Abstract

Over the past decades, simulation has become vital in vehicle development and virtual testing, especially for autonomous vehicles. High-performance hard real-time simulators, which are crucial for those undertakings, require efficient algorithms to accurately model vehicle behavior within virtual environments. A prime example is tire-ground contact modeling, which is pivotal if we aim to achieve a high level of realism when simulating wheeled vehicles. Contact modeling focuses on an accurate estimation of the parameters needed to compute the forces and torques generated by vehicle-ground interaction. However, the complexity of this task is compounded by the fact that tire-ground contact is a highly nonlinear phenomenon, which is further exacerbated by the need to perform tests to fine-tune state-of-the-art tire-ground contact models. To tackle those challenges, we have developed a novel enveloping model that does not require any fitting of experimental data and is based on the 3D geometry of the intersection between undeformed volumes. In this paper, we provide a detailed description of the algorithm's formulation, the current software implementation (available as an open-source library), as well as the achieved scalability and real-time performance.

References

1.
Pacejka
,
H. B.
,
2012
,
Tire and Vehicle Dynamics
, 3rd ed.,
Butterworth-Heinemann
,
Oxford, UK
.
2.
Pacejka
,
H. B.
,
2005
, “
Spin: Camber and Turning
,”
Veh. Syst. Dyn.
,
43
, pp.
3
17
.10.1080/00423110500140013
3.
Gallrein
,
A.
,
Bäcker
,
M.
,
Burger
,
M.
, and
Gizatullin
,
A.
,
2014
, “
An Advanced Flexible Realtime Tire Model and Its Integration Into Fraunhofer's Driving Simulator
,” SAE Paper No. 2014-01-0861. 10.4271/2014-01-0861
4.
Serban
,
R.
,
Taves
,
J.
, and
Zhou
,
Z.
,
2023
, “
Real-Time Simulation of Ground Vehicles on Deformable Terrain
,”
ASME J. Comput. Nonlinear Dyn.
,
18
(
8
), p.
081007
.10.1115/1.4056851
5.
Schmeitz
,
A. J. C.
,
2004
, “
A Semi-Empirical Three-Dimensional Model of the Pneumatic Tyre Rolling Over Arbitrarily Uneven Road Surfaces
,” Ph.D. thesis,
TU Delft
,
Delft, The Netherlands
.
6.
Davis
,
D. C.
,
1975
, “
A Radial-Spring Terrain-Enveloping Tire Model
,”
Veh. Syst. Dyn.
,
4
(
1
), pp.
55
69
.10.1080/00423117508968461
7.
Badalamenti
,
J. M.
, and
Doyle
,
G. R.
,
1988
, “
Radial-Interradial Spring Tire Models
,”
ASME J. Vib. Acoust.
,
110
(
1
), pp.
70
75
.10.1115/1.3269483
8.
Negrut
,
D.
, and
Freeman
,
J. S.
,
1994
, “
Dynamic Tire Modelling for Application With Vehicle Simulations Incorporating Terrain
,”
SAE Trans.
,
103
, pp.
96
103
.10.4271/940223
9.
Mousseau
,
R.
, and
Markale
,
G.
,
2003
, “
Obstacle Impact Simulation of an ATV Using an Efficient Tire Model
,”
Tire Sci. Technol.
,
31
(
4
), pp.
248
269
.10.2346/1.2135271
10.
Kim
,
S.
,
Nikravesh
,
P. E.
, and
Gim
,
G.
,
2008
, “
A Two-Dimensional Tire Model on Uneven Roads for Vehicle Dynamic simulation
,”
Veh. Syst. Dyn.
,
46
(
10
), pp.
913
930
.10.1080/00423110701729994
11.
Rill
,
G.
,
2013
, “
TMeasy—A Handling Tire Model Based on a Three-Dimensional Slip Approach
,”
Proceedings of the XXIII International Symposium on Dynamic of Vehicles on Roads and on Tracks (IAVSD 2013)
, Quingdao, China, Aug. 19–23, pp.
19
23
.https://www.researchgate.net/publication/317037031_T Measy_--_A_Handling_Tire_Model_based_on_a_three-dimensional_slip_approach
12.
Kageyama
,
I.
, and
Kuwahara
,
S.
,
2002
, “
A Study on Tire Modeling for Camber Thrust and Camber Torque
,”
JSAE Rev.
,
23
(
3
), pp.
325
331
.10.1016/S0389-4304(02)00204-7
13.
Rill
,
G.
,
2018
, “
Sophisticated but Quite Simple Contact Calculation for Handling Tire Models
,”
Multibody Syst. Dyn.
,
45
(
2
), pp.
131
153
.10.1007/s11044-018-9629-4
14.
Gipser
,
M.
,
2005
, “
FTire: A Physically Based Application-Oriented Tyre Model for Use With Detailed MBS and Finite-Element Suspension Models
,”
Veh. Syst. Dyn.
,
43
, pp.
76
91
.10.1080/00423110500139940
15.
Gallrein
,
A.
, and
Bäcker
,
M.
,
2007
, “
CDTire: A Tire Model for Comfort and Durability Applications
,”
Veh. Syst. Dyn.
,
45
, pp.
69
77
.10.1080/00423110801931771
16.
Rieff
,
B.
, and
Gipser
,
M.
,
2021
, “
FTire—Full Tire Dynamics in Real-Time on Driving Simulators
,” in
Proceedings of the 20th Driving Simulation and Virtual Reality Conference and Exhibition
, Münich, Germany, Sept. 14–17.
17.
Gipser
,
M.
,
2008
, “
FTire: 10 Years of Development and Application
,”
Automotive Engineering Faculty, Esslingen University of Applied Sciences
,
Germany
.
18.
Stocco
,
D.
, and
Bertolazzi
,
E.
,
2021
, “
Acme: A Small 3D Geometry Library
,”
SoftwareX
,
16
, p.
100845
.10.1016/j.softx.2021.100845
19.
Piccinini
,
M.
,
Larcher
,
M.
,
Pagot
,
E.
,
Piscini
,
D.
,
Pasquato
,
L.
, and
Biral
,
F.
,
2022
, “
A Predictive Neural Hierarchical Framework for on-Line Time-Optimal Motion Planning and Control of Black-Box Vehicle Models
,”
Veh. Syst. Dyn.
,
61
(
1
), pp.
83
110
.10.1080/00423114.2022.2035776
20.
Piccinini
,
M.
,
Taddei
,
S.
,
Larcher
,
M.
,
Piazza
,
M.
, and
Biral
,
F.
,
2023
, “
A Physics-Driven Artificial Agent for Online Time-Optimal Vehicle Motion Planning and Control
,”
IEEE Access
,
11
, pp.
46344
46372
.10.1109/ACCESS.2023.3274836
21.
ISO
,
2011
, “
Road Vehicles—Vehicle Dynamics and Road-Holding Ability—Vocabulary
,” ISO 8855:2011.
22.
Stoer
,
J.
, and
Bulirsch
,
R.
,
2002
,
Introduction to Numerical Analysis
,
Springer
,
Berlin
.
23.
Stroustrup
,
B.
,
2013
,
The C++ Programming Language
, 4th ed.,
Addison-Wesley Professional
,
Boston, MA
.
24.
Guennebaud
,
G.
,
Jacob
,
B.
, et al.,
2010
, “
Eigen v3
,” http://eigen.tuxfamily.org
25.
Anderson
,
E.
,
Bai
,
Z.
,
Bischof
,
C.
,
Blackford
,
L. S.
,
Demmel
,
J.
,
Dongarra
,
J.
,
Du Croz
,
J.
,
Greenbaum
,
A.
,
Hammarling
,
S.
,
McKenney
,
A.
, et al.,
1999
,
LAPACK Users' Guide
, 3rd ed.,
Siam
,
Philadelphia, PA
.
26.
Stocco
,
D.
,
Bertolazzi
,
E.
, and
Larcher
,
M.
,
2024
, “
ENVE GitHub Repository
,” accessed Feb. 1, 2024, http://stoccodavide.github.io/enve/
27.
SAE
,
2018
, “
Low Speed Enveloping Test With Perpendicular and Inclined Cleats
,” SAE Paper No. J2731-201805. 10.4271/J2731_201805
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