Abstract

In this paper, we focus on developing a multi-step uncertainty propagation method for systems with state- and control-dependent uncertainties. System uncertainty creates a mismatch between the actual system and its control-oriented model. Often, these uncertainties are state- and control-dependent, such as modeling error. This uncertainty propagates over time and results in significant errors over a given time horizon, which can disrupt the operation of safety-critical systems. Stochastic predictive control methods can ensure that the system stays within the safe region with a given probability, but requires prediction of the future state distributions of the system over the horizon. Predicting the future state distribution of systems with state- and control-dependent uncertainty is a difficult task. Existing methods only focus on modeling the current or one-step uncertainty, while the uncertainty propagation model over a horizon is generally over-approximated. Hence, we present a multi-step Gaussian process regression method to learn the uncertainty propagation model for systems with state- and control-dependent uncertainties. We also perform a case study on vehicle lateral control problems, where we learn the vehicle’s error propagation model during lane changes. Simulation results show the efficacy of our proposed method.

References

1.
Guanetti
,
J.
,
Kim
,
Y.
, and
Borrelli
,
F.
,
2018
, “
Control of Connected and Automated Vehicles: State of the Art and Future Challenges
,”
Annu. Rev. Control.
,
45
.
2.
Paden
,
B.
,
Čáp
,
M.
,
Zheng Yong
,
S.
,
Yershov
,
D.
, and
Frazzoli
,
E.
,
2016
, “
A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles
,”
IEEE Trans. Intell. Veh.
,
1
(
1
), pp.
33
55
.
3.
Hewing
,
L.
,
Liniger
,
A.
, and
Zeilinger
,
M. N.
,
2018
, “
Cautious NMPC With Gaussian Process Dynamics for Autonomous Miniature Race Cars
,”
European Control Conference
,
Limassol, Cyprus
,
June 12–15
, pp.
1341
1348
.
4.
Hewing
,
L.
,
Kabzan
,
J.
, and
Zeilinger
,
M. N.
,
2019
, “
Cautious Model Predictive Control Using Gaussian Process Regression
,”
IEEE Trans. Control Syst. Technol.
,
28
(
6
), pp.
2736
2743
.
5.
Pan
,
Y.
,
Yan
,
X.
,
Theodorou
,
E. A.
, and
Boots
,
B.
,
2017
, “
Prediction Under Uncertainty in Sparse Spectrum Gaussian Processes With Applications to Filtering and Control
,”
International Conference on Machine Learning
,
Sydney Australia
,
Aug. 6–11
,
PMLR
, pp.
2760
2768
.
6.
Lázaro-Gredilla
,
M.
,
Quinonero-Candela
,
J.
,
Edward Rasmussen
,
C.
, and
Figueiras-Vidal
,
A. R.
,
2010
, “
Sparse Spectrum Gaussian Process Regression
,”
J. Mach. Learn. Res.
,
11
(
1
), pp.
1865
1881
.
7.
Ning
,
J.
, and
Behl
,
M.
,
2023
, “
Vehicle Dynamics Modeling for Autonomous Racing Using Gaussian Processes
,” arXiv:2306.03405.1809.04509
8.
Broderick
,
D. J.
,
2012
, “Dynamic Gaussian Process Models for Model Predictive Control of Vehicle Roll,” PhD thesis,
Auburn University
,
Auburn, AL
.
9.
Hewing
,
L.
,
Kabzan
,
J.
, and
Zeilinger
,
M. N.
,
2020
, “
Cautious Model Predictive Control Using Gaussian Process Regression
,”
IEEE Trans. Control Syst. Technol.
,
28
(
6
), pp.
2736
2743
.
10.
Gao
,
Y.
,
Gray
,
A.
,
Eric Tseng
,
H.
, and
Borrelli
,
F.
,
2014
, “
A Tube-Based Robust Nonlinear Predictive Control Approach to Semiautonomous Ground Vehicles
,”
Veh. Syst. Dyn.
,
52
(
6
), pp.
802
823
.
11.
Carson, III
,
J. M.
,
Açıkmeşe
,
B.
,
Murray
,
R. M.
, and
MacMartin
,
D. G.
,
2013
, “
A Robust Model Predictive Control Algorithm Augmented With a Reactive Safety Mode
,”
Automatica
,
49
(
5
), pp.
1251
1260
.
12.
Mayne
,
D. Q.
,
Kerrigan
,
E. C.
, and
Falugi
,
P.
,
2011
, “
Robust Model Predictive Control: Advantages and Disadvantages of Tube-Based Methods
,”
IFAC Proc. Vol.
,
44
(
1
), pp.
191
196
.
13.
Limon
,
D.
,
Alvarado
,
I.
,
Alamo
,
T.
, and
Camacho
,
E. F.
,
2010
, “
Robust Tube-Based MPC for Tracking of Constrained Linear Systems With Additive Disturbances
,”
J. Process Control
,
20
(
3
), pp.
248
260
.
14.
Paulson
,
J. A.
, and
Mesba
,
A.
,
2018
, “
Nonlinear Model Predictive Control With Explicit Backoffs for Stochastic Systems Under Arbitrary Uncertainty
,”
IFAC-PapersOnLine
,
51
(
20
), pp.
523
534
.
15.
Kousik
,
S.
,
Vaskov
,
S.
,
Johnson-Roberson
,
F. B. M.
, and
Vasudevan
,
R.
,
2020
, “
Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots
,”
Int. J. Robot. Res.
,
39
(
12
), pp.
1419
1469
.
16.
Lewis Chiang
,
H.-T.
,
HomChaudhuri
,
B.
,
Vinod
,
A. P.
,
Oishi
,
M.
, and
Tapia
,
L.
,
2017
, “
Dynamic Risk Tolerance: Motion Planning by Balancing Short-Term and Long-Term Stochastic Dynamic Predictions
,”
International Conference on Robotics and Automation
,
Marina Bay Sands, Singapore
,
May 29–June 3
, pp.
3762
3769
.
17.
Rajamani
,
R.
,
2012
,
Vehicle Dynamics and Control
(
Mechanical Engineering Series
),
Springer US
,
Boston, MA
.
18.
van Nieuwstadt
,
M.
,
Rathinam
,
M.
, and
Murray
,
R. M.
,
1998
, “
Differential Flatness and Absolute Equivalence of Nonlinear Control Systems
,”
SIAM J. Control Optim.
,
36
(
4
), pp.
1225
1239
.
19.
Wang
,
M.
,
Wang
,
Z.
,
Paudel
,
S.
, and
Schwager
,
M.
,
2018
, “
Safe Distributed Lane Change Maneuvers for Multiple Autonomous Vehicles Using Buffered Input Cells
,”
IEEE International Conference on Robotics and Automation
,
Brisbane, Australia
,
May 21–25
, pp.
1
7
.
20.
Haddad
,
S.
,
Halder
,
A.
, and
Singh
,
B.
,
2022
, “
Density-Based Stochastic Reachability Computation for Occupancy Prediction in Automated Driving
,”
IEEE Trans. Control Syst. Technol.
,
30
(
6
), pp.
2406
2419
.
21.
Bakker
,
E.
,
Pacejka
,
H. B.
, and
Lidner
,
L.
,
1989
, “
A New Tire Model With an Application in Vehicle Dynamics Studies
,”
SAE Trans.
,
98
(
1
), pp.
101
113
.
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