cooperative localization in robotic missions has gained significant interest in recent years, as shown in (Kia et al. 2018; Xia et al. 2017; Rui and Chitre 2010). Indeed, the ability to localize a robot or set of robots is critical for many missions of interest. While the most straightforward solution to localization is to use a global positioning system (GPS), in many cases GPS, or an equivalent, is not available in important robotic applications (Webster et al. 2012; Bayat et al. 2015). A good example of one such application is underwater robotics, wherein every vehicle cannot have access to GPS at all times, environmental disturbances effect vehicle trajectories, and only limited information can be shared between robots (Arrichiello et al. 2013; Glotzbach et al. 2014; Quenzer and Morgansen 2014). Aerial and ground robots, too, must deal with a lack of direct pose measurement and
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Larkin Heintzman [email protected] Ryan K. Williams [email protected]
1
Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
varying environmental disturbances in certain applications, such as indoor drone flight (Chowdhary et al. 2013), bridge inspection via unmanned aerial vehicles (Ellenberg et al. 2016), or ground-based mobile robots with only inter-robot sensing (Roumeliotis and Bekey 2002). Without access to GPS, robots must rely on indirect methods of pose estimation such as range-based navigation (Bahr et
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