MICP-L Mesh-based ICP for Robot Localization using Hardware-Accelerated Ray Casting Alexander Mock1 Thomas Wiemann3 Sebastian P utz2and Joachim Hertzberg12

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MICP-L: Mesh-based ICP for Robot Localization using

Hardware-Accelerated Ray Casting

Alexander Mock1, Thomas Wiemann3, Sebastian P¨

utz2and Joachim Hertzberg1,2

Abstract— Triangle mesh maps are a versatile 3D environment

representation for robots to navigate in challenging indoor

and outdoor environments exhibiting tunnels, hills and varying

slopes. To make use of these mesh maps, methods are needed

to accurately localize robots in such maps to perform essential

tasks like path planning and navigation. We present Mesh ICP

Localization (MICP-L), a novel and computationally efﬁcient

method for registering one or more range sensors to a triangle

mesh map to continuously localize a robot in 6D, even in GPS-

denied environments. We accelerate the computation of ray

casting correspondences (RCC) between range sensors and mesh

maps by supporting different parallel computing devices like

multicore CPUs, GPUs and the latest NVIDIA RTX hardware.

By additionally transforming the covariance computation into a

reduction operation, we can optimize the initial guessed poses

in parallel on CPUs or GPUs, making our implementation

applicable in real-time on many architectures. We demonstrate

the robustness of our localization approach with datasets from

agricultural, aerial, and automotive domains.

I. INTRODUCTION

Localization is the task of estimating the state of a

mobile robot in a reference coordinate system. It is the

foundation for any mobile robot to operate autonomously in

a given application environment. In many outdoor scenarios,

localization is done via GPS or triangulation with predeﬁned

landmarks. However, in many cases, GPS is unreliable or not

available at all, therefore other localization strategies have

to be considered. Algorithms such as LiDAR-based SLAM

have been developed to address this problem. In recent years,

such SLAM algorithms have been improved in a way that

even robots with low computational resources can estimate

their current state in 6DoF while simultaneously mapping

their environment in 3D. An increasingly important map

representation in the context of SLAM is a Truncated Signed

Distance Field (TSDF) [1]. TSDFs can be transferred easily

into 3D triangle meshes to compress the information encoded

in the original map. Recently, algorithms have been developed

to plan the motion of a robot over the mesh’s surface to a

given goal [2]. To execute such plans, reliable, frequent, and

accurate localization in mesh maps is required.

Knowledge-Based Systems group, Institute of Computer Science, Os-

nabr

uck University, Hamburger Straße 24, 49084 Osnabr

uck, Germany

amock@uos.de, joachim.hertzberg@uos.de

DFKI Robotics Innovation Center, Osnabr

uck branch, Hamburger Straße

24, 49084 Osnabr¨

uck, Germany sebastian.puetz@dfki.de

Robotics in Computer Science, Fulda Uni-

versity of Applied Sciences, Fulda, Germany

thomas.wiemann@informatik.hs-fulda.de

The DFKI Niedersachsen Lab (DFKI NI) is sponsored by the Ministry of

Science and Culture of Lower Saxony and the VolkswagenStiftung

Fig. 1: The Lero agricultural monitoring robot uses MICP-L for

localization for mesh-based navigation between beds in a market

garden micro-farming environment.

Our paper presents a novel approach called MICP-L

which enables robots equipped with arbitrary range sensors

to be localized directly in triangle mesh maps. It is designed

to be applicable to robots with varying computational capa-

bilities. For that, MICP-L builds upon the open-source library

Rmagine, presented in previous work [3]. We contribute

•

Robust range-sensor-to-mesh registration via hardware-

accelerated ray casting correspondences (RCC),

•

Accurate and reliable localization, tested in various real-

world domains as shown in Fig. 1,

•

Flexible workload distribution over CPU or GPU, en-

abling application on various hardware platforms,

•Support of arbitrary range sensor combinations.

II. RELATED WORK

Localization is a key capability required in many robotics

applications and in the last decade researchers generated

many approaches using various map representations, ranging

from point clouds [4]–[8] to occupancy grids, signed distance

ﬁelds (SDF) [1], [9], [10], meshes [11]–[16], and more, e.g.,

neural representations [17], [18].

Generating 3D triangle meshes online [16], on system-on-

chip (SoC) devices [1] and for large scales environments [11],

[12], [19], [20] have become available. Meshes feature a

closed surface and can be used for planning and executing

paths of autonomously driving robots in unstructured en-

vironments [2]. The success of mesh navigation software

heavily depends on the robot’s ability to frequently and

reliably localize itself with respect to the mesh map. In

1Source code is available here https://github.com/uos/rmcl

arXiv:2210.13904v4 [cs.RO] 8 Jul 2024

principle, global localization in triangle meshes can be done

using particle ﬁlters [14]. Chen et al. introduced a Monte

Carlo Localization (MCL) method for meshes, which utilizes

LiDARs and OpenGL-simulated range images for importance

sampling [15]. However, particle ﬁlter-based approaches

produce high computational loads to track the robot’s pose.

To overcome this issue, relative localization methods such as

iterative closest point (ICP) are often used to track the robot’s

pose [4], [5], [21]–[23]. All of them register a measured

point cloud to a reference point cloud. Several publications,

spanning from computer graphics to robotics research, have

presented ICP-like methods that can register point clouds to

reference meshes instead [11], [24]–[28].

In 2019, Mejia-Parra et al. solved point cloud to mesh reg-

istration with a novel approach of ﬁnding the closest surface

point for each point cloud point using hash grids [27]. They

evaluated their approach by registering point clouds to single

meshes of closed objects. However, dealing with meshes of

large environments, as in [15], introduces challenges beyond

the scope of their methodology. For example, triangle mesh

maps of interiors usually consist of walls with two parallel

surfaces. If the initial pose estimate deviates just a little from

the optimum, this would lead to matches between wrong

wall surfaces. In addition, large meshes would drastically

increase the size of the hash table, making it impossible to

use on mobile robots. In 2021, Vizzo et al. presented an

approach for mesh-based SLAM named PUMA [11]. They

generated a mesh from a scan and registered the following

scan to it by using ray casting correspondences (RCC). Their

correspondences seem to be suitable to solve the mentioned

issues of [27]. However, real-time capability was not even

achieved for fractions of the entire mesh map, making it

unsuitable for online operation on autonomous vehicles.

With MICP-L, we address the problems of [11] and [27] by

introducing a light-weight method to ﬁnd RC correspondences

and optimize the pose estimation by utilizing NVIDIA’s RTX

hardware for acceleration. We reach more than real-time

localization even in large-scale mesh maps and overcome

convergence issues of classical point cloud-based ICP [29].

III. MICP-L

MICP-L continuously registers range data acquired from

one or multiple range sensors to a triangle mesh map, starting

at an initial pose estimate. The general workﬂow can be

summarized as follows:

Find ray casting (RC) or closest point (CP) correspon-

dences,

Estimate the optimal transformation parameters

∆T

through covariance reduction and SVD using either

P2P or P2L as error measure,

3) Apply ∆Tto the pose guess and repeat step 1).

A. Closest Point Correspondences

For point-cloud maps, locating the nearest model point to

a dataset point is typically sped up by pre-building kd-trees

or hash grids over the model. In mesh maps, the task differs

slightly as ﬁnding the closest point on a mesh surface may

Room 2

Room 1

Room 2

Room 1

RCCCPC

Fig. 2: A 2D map consists of two rooms. Left: Conventional closest

point correspondences fail since they match on the wall’s surface

of the wrong room. Right: RCCs overcome these problems, by ﬁrst

ray casting along the real measurement’s direction (red line) to ﬁnd

the next intersection with the map (green circle). For point-to-plane

(P2L) optimization, the actual correspondence is the projection onto

the plane (dark blue arrow).

not necessarily involve vertices but requires searching the

nearest point on each face. We use the BVH implementation

of Embree [30] to accelerate this operation.

B. Ray Casting Correspondences

Dealing with meshes allows us to use specialized RTX

chips on the NVidia GPUs to efﬁciently compute ray-to-mesh

intersections. We use this technique to accelerate ﬁnding so-

called ray casting correspondences (RCC), introduced with

PUMA [11]. For computing RCCs, we ﬁrst convert each

measurement

of a range sensor into a ray representation,

consisting of origin, direction, and range. Next, we use the

given pose estimate to trace virtual rays along the paths

that the real sensor would scan. The intersection with the

map represents the actual point that would be measured if

the sensor were at the estimated pose. We then project the

Cartesian point of the real scan measurement onto the plane

of intersection to determine the map correspondence. These

RCCs allow matching scan points only to the surface closest

to the range sensor, as shown in Fig. 2. This reduces the

likelihood of drifting into other rooms during registration as

shown in the experiments, subsequently.

We use Rmagine, a library to ﬂexibly build ray tracing-

based sensor simulations [3], for all ray casts. It decides at

run time whether to compute the RCC on CPU [30] or on

a NVIDIA GPU and, if available, utilize the RTX units for

hardware-acceleration [31].

C. Correction

Finding RC or CP correspondences returns a list of scan

points

and map points

, where the

-th scan point

corresponds to the

-th map point

. All points are located

in the same coordinate system, e.g., the robots base frame.

Next, we search for the transformation parameters

∆T

consisting of a rotation

∆R

and a translation

∆t

, that best

ﬁt the scan points (dataset)

to the map points (model)

This can be done by minimizing the following equation:

E(∆R, ∆t) = 1

i=1

∥mi−(∆Rdi+ ∆t)∥2

2(1)

Our solver is based on Umeyama’s method [32] and enhances

the computation of the covariance matrix for both CPU and

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MICP-L:Mesh-basedICPforRobotLocalizationusingHardware-AcceleratedRayCastingAlexanderMock1,ThomasWiemann3,SebastianP¨utz2andJoachimHertzberg1,2Abstract—Trianglemeshmapsareaversatile3Denvironmentrepresentationforrobotstonavigateinchallengingindoorandoutdoorenvironmentsexhibitingtunnels,hillsandvarying...

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MICP-L Mesh-based ICP for Robot Localization using Hardware-Accelerated Ray Casting Alexander Mock1 Thomas Wiemann3 Sebastian P utz2and Joachim Hertzberg12

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