DGORL Distributed Graph Optimization based Relative Localization of Multi-Robot Systems Ehsan Latif and Ramviyas Parasuraman

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DGORL: Distributed Graph Optimization based

Relative Localization of Multi-Robot Systems

Ehsan Latif and Ramviyas Parasuraman

School of Computing, University of Georgia, Athens, GA 30602, USA.

email: ehsan.latif@uga.edu, ramviyas@uga.edu

Codes https://github.com/herolab-uga/DGORL

Abstract. An optimization problem is at the heart of many robotics estimating,

planning, and optimum control problems. Several attempts have been made at

model-based multi-robot localization, and few have formulated the multi-robot

collaborative localization problem as a factor graph problem to solve through

graph optimization. Here, the optimization objective is to minimize the errors

of estimating the relative location estimates in a distributed manner. Our novel

graph-theoretic approach to solving this problem consists of three major compo-

nents; (connectivity) graph formation, expansion through transition model, and

optimization of relative poses. First, we estimate the relative pose-connectivity

graph using the received signal strength between the connected robots, indicating

relative ranges between them. Then, we apply a motion model to formulate graph

expansion and optimize them using g2o graph optimization as a distributed solver

over dynamic networks. Finally, we theoretically analyze the algorithm and nu-

merically validate its optimality and performance through extensive simulations.

The results demonstrate the practicality of the proposed solution compared to a

state-of-the-art algorithm for collaborative localization in multi-robot systems.

Keywords: Multi-Robot, Localization, Graph Theory, Distributed Optimization

1 Introduction

The estimation of a relative pose, including position and orientation, [1], for multi-

robot systems (MRS) [2] is the foundation for higher-level tasks like collision avoid-

ance, cooperative transportation, and object manipulation. Motion capture systems [3],

ultra-wideband (UWB) systems with anchors, and RTK-GPS systems are a few exam-

ples of established multi-robot relative positioning solutions that currently rely on the

deployment of physical anchor or base stations in the application. These plans, how-

ever, are not suitable for large areas or interior settings where it is difﬁcult to convert

the infrastructure, which limits the overall performance and application possibilities of

multi-robot systems and makes their use more difﬁcult and expensive. Furthermore,

extraction of range and bearing measurements from cameras and visual makers, while

another practical approach, has the drawbacks of having a small ﬁeld of vision, a short-

range, obscured by nearby objects, and maybe requiring much computational power.

The use of distance measurements from sensors like radars, Lidars, and UWB to achieve

relative localization, on the other hand, has recently attracted more signiﬁcant interest.

arXiv:2210.01662v1 [cs.RO] 4 Oct 2022

2 Latif and Parasuraman

X1, (v, ω)1

R01

R02 R03

X4, (v, ω)4

R04

R45

R43

Connected Robots

Connecting Robots

Connected and

Connecting Robots

Rij Computed range of i & j

X2, (v, ω)2

X3, (v, ω)3

X5, (v, ω)5

Xj, (v, ω)j Sending State and

velocity of j to i

Fig. 1. Overview of conﬁguration space of a multi-robot system, sharing their pose (xi) and rela-

tive range (Rj

i) measurements in our DGORL solution.

The multi-robot relative localization (MRL) problem, which refers to detecting and

locating the relative conﬁgurations of mobile agents (typically with fewer sensor data

such as relative range or bearing) concerning other agents or landmarks, is critical in

MRS because it is required for robot teaming and swarming [4,5]. As a result, many

applications are frequently confronted with the relative localization problem, includ-

ing formation control, cooperative transportation, perimeter surveillance, area cover-

age, and situational awareness. The relative localization and mapping (aka multi-robot

SLAM) is an extension of the MRL problem. While several researchers have proposed

novel solutions to the multi-robot map merging problem using pose graph matching

and optimization techniques, they rely on extensive sensor data inputs (such as point

clouds or Lidar scans) [6,7,8]. Therefore, solving the MRL problem with relative range

or bearing in a distributed manner is desirable and scalable in MRS [9].

Distributed optimization is the problem of minimizing a joint objective function

that is the sum of many local objective functions, each corresponding to a computer

node. We can model many fundamental activities in this area as distributed optimiza-

tion problems, which have signiﬁcant implications for multi-robot systems. Examples

include cooperative estimation [10], multiagent learning [11], and collaborative motion

planning. The distributed optimization formulation provides a versatile and effective

paradigm for creating distributed algorithms for numerous multi-robot problems.

In consumer electronics, Wi-Fi is one of the most extensively utilized wireless tech-

nology for indoor wireless networks. The ubiquitous availability of Received Signal

Strength Indicator (RSSI) measurement on such inexpensive commercial devices is

the RSSI measured from an Access Point (AP) or a Wireless Sensor Robot (WSN).

The RSSI value can be used in various applications, including relative localization

[12,13,14], cooperative control [15,16], and communication optimization [17,18].

In this paper, we formulate the MRL problem as a graph optimization problem and

solve it in a distributed manner using a polynomial-time optimizer called the General

Graph Optimization (g2o [19]). g2o is an open-source graph-based framework to handle

the nonlinear error problems and is used to optimize global measurement pose using the

initial global measurement poses and local relative pose constraints.

Our solution, termed DGORL, aims to achieve high localization accuracy efﬁciently

in a distributed fashion. DGORL forms relative position-weighted connectivity graphs

Distributed Graph Optimization based Relative Localization 3

using RSSI as local sensor data then expands graphs based on possible positions at

an instant and further optimizes to fetch relative position estimates for all connected

robots. See Fig. 1for an overview of the conﬁguration space of DGORL.

The main contributions of this paper are listed below.

1. A novel distributed, efﬁcient, and precise relative localization system based on

shared inertial measurements and RSSI inputs from connected robots.

2. Position-weighted connectivity graph construction and optimization strategy tai-

lored speciﬁcally for obtaining reliable relative pose estimates.

3. Theoretical and numerical analysis to evaluate the performance of the algorithm.

4. Validation of accuracy and efﬁciency of the DGORL compared to the recent collab-

orative multi-robot localization algorithm [20], which used covariance intersection

technique to address the temporal correlation between received signals.

5. Open-sourcing of the codes1for use and improvement by the research community.

2 Related Work

Most recent solutions to the simultaneous localization and mapping (SLAM) and MRL

problem are based on graph optimization (i.e., all robot poses and landmark positions

compose the graph’s nodes, while each edge encodes a measurement constraint) [19].

A conventional graph formulation, on the other hand, may suffer from unbounded pro-

cessing and memory complexity, which might constantly expand over time. This is

because new robot poses (and new landmarks in the case of feature-based SLAM) are

constantly being added to the graph, resulting in an increase in the number of nodes

over time; additionally, if frequent loop-closing events occur in SLAM, loop-closure

constraints (edges) can signiﬁcantly increase the graph density [21]. For example, this

could be the case if a service robot works for an extended time inside an ofﬁce building.

Particularly, graph optimization and factoring have been recently proposed in the

literature to solve different variants of the MRL problem [22,23,24]. Even though the

issue of reducing the complexity of graph optimization has recently been addressed

[25,26], to the best of our knowledge, little work has yet explicitly taken into account

estimation consistency (i.e., unbiased estimates and an estimated covariance more sig-

niﬁcant than or equal to the actual covariance [27]) in the design of graph reduction

(sparsiﬁcation) schemes. This is a critical ﬂaw because if an estimator is inconsistent,

the accuracy of the derived state estimations is unclear, making it untrustworthy [28].

Moreover, the performance and efﬁciency of approaches to the localization problem in

dynamic environments are signiﬁcantly traded off.

Most cooperative localization methods entail robot communication and observa-

tion, which makes any step prone to inaccuracy. In a recent attempt at multi-robot lo-

calization, many robots can locate themselves jointly using Terrain Relative Navigation

(TRN) [20]. The localization estimation utilizing shared information fusion has been

improved by using an estimator structure that takes advantage of covariance intersec-

tion (CI) to reduce one source of measurement correlation while properly including oth-

ers. Similarly, a work [29] developed a CI-based localization method with an explicit

1http://github.com/herolab-uga/DGORL

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DGORL:DistributedGraphOptimizationbasedRelativeLocalizationofMulti-RobotSystemsEhsanLatifandRamviyasParasuramanSchoolofComputing,UniversityofGeorgia,Athens,GA30602,USA.email:ehsan.latif@uga.edu,ramviyas@uga.eduCodeshttps://github.com/herolab-uga/DGORLAbstract.Anoptimizationproblemisattheheartofmanyr...

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DGORL Distributed Graph Optimization based Relative Localization of Multi-Robot Systems Ehsan Latif and Ramviyas Parasuraman

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