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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

arXiv:2610.12196v1cs.RO

TL;DR

Autonomous racing needs accurate, low-latency tracking near vehicle handling limits, while geometric MAP retains look-ahead planning and can mismatch actual vehicle dynamics. MAP2 combines kinematic MPC with SGP correction to LUT-based steering. In real-vehicle tests, it reduced average lateral tracking error against MAP and Pure Pursuit and reduced lap time against both.

  • Problem

    Geometric MAP retains look-ahead-based lateral-acceleration planning and its offline LUT may mismatch actual vehicle dynamics, limiting tracking near handling limits.

    Source: §I · p. 1

  • Method

    MAP2 combines a Frenet-frame kinematic MPC for predictive lateral-acceleration planning with an SGP that corrects LUT-based steering commands.

    Source: §I · p. 1, I MPC-Based Predictive… · p. 1

  • Results

    MAP2 reduced average lateral tracking error by 37.99% versus MAP and 44.65% versus PP at the highest speed of 75%.

    Source: D. Experiment Results · p. 6

  • Takeaways & Limitations

    Experiments on two tracks and multiple speeds demonstrate reduced high-speed lateral errors and lap times relative to MAP and PP, with robustness to tire-parameter mismatch.

    Source: §V · p. 7

    Online adaptation of SGP inducing points remains future work for runtime updates without offline retraining as operating conditions change.

    Source: §V · p. 7

Abstract

from arXiv · show

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%.

I. INTRODUCTION

MAP2 combines predictive lateral-acceleration planning with sparse residual learning to address geometric and model-mismatch limitations in MAP. The paper motivates the design for computationally constrained racing and reports experimental comparisons with MAP and Pure Pursuit.

I. INTRODUCTION

  • MAP2 was experimentally validated on a computationally constrained 1:10-scale F1TENTH platform against MAP and Pure Pursuit, including an ablation without SGP correction.The evaluation reports reduced lateral tracking errors and lap times and robustness to tire-parameter modeling errors.Source: §I · p. 1, I MPC-Based Predictive… · p. 2

I MPC-Based Predictive Lateral-Acceleration Gener-

  • MAP2 combines a Frenet-frame kinematic MPC with SGP residual correction of LUT-based steering commands to address geometric planning and vehicle-model mismatch.The MPC replaces look-ahead-based lateral-acceleration calculation, while the SGP learns residuals from real-vehicle data; sparse inference takes 2.0 ms.Source: I MPC-Based Predictive… · p. 1, §I · p. 1

II. RELATED WORK

  • Geometric controllers are computationally efficient, but their assumptions become less accurate near handling limits, where tire slip and nonlinear lateral dynamics matter.Pure Pursuit's look-ahead distance also trades oscillatory steering at short distances against larger tracking error and corner cutting at long distances.Source: §I · p. 1, §II · p. 2
  • MAP uses a tire-model lookup table to map desired lateral acceleration and velocity to steering, but still derives acceleration geometrically and remains sensitive to LUT errors.MAP retains low online computational cost while accounting for tire slip and velocity-dependent steering response.Source: §II · p. 2
  • Unlike GP augmentation inside dynamic MPC, MAP2 applies sparse GP residual learning to the LUT steering map to keep the nominal controller lightweight.Sparse inducing points reduce inference cost for real-time compensation.Source: §II · p. 2

III. METHODOLOGY

The framework separates longitudinal and lateral control, with the paper focusing on the lateral controller. Its three components combine predictive planning, model-based steering, and residual correction.

III. METHODOLOGY

  • The broader control structure separates longitudinal velocity and motor control from lateral control, which is the focus of this paper.The longitudinal controller computes the velocity input and a lower-level PID controller manages the motors.Source: §III · p. 2, Figure 1 · p. 3
  • The lateral controller uses a Frenet-frame kinematic MPC to choose virtual velocity and yaw-rate inputs, then converts the first-stage solution into a lateral-acceleration request.The first-stage optimal longitudinal velocity is returned as the velocity command.Source: §III · p. 2
  • A model- and acceleration-based pursuit controller uses an estimated front-axle longitudinal force, while an SGP estimates residual steering correction for LUT-to-vehicle mismatch.These components follow the MPC stage in the lateral-control framework.Source: §III · p. 2

A. Curvature Model Predictive Control

The curvature MPC uses a Frenet-frame kinematic model and optimizes virtual inputs under track-boundary constraints. It applies only the first optimized input to request lateral acceleration.

A. Curvature Model Predictive Control

  • The Frenet model represents reference curvature, vehicle heading and yaw rate, distance along the trajectory, lateral deviation, and heading error.Its input variables include longitudinal velocity, lateral velocity, and yaw rate.Source: A. Curvature Model Predictive Control · p. 3
  • At high speeds, pure-pursuit Ackermann assumptions may fail to keep the vehicle within road boundaries, while MPC optimizes within vehicle-model and track-boundary constraints.The Frenet kinematic model excludes tire forces and facilitates construction of the MPC cost and constraints.Source: A. Curvature Model Predictive Control · p. 3
  • The MPC discretizes the model with Runge–Kutta at 0.05 s and optimizes over a prediction horizon using the current estimated state and admissible inputs.The slack factor softens lateral constraints and widens the feasible set.Source: A. Curvature Model Predictive Control · p. 3
  • Only the first-stage MPC input is used to calculate the optimal lateral-acceleration request.The controller therefore replans rather than applying the full predicted input sequence at once.Source: A. Curvature Model Predictive Control · p. 3

B. Model- and Acceleration-based Pursuit

MAP uses lateral vehicle dynamics to build a steering lookup, extending pursuit control beyond target-point geometry. For AWD, the lookup also accounts for front-axle longitudinal force.

B. Model- and Acceleration-based Pursuit

  • Pure Pursuit derives requested lateral acceleration from look-ahead geometry under Ackermann steering, assuming no sideslip so longitudinal and tangential speeds are equal.The requested acceleration and tangential speed are related to the look-ahead distance and angle.Source: B. Model- and Acceleration-based Pursuit · pp. 3–4
  • MAP establishes its steering mapping from lateral vehicle dynamics, and the desired acceleration is interpolated between nearby lookup-table entries.The table stores a mapping among steering angle, lateral acceleration, front-axle longitudinal force, and longitudinal velocity.Source: B. Model- and Acceleration-based Pursuit · p. 4, Figure 2 · p. 4
  • For AWD, front-axle drive force changes combined tire-force distribution and achievable lateral acceleration, so MAP adds that force as a lookup-table input.The LUT is used to retrieve steering for the MPC's optimal lateral acceleration, estimated front-axle force, and vehicle velocity.Source: B. Model- and Acceleration-based Pursuit · p. 4
  • The tire model and forward lateral-dynamics simulation retain steady-state points to build a lookup table over steering, lateral acceleration, front-axle force, and velocity.The tire forces use the Pacejka formula, and racing points with high sideslip are excluded.Source: B. Model- and Acceleration-based Pursuit · p. 4

C. Sparse Gaussian Process Residual Correction

MAP2 learns a steering residual from real-vehicle data to compensate for mismatch between the lookup table and vehicle dynamics. A sparse Gaussian Process predicts the correction that is applied to the nominal steering command.

C. Sparse Gaussian Process Residual Correction

  • MAP2 learns a steering residual from F1TENTH driving data because the nominal LUT command may not yield the expected lateral acceleration on the real vehicle.The residual training label is the difference between response-equivalent and nominal steering angles, both computed with the LUT.Source: C. Sparse Gaussian Process Residual… · p. 4
  • The SGP input combines measured vehicle velocities, yaw rate, accelerations, previous steering, and sideslip angle.Training signals are evaluated at a response-delay-adjusted sampling time.Source: C. Sparse Gaussian Process Residual… · p. 5
  • The trained SGP predicts a steering-residual correction that is combined with the nominal LUT steering command before applying steering limits.The final command is constrained by steering magnitude and per-cycle steering-increment limits.Source: C. Sparse Gaussian Process Residual… · p. 5
  • The sparse GP uses 200 inducing points, with its hyperparameters optimized for 300 Adam steps.The implementation uses a constant mean, scaled RBF kernel, and Gaussian likelihood.Source: C. Sparse Gaussian Process Residual… · p. 5

A. Experimental Setup

Physical experiments used a 1:10-scale AWD car with onboard sensing, state fusion, and an Intel NUC computer running ROS.

A. Experimental Setup

  • The experimental platform was a 1:10-scale Serpent SRX8GTE AWD car.The study reports physical vehicle experiments on this platform.Source: A. Experimental Setup · p. 5
  • A Hokuyo UST-30LX LiDAR, VESC-embedded IMU, and odometry supplied data fused to estimate vehicle state.The LiDAR's maximum scan frequency was 40 Hz.Source: A. Experimental Setup · p. 5
  • An Intel NUC ran ROS onboard, and acados solved the MPC optimization problem.Source: A. Experimental Setup · p. 5

B. System Identification

System identification uses steady-state cornering data to fit the Pacejka tire model. The paper lists vehicle and controller parameters in Tables II and III.

B. System Identification

C. Objective and Test Procedure

The evaluation compares PP, MAP, and MAP2 across two maps, speed settings, and a cross-tire parameter-mismatch test.

C. Objective and Test Procedure

  • The study compares tracking performance and lap times for PP, MAP, and MAP2 on two maps, and separately evaluates robustness to tire-parameter mismatch.Source: C. Objective and Test Procedure · p. 6, Figure 6 · p. 6
  • Tests begin at 50% of ideal speed, increase speed until the car crashes into track boundaries, and attempt ten laps per test.The speed profile assumes perfect tracking.Source: C. Objective and Test Procedure · p. 6
  • Cross-tire validation applies tire A's offline LUT parameters to tire B; MAP2 with SGP additionally retrains on tire B driving data.The evaluation metrics are average and fastest lap time, and average and maximum lateral error.Source: C. Objective and Test Procedure · p. 6

D. Experiment Results

MAP2 improves high-speed tracking and lap-time results over MAP and PP, while cross-tire tests show improved performance under tire-parameter mismatch.

D. Experiment Results

  • At 75% speed, MAP2 reduces average lateral tracking error by 37.99%, maximum lateral tracking error by 57.48%, and lap time by 1.57% versus MAP.Source: D. Experiment Results · p. 6
  • At 75% speed, MAP2 reduces average and maximum lateral tracking errors by 44.65% and 47.81%, respectively, and lap time by 3.27% versus PP.Source: D. Experiment Results · p. 6
  • At 75% speed, SGP reduces MAP2's average lateral error, maximum lateral error, and average lap time by 26.15%, 22.16%, and 1.13%, respectively.For representative segments, SGP reduces lateral-acceleration tracking RMSE from 1.252 to 1.141 m/s2, an 8.87% reduction.Source: D. Experiment Results · p. 6
  • Under cross-tire mismatch, MAP2 reduces average and maximum lateral tracking errors by 23.89% and 36.89% at 70% speed; at 75%, it completes 10 laps while MAP crashes.SGP further improves performance without regenerating the nominal LUT.Source: D. Experiment Results · p. 6

V. CONCLUSIONS

MAP2 combines predictive kinematic MPC, a model-based steering lookup table, and SGP residual correction. Real-world experiments report improved high-speed performance and robustness to tire-parameter mismatch, with low computational cost.

V. CONCLUSIONS

  • MAP2 combines kinematic MPC for predictive lateral-acceleration generation, a model-based LUT for steering computation, and SGP residual correction.The framework is described as improving predictive tracking and compensating for model mismatch while maintaining low latency.Source: §V · p. 6
  • On a 1:10-scale F1TENTH platform, across two tracks and multiple speed settings, the proposed controller reduced high-speed lateral tracking errors and lap times relative to MAP and PP, with further improvements from SGP residual correction.Source: §V · p. 7
  • The experiments and low computational cost support MAP2's suitability for real-time autonomous racing on computationally constrained systems.Source: §V · p. 7
  • Future work will adapt SGP inducing points online so residuals can update at runtime without offline retraining when operating conditions change.Source: §V · p. 7
  • The validated controller's behavior on a full-scale racing car remains a proposed area for future testing.Source: §V · p. 8

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