M-LIO Multi-lidar multi-IMU odometry with sensor dropout tolerance Sandipan Das12 Navid Mahabadi3 Maurice Fallon4 Saikat Chatterjee1 We present a robust system for state estimation that fuses

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M-LIO: Multi-lidar, multi-IMU odometry with sensor dropout tolerance

Sandipan Das1,2, Navid Mahabadi3, Maurice Fallon4, Saikat Chatterjee1

We present a robust system for state estimation that fuses

measurements from multiple lidars and inertial sensors with

GNSS data. To initiate the method, we use the prior GNSS

pose information. We then perform incremental motion in

real-time, which produces robust motion estimates in a

global frame by fusing lidar and IMU signals with GNSS

translation components using a factor graph framework. We

also propose methods to account for signal loss with a

novel synchronization and fusion mechanism. To validate our

approach extensive tests were carried out on data collected

using Scania test vehicles (5 sequences for a total of

≈

7 Km).

From our evaluations, we show an average improvement of

61% in relative translation and 42% rotational error compared

to a state-of-the-art estimator fusing a single lidar/inertial

sensor pair.

I. INTRODUCTION

State estimation, which is a sub-problem of Simultaneous

Localization and Mapping (SLAM), is a fundamental building

block of autonomous navigation. To develop robust SLAM

systems, proprioceptive (IMU – inertial measurement unit,

wheel encoders) and exteroceptive (camera, lidar, GNSS

– Global Navigation Satellite System) sensing are fused.

Existing systems have achieved robust and accurate results [

[

], [

]; however, state estimation in dynamic conditions and

when there is measurement loss or noisy is still challenging.

Compared to visual SLAM, lidar-based SLAM has higher

accuracy as lidar range measurements of up to 100m directly

enable precise motion tracking. Moreover, owing to the falling

cost of lidars, mobile platforms are increasingly equipped with

multiple lidars [

], [

], to give complementary and complete

360◦

sensor coverage (see Fig. 1, for our data collection

platform). This also improves the density of measurements

which may be helpful for state estimation in degenerate

scenarios such as tunnels or straight highways. We can also

estimate the reliability of a state estimator by computing the

covariance of measurement errors produced from multiple

lidar measurements.

Meanwhile, IMUs are low cost sensors which can be used

to estimate a motion prior for lidar odometry by integrating

the rotation rate and accelerometry measurements. However,

IMUs suffer from bias instability and are susceptible to noise.

An array of multiple IMUs (MIMUs) could provide enhanced

signal accuracy with bias and noise compensation as well as

1KTH EECS, Sweden. {sandipan,sach}@kth.se

2Scania, Sweden. {sandipan.das}@scania.com

3Stockholm, Sweden. n.mahabadi@gmail.com

4Oxford Robotics Institute, UK. mfallon@robots.ox.ac.uk

Lidar Field of View

Fig. 1. Illustration of the four lidars with their embedded IMUs positioned

around the data collection vehicle. The vehicle base frame

, is located

at the center of the rear axle. The sensor frames of the lidars are:

LFR

LFL

LRR

and

LRL

, whereas, the sensor frames of the IMUs are:

IFR

IFL

IRR

and

IRL

: front-right,

: front-left,

: rear-right and

RL: rear-left.

increasing operational robustness to sensor dropouts. Multi-

lidar odometry [

], [

] and MIMU odometry [

], [

] have

been studied separately; however to the best of our knowledge

the fusion of the combined set has not yet been explored.

A. Motivation

As our vehicles are equipped with a GNSS system,

we perform the state estimation in global frame and take

advantage of it to limit the drift rate. Since GNSS information

is unreliable in urban environments (‘urban canyon’) or in

underground scenarios (such as mining) we also need to fuse

information from onboard sensors (which might be susceptible

to signal loss) to create robust state estimates.

To achieve this, we have identiﬁed two broad problems:

Problem 1: State estimation over long time horizons with

onboard sensing inherently suffers from drift. Problem 2:

Sensor signals are susceptible to loss, due to networking or

operational issues, which might affect reliability of the state

estimates using onboard sensing.

In our work we have addressed Problem 1) by fusing

the onboard state estimator with GNSS-based estimates. For

Problem 2) we provide our formulation for the fusion of

multiple lidars and MIMU to create robust signals under

noisy conditions, which can give robustness both to failure

of an individual lidar or IMU sensor as well as expanding

the lidar ﬁeld-of-view.

arXiv:2210.01154v2 [cs.RO] 9 Oct 2022

B. Contribution

Our work is motivated by the broad literature in lidar and

IMU based state estimation. Our proposed contributions are:

•

Multi-lidar odometry using a single fused local submap

and handling lidar dropout scenarios.

•

MIMU fusion which compensates for the Coriolis effect

and accounts for potential signal loss.

•

A factor graph framework to jointly fuse multiple lidars,

MIMUs and GNSS signals for robust state estimation

in a global frame.

•

Experimental results and veriﬁcation using data collected

from Scania vehicles with the sensor setup shown in

Fig. 2, with FoV schematics similar to Fig. 1.

II. RELATED WORK

There have been multiple studies of lidar and IMU-based

SLAM after the seminal LOAM paper by Zhang et al. [

]

which is itself motivated by generalized-ICP work by Se-

gal et al. [

]. In our discussion we brieﬂy review the relevant

literature.

A. Direct tightly coupled multi-lidar odometry

To develop real-time SLAM systems simple edge and plane

features are often extracted from the point clouds and tracked

between frames for computational efﬁciency [

], [

Using IMU propagation, motion priors can then be used to

enable matching of point cloud features between key-frames.

However, this principle cannot be applied to featureless

environments. Hence, instead of feature engineering, the

whole point cloud is often processed which has an analogy to

processing the whole image in visual odometry methods such

as LSD-SLAM, [

], which is known as direct estimation.

To support direct methods, recently Xu et al. [15] proposed

the ikd-tree in their Fast-LIO2 work which efﬁciently inserts,

updates, searches and ﬁlters to maintain a local submap.

The ikd-tree achieves its efﬁciency through “lazy delete” and

“parallel tree re-balancing” mechanisms.

Furthermore, instead of point-wise operations the authors

of Faster-LIO [

] proposed voxel-wise operations for point

cloud association across frames and reported improved

efﬁciency. In our work we also maintain an ikd-tree of the

fused lidar measurements and tightly couple the relative lidar

poses, IMU preintegration and GNSS prior in our propose

estimator. Since, we jointly estimate the state based on the

residual cost function built upon the multiple modalities we

consider this a tightly coupled system.

While there have been many studies of state estimation

using single lidar and IMU, there is limited literature available

for fusing multi-lidar and MIMU systems. Our idea closely

resembles M-LOAM [

], where state estimation with multiple

lidars and calibration was performed. However, the working

principles are different as M-LOAM is not a direct method

and MIMU system is not considered in their work.

Finally, most authors do not address how to achieve

reliability in situations of signal loss — an issue which is

important for practical operational scenarios.

Fig. 2. Reference frames conventions for our vehicle platform. The world

frame

is a ﬁxed frame, while the base frame

, as shown in Fig. 1, is

located at the rear axle center of the vehicle. Each sensor unit contains the

two optical frames

, an IMU frame,

, and lidar frame

. The cameras are

shown for illustration only and they are not used for this work.

III. PROBLEM STATEMENT

A. Sensor platform and reference frames

The sensor platform with its corresponding reference

frames is shown in Fig. 2 along with the illustrative sensor

ﬁelds-of-view in Fig. 1. Each of the sensor housings contain a

lidar with a corresponding embedded IMU and two cameras.

Although we do not use the cameras in this work they are

illustrated here to show the full sensor setup. We used logs

from a bus and a truck with similar sensor housings for our

experiments. The two lower mounted modules from the rear,

present in both the vehicles, are not shown here in the picture.

The embedded IMUs within the lidar sensors are used to

form the MIMU setup.

Now we describe the necessary notation and reference

frames used in our system according to the convention of

Furgale [

]. The vehicle base frame,

is located on the

center of the rear-axle of the vehicle. Sensor readings from

GNSS, lidars, cameras and IMUs are represented in their

respective sensor frames as

L(k)

C(k)

and

I(k)

respectively.

Here,

k∈[FL, FR, RL, RR]

denotes the location of the

sensor in the vehicle corresponding to front-left, front-right,

rear-left and rear-right respectively. The GNSS measurements

are reported in world ﬁxed frame,

and transformed to

frame by performing a calibration routine outside the

scope of this work. In our discussions the transformation

matrix is denoted as,

T=R3×3t3×1

0>1∈SE(3)

and

RRT=I3×3, since the rotation matrix is orthogonal.

B. Problem formulation

Our primary goal is to estimate the position

W WB

, orienta-

tion

W WB

, linear velocity

W WB

, and angular velocity

W WB

of the base frame

, relative to the ﬁxed world frame

Additionally, we also estimate the MIMU biases

B,ba

expressed in

frame, as that is where it can be sensed. Hence,

our estimate of vehicle’s state xiat time ti, is denoted as:

xi= [Ri,ti,vi,ωi,ba

i,bg

i]∈SE(3) ×R15,(1)

where, the corresponding measurements are in the frames

mentioned above.

IV. METHODOLOGY

A. Initialization

To provide an initial pose we use the GNSS measurements,

W WG

and determine an initial estimate of the starting yaw and

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M-LIO:Multi-lidar,multi-IMUodometrywithsensordropouttoleranceSandipanDas1;2,NavidMahabadi3,MauriceFallon4,SaikatChatterjee1WepresentarobustsystemforstateestimationthatfusesmeasurementsfrommultiplelidarsandinertialsensorswithGNSSdata.Toinitiatethemethod,weusethepriorGNSSposeinformation.Wethenperformi...

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M-LIO Multi-lidar multi-IMU odometry with sensor dropout tolerance Sandipan Das12 Navid Mahabadi3 Maurice Fallon4 Saikat Chatterjee1 We present a robust system for state estimation that fuses

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