Abstract

In this paper, we address nonlinear moving horizon estimation (NMHE) of vehicle lateral speed, as well as the road friction coefficient, using measured signals from sensors common to modern series-production automobiles. Due to nonlinear vehicle dynamics, a standard nonlinear moving horizon formulation leads to non-convex optimization problems, and numerical optimization algorithms can be trapped in undesirable local minima, leading to incorrect solutions. To address the challenge of non-convex cost functions, we propose an estimator with a two-level hierarchy. At the high level, a grid search combined with numerical optimization aims to find reference estimates that are sufficiently close to the global optimum. The reference estimates are refined at the low level leading to high-precision solutions. Our algorithm ensures that the estimates converge to the true values for the nominal model without the need for accurate initialization. Our design is tested in simulation with both the nominal model as well as a high-fidelity model of Autonomoose, the self-driving car of the University of Waterloo.

References

References
1.
Ahn
,
C.
,
Peng
,
H.
, and
Tseng
,
H. E.
,
2011
, “
Robust Estimation of Road Friction Coefficient
,”
Proceedings of the 2011 American Control Conference
,
San Francisco, CA
, pp.
3948
3953
.
2.
Baffet
,
G.
,
Charara
,
A.
, and
Stephant
,
J.
,
2006
, “
Sideslip Angle, Lateral Tire Force and Road Friction Estimation in Simulations and Experiments
,”
IEEE International Symposium on Intelligent Control
,
Munich, Germany
, pp.
903
908
.
3.
Chen
,
B. C.
, and
Hsieh
,
F. C.
,
2008
, “
Sideslip Angle Estimation Using Extended Kalman Filter
,”
Veh. Syst. Dyn.
,
46
(
S1
), pp.
353
364
. 10.1080/00423110801958550
4.
Ray
,
L. R.
,
1997
, “
Nonlinear Tire Force Estimation and Road Friction Identification: Simulation and Experiments
,”
Automatica
,
33
(
10
), pp.
1819
1833
. 10.1016/S0005-1098(97)00093-9
5.
Grip
,
H. F.
,
2007
, “
Nonlinear Observer for Vehicle Velocity With Friction and Road Bank Angle Adaptation—Validation and Comparison With an Extended Kalman Filter
,”
SAE World Congress 2007
,
Detroit, USA
.
6.
Canale
,
M.
,
Fagiano
,
L.
, and
Novara
,
C.
,
2014
, “
A DVS-MHE Approach to Vehicle Side-Slip Angle Estimation
,”
IEEE Trans. Control Syst. Technol.
,
22
(
5
), pp.
2048
2055
. 10.1109/TCST.2013.2295974
7.
Zhao
,
H.
, and
Chen
,
H.
,
2006
, “
Estimation of Vehicle Yaw Rate and Side Slip Angle Using Moving Horizon Strategy
,”
Proceedings of the 6th World Congress on Intelligent Control and Automation
,
Paris, France
.
8.
Jin
,
C.
,
Maitland
,
A.
, and
McPhee
,
J.
,
2019
, “
Hierarchical Nonlinear Moving Horizon Estimation of Vehicle Lateral Speed and Road Friction Coefficient
,”
Proceedings of the ASME 2019 Dynamic Systems and Control Conference
,
Park City, UT
, p.
V003T18A005
.
9.
Kiencke
,
U.
, and
Nielsen
,
L.
,
2000
,
Automotive Control System for Engine, Driveline, and Vehicle
,
Springer-Verlag
,
Berlin
.
10.
Van Gennip
,
M. D.
, and
McPhee
,
J.
,
2018
, “
Parameter Identification and Validation for Combined Slip Tire Models Using a Vehicle Measurement System
,”
SAE Int. J. Veh. Dyn. Stab. NVH
,
2
(
4
), pp.
1109
1118
. 10.4271/2018-01-1339
11.
Grip
,
H. F.
,
Imsland
,
L.
,
Johansen
,
T. A.
,
Fossen
,
T. I.
,
Kalkkuhl
,
J. C.
, and
Suissa
,
A.
,
2008
, “
Nonlinear Vehicle Side-Slip Estimation With Friction Adaptation
,”
Automatica
,
44
(
3
), pp.
611
622
. 10.1016/j.automatica.2007.06.017
12.
Maitland
,
A.
,
Bhatra
,
M.
, and
McPhee
,
J.
,
2018
, “
Nonlinear Model Predictive Control Reduction Using Truncated Single Shooting
,”
2018 Annual American Control Conference (ACC)
,
Milwaukee, WI
, pp.
3165
3170
.
13.
Maitland
,
A.
, and
McPhee
,
J.
,
2017
, “
Improving Model Predictive Controller Turnaround Time Using Restricted Lagrangians
,”
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
,
Melbourne, VIC
, pp.
3811
3816
.
14.
Hosking
,
B. A.
, and
McPhee
,
J.
,
2018
, “
Powertrain Modeling and Model Predictive Longitudinal Dynamics Control for Hybrid Electric Vehicles
,”
SAE Technical Paper 2018-01-0996
.
You do not currently have access to this content.