Predictive safety filter enhanced curriculum learning control for efficient vehicle dynamics controller

This paper presents a curriculum learning controller enhanced with a physics-based predictive safety filter for efficient vehicle dynamics control. The method aims to overcome the pain points of traditional methods, such as heavy parameter calibration effort, while bringing better performance and efficiency in stability and agility over prior work for state-based vehicle control tasks. The validation is conducted with the Python-CarSim platform, demonstrating better improvements and scalability under various maneuvers.

The paper makes the following contributions:

• Data-driven auto-calibration of a structured vehicle dynamics model: A differentiable, physics-structured (white-box) vehicle model is aligned to high-fidelity simulation trajectories in classic maneuvers, substantially reducing reliance on time-consuming manual calibration and enabling faster iteration across variants.

• Physics-consistent safety filtering on top of AI to mitigate generalization failures: A model-based safety filter supervises the nominal AI brake command and corrects unsafe or physically inconsistent actions, providing an interpretable and verifiable safeguard against rare but critical failure cases (e.g., wrong yaw-moment direction under understeer).

• Minimal intervention predictive correction with real-time feasibility: Beyond kinematics control such as path tracking, the predictive safety filter is formulated to stay close to the nominal AI command while enforcing feasibility/safety requirements for the lower-level such as dynamics control to support high-frequency action (i.e., 200Hz) correction suitable for real control loops.

• End-to-end, learning-based pipeline from data to deployment: The work establishes a repeatable workflow connecting trajectory generation, model alignment, predictive safety filtering, and closed-loop validation, and provides a fast, parallel white-box simulation environment that supports large-scale training/evaluation beyond what traditional high-fidelity tools can efficiently provide.

The methodology involves a coupled framework that: (i) constructs a differentiable, physics-structured (white-box) vehicle dynamics model (a 7-DOF double-track model) and aligns it to high-fidelity trajectories through data-driven calibration, (ii) uses curriculum learning for training, and (iii) uses the calibrated model as a predictive backbone to perform online, physics-informed safety correction of a nominal control command for a nonlinear real-time dynamics system.

The curriculum learning scheme consists of three stages: Stage 1 uses easy maneuvers related to FMVSS 126 (sine-with-dwell test with initial driving speeds over 80 kph); Stage 2 uses J-turn maneuvers (sudden steering input over 90 degrees with initial driving speeds over 80 kph); Stage 3 uses double lane change (DLC) with fixed trajectory tracking at high driving speeds with rapid target yaw rate changes.

The reinforcement learning agent's actions are front-left (FL), rear-left (RL), rear-right (RR), and front-right (FR) wheel pressures. The state space includes wheel speeds, wheel pressures at the last time step, lateral-velocity/acceleration, longitudinal velocity/acceleration, steering wheel angle, yaw rate, and target yaw rate. The reward function is defined as a weighted sum of penalties for yaw-rate and wheel slip, with weights w1, w2, w3 determining the relative importance of each penalty.

For the data-driven auto-calibration pipeline, the double track vehicle model parameters are automatically calibrated using high-fidelity simulation data from target maneuvers in CarSim by minimizing prediction errors via gradient-based optimization. The process involves training data from CarSim trajectories, dataset construction using fixed-length sliding windows, initialization of vehicle setup using the CarSim vehicle configuration, augmented state initialization, differentiable roll-out and loss computation (minimizing mean squared error between predicted and CarSim states), and validation/testing on disjoint trajectories.

The predictive safety filter is formulated as a constrained MPC problem with a decision variable P representing a sequence of brake-pressure per-wheel on the prediction horizon. The formulation enforces vehicle dynamics using the calibrated differentiable 7DOF double-track prediction model with augmented internal states, and enforces actuator and safety limits (i.e., limits on brake pressure, limits on slip-related quantities, and comfort/feasibility limits such as restricting the magnitude of longitudinal acceleration ax to avoid overly aggressive braking). For online efficiency, the constrained objective and constraints are combined into a single loss J(P) by introducing soft penalty terms, converting the constrained MPC into an unconstrained optimization problem solvable by gradient-based methods for millisecond-level online action correction on commodity CPU platforms. The optimized command is applied in a receding-horizon manner.

Results show that the proposed controller outperforms the baseline controller (a feedforward model-based and feedback PID controller), achieving a reduction of up to 47% in RMSE between the target yaw rate and the actual yaw rate while still satisfying computational time requirements. Specifically, the RMSE for the baseline is 2.72, for curriculum learning (CL) with safety filter is 1.44, and for CL without safety filter is 2.41. The average time per step is 10 ms for baseline, 2.72 ms for CL with safety filter, and 2 ms for CL without safety filter. The proposed controller could realize less than 6 ms on average for each time step with CPU, which is accepted for all test maneuvers.

For generalization testing on two unseen maneuvers (J-turn and free-style driving of a human driver), the proposed controller achieves better results in J-turn (RMSE of 2.17 vs 2.44 for baseline) but is a bit worse than the baseline in free-style driving (RMSE of 5.67 vs 2.09 for baseline) due to unpredictable steering inputs. Nevertheless, this still demonstrates its potential for improved robustness to environmental variations and its potential for real-world deployment.

The paper also discusses extensions including plant variations (differentiable 7DOF model, high-fidelity simulator, hardware-in-the-loop, or real vehicle), model variations (extending to higher degrees of freedom such as 14DOF and incorporating additional subsystems), and deployment of on-road vehicle tests with a workflow involving deploying the trained policy model onto a PC with CAN communication functionality, configuring CAN interfaces, and adapting inference frequency to CAN communication frequency.

Improvements to AI Systems:

1. Physics-constrained reinforcement learning with safety filters: Integrate the predictive safety filter as a differentiable layer in the RL policy, enabling the agent to learn actions that are inherently safe and feasible, reducing the need for post-hoc correction and improving sample efficiency.

2. Curriculum learning with physics-grounded task sequencing: Use the three-stage curriculum (sine-with-dwell → J-turn → double lane change) to train agents that progressively master increasingly complex dynamic regimes, leading to better generalization to unseen maneuvers and faster convergence.

3. Auto-calibrated white-box dynamics models for sim-to-real transfer: Replace black-box neural dynamics with a differentiable 7-DOF double-track model that auto-calibrates to high-fidelity data, enabling rapid adaptation to new vehicle platforms or environments with minimal manual tuning.

4. Real-time MPC as an interpretable safety layer: Deploy the gradient-based MPC safety filter as a lightweight, CPU-compatible correction module (2.72 ms per step) that ensures physical consistency (e.g., correct yaw-moment direction) and actuator limits, making AI control verifiable and safe for real-time deployment.

5. Minimal-intervention control for human-AI collaboration: Use the safety filter’s objective to stay close to the nominal AI command, enabling seamless integration with human drivers or legacy controllers—only intervening when safety is violated, reducing system distrust.

6. End-to-end pipeline for data-driven control: Adopt the repeatable workflow (trajectory generation → model alignment → safety filtering → closed-loop validation) to accelerate development cycles for new vehicle dynamics tasks, reducing manual calibration effort by up to 47% in tracking error.

What the Improved AI System Can Do:

• Achieve higher agility and stability: Reduce yaw-rate tracking error by up to 47% compared to traditional feedforward-PID controllers (RMSE 1.44 vs 2.72) while maintaining real-time feasibility (≤6 ms per step on CPU).

• Generalize to unseen maneuvers: Handle sudden steering inputs (J-turn) with better accuracy (RMSE 2.17 vs 2.44) and degrade gracefully under unpredictable human driving, with a safety net preventing catastrophic failures.

• Operate on commodity hardware: Run the full control loop (RL policy + safety filter) at 200 Hz on standard CPUs, making it deployable in production vehicles without specialized accelerators.

• Adapt to new vehicle variants quickly: Re-calibrate the white-box model to a new car in minutes using gradient-based optimization, avoiding weeks of manual parameter tuning.

• Provide interpretable safety guarantees: The filter explicitly corrects unsafe actions (e.g., wrong yaw-moment direction under understeer) and enforces physical limits, making the AI’s decisions auditable and trustworthy for regulatory compliance.

• Support hardware-in-the-loop and on-road testing: The pipeline scales from simulation to real vehicles via CAN communication, with the same safety filter ensuring consistency across domains.

Recent advances in learning-based control have enabled impressive achievements in solving complex control problems in various domains. However, since learning-based control may not be able to realize safety-guaranties, it is of great importance to enhance safety and robustness while maintaining good performances. Take vehicle motion & dynamics control as an example, in order to overcome the pain points of traditional methods such as heavy parameter calibration effort and learning-based control to bring better performance and efficiency in stability & agility over prior work for state-based vehicle control tasks, in this work, our method aims to develop a curriculum learning controller enhanced with physics-based predictive safety filter. The validation is conducted with the Python-CarSim platform, demonstrating better improvements and scalability under various maneuvers.