MAP2: Model- and Acceleration-Based Pursuit with MPC and Gaussian Process Residual Learning for Autonomous Racing

Weizhan Huang; Cheng Hu; Edoardo Ghignone; Nicolas Baumann; Yiqin Wang; Hongye Su; Lei Xie; Michele Magno

cs.ROOct 8, 2026

MAP2: Model- and Acceleration-Based Pursuit with MPC and Gaussian Process Residual Learning for Autonomous Racing

Authors: Weizhan Huang, Cheng Hu, Edoardo Ghignone, Nicolas Baumann, Yiqin Wang, Hongye Su, Lei Xie, Michele Magno

Organizations: Zhejiang University · Center for Project-Based Learning, D-ITET, ETH Zurich

Abstract

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 $\dagger$	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.

Parameters	Value	Parameters	Value
$m$	$4.24$ kg	$[B_{f},B_{r}]$	$[6.03,18.67]$
$I_{z}$	$0.067$ kg $\cdot$ m 2	$[C_{f},C_{r}]$	$[1.26,1.27]$
$l_{f}$	$0.168$ m	$[D_{f},D_{r}]$	$[0.87,0.87]$
$l_{r}$	$0.162$ m	$[E_{f},E_{r}]$	$[0.19,0.27]$
$\mu$	$1.0$

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
$N$	$64$	$\Delta t$	$0.05\,\mathrm{s}$
$q_{n}$	$100.0$	$q_{e_{\psi}}$	$30.0$
$q_{v}$	$14.0$	$r_{v_{y}}$	$2.0$
$r_{\dot{\Psi}}$	$3.0$	$p_{n}$	$300.0$
$p_{e_{\psi}}$	$50.0$	$\rho$	$500.0$
$v_{x,\min}$	$0.5\,\mathrm{m/s}$	$v_{x,\max}$	$12.0\,\mathrm{m/s}$

TABLE III : MAP2 Control Parameters

Panel of Figure 9 — Fig. 6 : The tracks of two different maps.

Panel of Figure 10 — Fig. 7 : Effect of SGP on lateral-acceleration tracking for a representative MAP2 segment.

Panel of Figure 11 — 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)
Velocity scale (%)	Controller	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)
Velocity scale (%)	Controller	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

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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.

Abstract

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