Autonomous racing requires accurate trajectory tracking near the handling limits of a vehicle while maintaining low computational latency. Geometric controllers are computationally efficient, but the Ackermann steering geometry becomes invalid under limit-handling conditions. Model- and Acceleration-based Pursuit (MAP) preserves the simplicity of geometric approaches while leveraging tire dynamics. Yet MAP remains fundamentally a geometric controller that relies on Ackermann steering geometry, and its tire model may not fully capture the vehicle's actual dynamic response. This paper presents MAP2, a model-based pursuit controller that combines a curvature-based kinematic MPC and a Sparse Gaussian Process (SGP) residual correction. The proposed algorithm uses MPC to optimize kinematic control inputs over a prediction horizon and maps them to steering commands through a tire dynamics model augmented with SGP residual correction. Real-world vehicle experiments demonstrate substantial reductions in lateral tracking error and lap time. Compared with MAP and Pure Pursuit (PP), MAP2 reduces the average lateral tracking error by 37.99% and 44.65%, respectively, while reducing average lap time by at least 1.5%.
Figures & tables
Controller
Compute
High-speed tracking †
Model sensitivity
Pure Pursuit (PP)
Low
Limited
Low
MPC/MPCC
High
High
High
MAP
Low
Improved
High
MAP2 (ours)
Medium
High
Low
TABLE I : Comparison of representative autonomous racing controllers
Fig. 1 : Control structure of the racing car.
Fig. 2 : Visualization of the lookup table generated from the identified car model. From an implementation perspective, the desired acceleration is obtained by interpolating between the closest elements in the table.
Fig. 3 : 1:10-scale autonomous F1TENTH racing platform.
Fig. 4 : Real-world experiment.
Parameters
Value
Parameters
Value
m
4.24 kg
[Bf,Br]
[6.03,18.67]
Iz
0.067 kg ⋅ m 2
[Cf,Cr]
[1.26,1.27]
lf
0.168 m
[Df,Dr]
[0.87,0.87]
lr
0.162 m
[Ef,Er]
[0.19,0.27]
μ
1.0
TABLE II : Vehicle Parameters
Fig. 5 : Data points obtained from the steady-state cornering experiment and the resulting model fit of the Pacejka model.
Parameters
Value
Parameters
Value
N
64
Δt
0.05s
qn
100.0
qeψ
30.0
qv
14.0
rvy
2.0
rΨ˙
3.0
pn
300.0
peψ
50.0
ρ
500.0
vx,min
0.5m/s
vx,max
12.0m/s
TABLE III : MAP2 Control Parameters
Fig. 6 : The tracks of two different maps.
Fig. 7 : Effect of SGP on lateral-acceleration tracking for a representative MAP2 segment.
Fig. 8 : The comparison of the controllers when tires and tire parameters mismatch (MAP in 75% velocity crashed into the wall and did not finish)
Velocity scale (%)
Controller
Avg. Lateral error (m)
Max. Lateral error (m)
Lap time (s)
Avg.
Std.
Avg.
Std.
Fastest
Avg.
Std.
50
PP
0.0298
0.0007
0.1035
0.0085
11.054
11.097
0.021
MAP
0.0325
0.0018
0.0851
0.0030
10.946
10.981
0.034
MAP2 w/o SGP
0.0471
0.0022
0.1076
0.0078
11.070
11.121
0.034
MAP2 w/ SGP
0.0504
0.0028
0.1190
0.0087
10.942
10.997
0.031
60
PP
0.0723
0.0015
0.2100
0.0171
9.582
9.600
0.014
TABLE IV : Controller performance on the physical system in map I
Velocity scale (%)
Controller
Avg. Lateral error (m)
Max. Lateral error (m)
Lap time (s)
Avg.
Std.
Avg.
Std.
Fastest
Avg.
Std.
50
PP
0.0466
0.0013
0.1655
0.0063
8.146
8.172
0.018
MAP
0.0243
0.0008
0.1140
0.0063
8.054
8.080
0.019
MAP2 w/o SGP
0.0503
0.0022
0.1088
0.0064
8.159
8.203
0.032
MAP2 w/ SGP
0.0371
0.0018
0.1056
0.0097
8.047
8.099
0.038
60
PP
0.1327
0.0029
0.3584
0.0160
7.031
7.087
0.033
TABLE V : Controller performance on the physical system in map II
Autonomous race cars, such as in Formula Student Driverless, operate close to their physical handling limits. The resulting highly nonlinear vehicle behavior increases the path tracking complexity, especially on narrow tracks. Model Predictive Control (MPC) is commonly used to address this issue, a method whose performance is closely tied to the accuracy of the underlying prediction model. This paper presents a novel, real-time capable prediction model for autonomous race cars that adjusts to changing conditions by combining information from past runs and the current driving situation. Our model is divided into three consecutive submodels: a nominal Kinematic Bicycle Model, an offline Bayesian Linear Regression (BLR) model, and an online Sparse Gaussian Process Regression (SGPR) model. The proposed approach enables efficient integration of all available data without significantly increasing computational cost, ensuring high prediction accuracy and a quantitative uncertainty assessment right from the start of the run. Compared to existing approaches, an improvement in prediction accuracy of up to 57% was achieved. Further, we successfully demonstrated the practical applicability of the model within an MPC-based path tracking controller on a real Formula Student race car.
Sebastian Baader, Tamara Bergerhoff, Pascal Meißner +1
Center for Artificial Intelligence and Robotics (CAIRO); TUAS Würzburg-Schweinfurt, Germany
This paper presents Adaptive Differentiable Model Predictive Contouring Control (AD-MPCC), a framework for autonomous racing that integrates differentiable MPCC with online parameter estimation to handle varying road-surface conditions. For online parameter estimation, we leverage a parameterized Pacejka Magic Formula together with a regularized moving-horizon estimation scheme with exponentially decaying weights to capture road interactions and update parameters in real time. Furthermore, we propose a differentiable MPCC (Diff-MPCC) framework that enables optimal adjustment of objective weights based on predefined long-horizon performance costs. To implement Diff-MPCC for online objective weight adaptation, we propose a Pacejka-informed machine learning model that is trained in a supervised manner using data generated by Diff-MPCC to tune the objective weights. Simulation results demonstrate that AD-MPCC reliably ensures safety and achieves faster lap times compared to baseline controllers in both single-surface and multiple-surface scenarios.
Nam T. Nguyen, Binh Nguyen, Ahmad Amine +3
Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA. · Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA. · CTI Lab4EV, School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam.
This paper presents a Model Predictive Control-based motion planning and control pipeline for autonomous car racing capable of adapting to different driving contexts, such as overtaking, nominal driving, and countersteering. A Cost Blending state machine manages the identification of different driving contexts and the selection of their predefined weights to be applied to the Model Predictive Planning (MPP) and Control (MPC) modules. The two optimization-based solutions share the same problem formulation and model, differing only in horizon length, rate, tuning, and in their open-loop versus closed-loop approach to maximize the effectiveness of their interaction. The work is validated on the fully autonomous open-wheel racecar Superformula EAV-25, with a lap time achieved that is within 2% of the best human driver reference. The results demonstrate the capability of the solution in driving at the limit of handling, smoothly executing overtaking maneuvers, and quickly reacting to high oversteering conditions to recover the vehicle stability.
Ayoub Raji, Federico Sacco, Nicola Musiu +1
University of Modena and Reggio Emilia, 41125 Modena, Italy · Hipert S.r.l., Modena, Italy