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Driving Context-guided Model Predictive Planning and Control for Autonomous Car Racing at the Limit and Beyond

Ayoub Raji, Federico Sacco, Nicola Musiu, Marko Bertogna

arXiv:2609.12660v1cs.ROcs.SYeess.SY

TL;DR

Autonomous racing controllers face challenges adapting to different driving contexts and handling beyond-limit conditions such as high sideslip. This paper combines context-selected planning and control costs with a dual-MPC pipeline, and reports a lap time within 2% of the best human reference.

  • Problem

    Prior autonomous-racing work gives limited attention to transient, adaptive drifting and driving-style switching, while reference-tracking MPC requires weight tuning to accommodate new objectives.

    Source: §I · p. 1

  • Method

    A context-detecting state machine selects cost weights for planning and control, whose MPC modules share a vehicle model but use different tuning and open-loop versus closed-loop operation.

    Source: §I · pp. 1–2, D. Cost Blending · p. 3, A. VEHICLE MODEL · p. 4

  • Results

    Within 2% of the best human reference, the autonomous open-wheel racecar achieved a lap time of 58.76 s versus 57.57 s by a former Formula 1 driver.

    Source: §I · p. 2, B. Nominal Driving Scenario · p. 6

  • Takeaways & Limitations

    The authors conclude that the context-switching solution addresses path-tracking-oriented cost limitations and can be adapted to additional driving contexts.

    Source: §VI · p. 8

Abstract

from arXiv · show

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.

I. INTRODUCTION

Prior work leaves limited coverage of transient, adaptive drifting and driving-style switching, while reference-tracking MPC requires retuning for new objectives. This paper proposes context-aware planning and control for switching driving modes and managing their priorities.

I. INTRODUCTION

  • The paper proposes a hierarchical, modular approach in which a state machine detects driving context and selects cost weights for planning and control.It is designed to switch driving modes while dynamically managing priorities between them.Source: §I · p. 1
  • Within 2% of the best human reference lap time, the system was demonstrated on a fully autonomous open-wheel racecar.The platform is the Dallara Superformula EAV-25.Source: §I · p. 2
  • The system targets beyond-limit vehicle control in extreme racing, including high sideslip and model mismatch not addressed by prior countersteering controllers.The stated scenarios include nominal driving, overtaking, and oversteering.Source: §I · p. 2
  • The dual-MPC architecture uses the same vehicle model for planning and control, with different tuning and open-loop versus closed-loop operation.The paper positions this design as supporting coherent interaction between the modules.Source: §I · p. 2

II. SYSTEM OVERVIEW

The system assigns trajectory generation and tracking to two modules that share a vehicle model but serve different roles. A separate longitudinal planner supplies speed targets, while the open-loop MPP generates feasible paths for the closed-loop controller.

II. SYSTEM OVERVIEW

  • MPP and MPC share the same vehicle model and parameters, letting the planner generate feasible references and the controller track them aggressively.The planner is tuned for smoothness and stability; the controller prioritizes tracking performance.Source: §II · p. 2

A. Longitudinal Planner

  • A dedicated longitudinal planner computes pathwise velocity profiles by forward–backward integration under lateral and longitudinal acceleration constraints.It translates normalized friction-ellipse performance requests into velocity targets for the MPP.Source: A. Longitudinal Planner · p. 2

B. Model Predictive Planner (MPP)

  • The MPP runs open-loop at 20 Hz over 150 steps (6 s), generating smooth, feasible paths within track margins and dynamic constraints.Its previous solution can be reprojected to the current longitudinal position; replanning is triggered by errors or an objective change.Source: B. Model Predictive Planner (MPP) · pp. 2–3
  • Open-loop planning preserves a stable, continuous reference so the shorter-horizon, higher-frequency controller can handle tracking errors and disturbances.The paper also cites independent evaluation and simpler tuning as reasons for the open-loop design.Source: B. Model Predictive Planner (MPP) · p. 3

C. Model Predictive Controller (MPC)

The MPC closes the loop using vehicle feedback and focuses on tracking and stability, leaving trajectory changes for non-nominal scenarios to the planner. Track constraints are softened so stability can take priority during critical maneuvers.

C. Model Predictive Controller (MPC)

  • The MPC runs closed-loop at 100 Hz over 64 steps (2.6 s), updating its initial state from vehicle feedback filtered through localization and state estimation.It uses the same sampling time as the MPP: 0.04 s.Source: C. Model Predictive Controller (MPC) · p. 3
  • The controller focuses on tracking and stability, while the planner handles non-nominal scenarios by producing an appropriate new reference trajectory.Handling model mismatch, compensating errors, and path-following are assigned to the controller.Source: C. Model Predictive Controller (MPC) · p. 3
  • Soft track constraints let the controller prioritize stability during critical maneuvers; its longitudinal-acceleration output is converted to throttle and brake commands by low-level control.The low-level module combines feedforward and PID feedback compensation.Source: C. Model Predictive Controller (MPC) · p. 3

D. Cost Blending

The cost-blending state machine selects among scenario-specific cost sets for the planning and control modules. Sigmoid-based interpolation makes transitions gradual, and the state-machine scheme distinguishes planner, controller, and shared states.

D. Cost Blending

  • Because a single cost function may not suit distinct racing maneuvers, the state machine selects scenario-specific MPPC cost sets and blends them smoothly using sigmoid interpolation.The stated scenarios include nominal driving, line switching, overtaking, and out-of-track conditions.Source: D. Cost Blending · p. 3

III. MPPC FORMULATION

  • The MPP and MPC optimization problems use a custom SQP framework with HPIPM and CppAD-CodeGen for real-time computation.HPIPM is described as a high-performance quadratic-programming solver for MPC applications.Source: §III · pp. 3–4

D. Cost Blending

  • The Cost Blending State Machine separates planner states, controller states, and states shared by both modules.Table III is identified as listing MPPC cost-blending states and activation criteria.Source: Figure 3 · p. 4, Table III · p. 4

A. VEHICLE MODEL

MPP and MPC use an enhanced nonlinear single-track model with Pacejka tires, formulated in curvilinear coordinates. At low speed, the model switches to kinematic dynamics and blends back to dynamic behavior as speed increases.

A. VEHICLE MODEL

  • MPP and MPC share an enhanced nonlinear single-track model incorporating the Pacejka Magic Formula tire model.Its inputs include steering rate and longitudinal jerk.Source: A. VEHICLE MODEL · p. 4
  • The model is discretized with a 4th-order Runge-Kutta method and formulated in curvilinear coordinates.Source: A. VEHICLE MODEL · p. 4
  • At speeds of 8 m/s or below, kinematic dynamics replace the dynamic model, with exponential blending back to dynamic behavior as speed increases.Source: A. VEHICLE MODEL · p. 4

B. Problem Formulation

The formulation constrains vehicle motion and inputs while weighting tracking, stability, and smooth control. Separate context-based cost blending assigns planner and controller objectives, with oversteer prioritized for stability.

B. Problem Formulation

  • The optimization is expressed over state and input vectors across the horizon, subject to the stated dynamics and constraints.Source: B. Problem Formulation · p. 4
  • Track and tire-friction-ellipse constraints bound the state trajectory, while box constraints bound inputs and their rates of change.Source: B. Problem Formulation · p. 4
  • The objective weights path following, velocity tracking, and yaw rate, penalizes input variation, and adds a sideslip penalty for stability near tire-friction limits.Source: B. Problem Formulation · p. 4

IV. DRIVING CONTEXT-BASED COST WEIGHTING

  • The planner blends costs for nominal driving, line switching, overtaking, and out-of-track scenarios.Source: §IV · p. 4
  • The controller blends nominal and oversteer objectives to handle trajectory tracking and tracking-error compensation.Source: §IV · p. 5
  • Oversteer can be entered directly from any context; other context changes require returning to nominal after satisfying exit conditions.Source: §IV · p. 5

A. Cost Blending

Cost blending uses sigmoid-based weighting for some context changes and discrete switching for others. Vehicle-state conditions govern the transitions, with lateral displacement and understeer degree regulating selected costs.

A. Cost Blending

  • The new cost is computed within an interval [a, b], using a sigmoid-dependent multiplier and a negative sigmoid whose maximum and minimum are swapped.Source: A. Cost Blending · p. 5
  • Line-switch cost shifts toward its designated cost as lateral displacement from the selected racing line increases; oversteering cost similarly depends on the understeer-degree threshold Uth.Source: A. Cost Blending · p. 5
  • Overtaking and out-of-bounds costs switch discretely on or off, while each transition monitors its corresponding vehicle states.Source: A. Cost Blending · p. 5

B. Tuning

MPP and MPC use separately tuned cost blends for planning and control tasks. The tuning relaxes the track constraint out of bounds and shifts controller priorities during oversteer to support stability recovery.

B. Tuning

  • Overtaking and line-switching share acceptable tuning, while the main differences across conditions concern path-tracking and sideslip weights.The tuning discussion identifies qn and qβ as the principal terms that differ.Source: B. Tuning · p. 5
  • Out-of-track tuning relaxes the track soft constraint to avoid abrupt return actions that may cause instability.Being out of track already indicates substantial performance mismatch or a hazardous operating condition.Source: B. Tuning · p. 5
  • Oversteer tuning lowers lateral-error weight, raises sideslip and heading-error weights, and increases track-limit soft constraints as a safety measure.The authors note that oversteer can occur during overtaking or near physical track boundaries.Source: B. Tuning · p. 5

A. Validation Setup

The system was validated on a full-scale open-wheel racecar, with onboard planning and control, and its lap time was within 2% of a former Formula 1 driver’s reference. The nominal-driving results also report tracking performance and explain mismatches associated with unmodeled vehicle or road effects.

A. Validation Setup

  • The proposed system was tested on a full-scale Dallara Superformula EAV-25, with MPP and MPC running onboard at 20 Hz and 100 Hz.Their average execution times were 15 ms and 5 ms, respectively.Source: A. Validation Setup · pp. 5–6
  • The onboard state estimation and localization use Extended Kalman Filters, while sensor fusion and motion forecasting support detection and prediction of other vehicles.The stated sensor suite includes LiDARs, RADARs, cameras, GNSS, IMUs, and an optical sideslip sensor.Source: A. Validation Setup · p. 6

B. Nominal Driving Scenario

  • 58.76 s versus 57.57 s: the autonomous agent’s lap time was within 2% of a former Formula 1 driver’s reference under the same vehicle, setup, and track conditions.The comparison used Yas Marina Circuit’s North Configuration during A2RL Season 2.Source: B. Nominal Driving Scenario · p. 6
  • The nominal-driving tracking differences include a Turn 1 turbo-lag mismatch, deliberate engine-performance overestimation, and a Turn 8 lateral outlier caused by an unmodeled three-dimensional road profile.The Turn 8 bump increases vertical axle load and affects lateral forces.Source: B. Nominal Driving Scenario · p. 6
  • The planner and controller track longitudinal velocity and yaw rate well, while the reported lateral deviation is generally within 40 cm.Figure 6 presents velocity, lateral deviation, heading error, and yaw rate along the lap, with planner-controller differences indicating tracking error.Source: Figure 6 · p. 6, B. Nominal Driving Scenario · p. 6

C. Overtaking Scenario

The system performed smooth overtaking maneuvers in real scenarios, while simulation results show how overtaking weights trade stricter path tracking for smoother, less aggressive motion. The paper also depicts planner and controller horizon changes during cost switching.

C. Overtaking Scenario

  • In simulation, overtaking weights reduce the predicted steering and steering-derivative peak from 0.11 to 0.036 rad, while lateral error increases from 2.64 to 3.46 m.The maneuver is less aggressive, with peak lateral velocity decreasing from 0.92 to 0.49 m while still allowing a safe overtaking action.Source: C. Overtaking Scenario · pp. 6–7, Figure 7 · p. 7
  • The proposed solution performed smooth, effective overtaking maneuvers in real scenarios during the Gran Finale event of A2RL.Figure 8 depicts two maneuvers, with the planned trajectory, opponent position, and global racing line shown.Source: C. Overtaking Scenario · p. 7, Figure 8 · p. 7

D. Oversteer Scenario

During a real-world oversteer event, the controller countersteered and recovered stability after the vehicle entered the corner faster than the local planner calculated. The conclusion presents context switching as the approach and identifies further contexts and tuning automation as future directions.

D. Oversteer Scenario

  • After cost switching, the planned steering angle increased in magnitude from -0.017 rad to -0.11 rad as the controller prioritized stability over strict path tracking.The velocity and lateral-error terms were temporarily downweighted, and the steering-rate term enabled a faster, broader countersteer action.Source: D. Oversteer Scenario · pp. 7–8
  • During the real-world Turn 1 oversteer event, countersteering limited sideslip to approximately 13° and stability was recovered by s ≈320 m.The vehicle entered faster than the local planner calculated, and the understeer angle briefly became highly negative.Source: D. Oversteer Scenario · p. 8

VI. CONCLUSIONS

  • The conclusion proposes adapting the architecture to contexts such as comfort and jerk minimization, and names automated weight tuning and cost-switch decisions as future work.Other possible contexts include mechanical malfunctions or track sectors needing particular performance optimization.Source: §VI · p. 8
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