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Safe Overtaking for Autonomous Racing Using Hierarchical Optimization and Learning-Based Control

This paper proposes a hierarchical overtaking framework for autonomous racing that combines a high-level Mixed-Integer Quadratic Program for maneuver selection with a nonlinear Model Predictive Control controller enhanced by a reinforcement learning policy to adaptively tune safety barrier constraints, thereby achieving robust safety-performance trade-offs across varying track conditions without manual tuning.

Original authors: Hassan Jardali, Kai Yin, Lantao Liu

Published 2026-07-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hassan Jardali, Kai Yin, Lantao Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where robots aren't just following strict rules to avoid bumping into things, but are actually competing against each other at breakneck speeds. This is the thrilling, high-stakes arena of autonomous racing. Unlike a self-driving car on a highway, which prioritizes a smooth, comfortable ride and strict adherence to traffic laws, a racing robot has to dance on the very edge of its tires' grip to win. It's like trying to ride a bicycle at full speed while juggling, where the goal is to be the fastest without crashing. The biggest challenge in this sport is overtaking: how do you squeeze past a rival without hitting them or spinning out? To solve this, scientists use a special kind of "safety net" called a Control Barrier Function (CBF). Think of this as an invisible, stretchy bubble around the car that says, "You can go this fast, but if you get any closer to the edge, you must slow down." The tricky part is that if this safety bubble is too stiff, the car becomes a coward, refusing to pass anyone. If it's too loose, the car crashes. The big question is: how do you make this safety bubble smart enough to know when to be tight and when to be loose, all while the race is happening?

This paper introduces a clever new way to teach racing robots how to overtake safely and aggressively. The authors, Hassan Jardali, Kai Yin, and Lantao Liu, propose a "hierarchical" system, which is like giving the robot a brain with two distinct layers of thinking. The first layer is the "strategist." It looks at the race and makes big, discrete decisions, like "I will pass on the left" or "I will pass on the right." It uses a mathematical tool called Mixed-Integer Quadratic Programming (MIQP) to solve this puzzle, essentially picking the best path through the traffic before the car even starts moving. The second layer is the "pilot." Once the strategist picks a side, the pilot uses a sophisticated controller called Model Predictive Control (MPC) to actually steer the car, making sure it stays within the laws of physics and doesn't hit the walls.

However, the authors noticed a problem with how these safety bubbles usually work. Traditionally, the "stiffness" of the safety bubble is set to a fixed number by a human engineer. This is like driving a car with a cruise control that never changes its speed limit, no matter if you're on a straight highway or a tight corner. The paper argues that this fixed approach is too rigid; it often forces the car to be overly cautious, missing great opportunities to pass, or it requires constant manual tweaking for every single racetrack. To fix this, the team added a third ingredient: a "coach" powered by Reinforcement Learning (RL). This coach watches the race in real-time and adjusts the stiffness of the safety bubble on the fly. If the car is far from the opponent, the coach loosens the bubble to let the car be aggressive. If the car is right next to a rival, the coach tightens the bubble to ensure safety.

The researchers tested this three-part system in computer simulations across four different famous race tracks, including the Indianapolis Motor Speedway and Laguna Seca. They found that no single fixed setting for the safety bubble worked well on all tracks; a setting that was perfect for one track was terrible for another. In contrast, their adaptive "coach" learned to adjust the safety settings automatically. In these simulations, the adaptive strategy achieved the highest overall success rate of 67%, meaning the car finished the race without crashing more often than any of the fixed settings. It also managed to complete more laps and perform more overtakes without needing to be re-tuned for each new track.

To prove this wasn't just a computer trick, the team also built a smaller, scaled-down racing car and tested the system in the real world. They used a virtual "ghost" opponent to simulate a race. The results showed that the system could run fast enough to keep up with the car's movements, making decisions in milliseconds. The experiments confirmed that the hierarchical approach—separating the big decision of where to pass from the detailed control of how to drive—was crucial. When they tried to remove the "strategist" layer and let the "pilot" figure out the passing side on its own, the car got confused, got stuck in loops, and crashed much more often.

In short, the paper suggests that for autonomous racing to be truly competitive and safe, robots need a team approach: a strategist to pick the right lane, a pilot to handle the driving, and a smart coach to adjust the safety rules in real-time. While the system isn't perfect yet (it still relies on some simplifications about how opponents move), the results show that letting a robot learn to tune its own safety margins is a much better idea than trying to guess the perfect setting beforehand. This work, accepted for the 2026 IEEE/RSJ International Conference on Intelligent Robots and Systems, opens the door for robots that can race not just safely, but with the daring and adaptability of a human champion.

Technical Summary: Safe Overtaking for Autonomous Racing Using Hierarchical Optimization and Learning-Based Control

Problem Statement
Autonomous racing requires agents to operate at the limits of vehicle handling to minimize lap times while guaranteeing collision avoidance. Overtaking presents a critical challenge where competitive performance and safety must be balanced under nonlinear dynamics and real-time constraints. While Model Predictive Control (MPC) combined with Control Barrier Functions (CBFs) offers a principled mechanism for certifying the forward invariance of safe sets, standard implementations often rely on fixed-decay discrete-time CBF formulations. The authors argue that these fixed-decay approaches become overly conservative in interactive racing scenarios. By enforcing safety locally at each time step without explicit long-horizon maneuver awareness, fixed parameters can prematurely exclude dynamically recoverable states, limiting overtaking performance and necessitating manual tuning for different track conditions.

Methodology
The paper proposes a hierarchical overtaking framework that explicitly separates maneuver-level decision-making from safety-certified trajectory control. The architecture consists of three primary components:

High-Level Discrete Planning (MIQP): A Mixed-Integer Quadratic Program (MIQP) resolves the combinatorial problem of overtaking topology selection (e.g., passing on the left or right). Operating in the Frenet frame, the MIQP selects a feasible overtaking side and generates a smooth lateral reference trajectory. This layer isolates the non-convexity of maneuver selection from the continuous trajectory optimization, preventing local minima and oscillatory behavior often found in purely continuous planners.
Low-Level Trajectory Control (MPC-DCBF): A nonlinear MPC formulated in the Frenet frame tracks the reference trajectory generated by the MIQP. It enforces vehicle dynamics (modeled via a kinematic bicycle model) and actuator limits. Safety is guaranteed through embedded discrete-time Control Barrier Function (DCBF) constraints, which enforce the forward invariance of a velocity-aware collision-avoidance set. To ensure recursive feasibility, these constraints are implemented as soft constraints with slack variables.
Adaptive Safety Modulation (RL): To mitigate the sensitivity of fixed-decay CBFs, a Reinforcement Learning (RL) policy adapts the DCBF decay parameter ( $\gamma$ ) online. Using the Policy-optimization via Adaptive Smooth Tchebycheff Attention (PASTA) framework, the agent learns to modulate $\gamma$ based on context (e.g., relative velocity, inter-vehicle distance, and track geometry). This allows the system to dynamically adjust safety margins—operating more conservatively during close interactions and more aggressively when safe—without directly controlling vehicle inputs or altering the underlying safety constraint structure.

Key Contributions

Unified Hierarchical Architecture: The integration of high-level MIQP for discrete homotopy selection with low-level MPC-DCBF control. This decomposition handles non-convexity at the decision level while maintaining dynamic feasibility and formal safety certification at the control level.
RL-Based Parameter Adaptation: A mechanism for the online adaptation of the discrete-time CBF decay parameter. This introduces context-dependent safety modulation, reducing conservatism while preserving the mathematical structure of the safety constraints.
Empirical Validation: Extensive simulation and scaled-hardware experiments demonstrating that no single fixed decay parameter achieves uniformly strong performance across diverse tracks, whereas the adaptive strategy achieves superior aggregate success rates without per-track tuning.

Experimental Results
The framework was evaluated in a custom Python simulation environment using a nonlinear kinematic bicycle model across four tracks: Indianapolis Motor Speedway (IMS), Kentucky Speedway (KS), Laguna Seca (LS), and Monza.

Performance: The adaptive policy, trained exclusively on LS, achieved the highest aggregate success rate (67%) across all tracks, outperforming all fixed- $\gamma$ configurations. For instance, on IMS, the adaptive policy achieved 72% success compared to a maximum of 68% for the best fixed $\gamma$ (0.70).
Robustness: Fixed decay parameters showed high sensitivity to track geometry; a parameter optimal for one track often resulted in catastrophic failures on another. The adaptive strategy maintained competitive performance and safety without manual tuning.
Ablation Study: Removing the MIQP layer resulted in a significant degradation of performance (e.g., success rate dropping from 50% to 20% on LS for the adaptive strategy), confirming that the hierarchical decomposition is critical for resolving discrete side-selection decisions in non-convex environments.
Real-Time Feasibility: Computational profiling on an Intel i7-12700H CPU showed the total latency (MPC: ~1.6ms, MIQP: ~5.5ms, RL: ~0.8ms) remains well within a 20ms control cycle (50 Hz).
Hardware: Scaled hardware experiments on an F1TENTH platform with a virtual opponent demonstrated the deployability of the framework under real sensing and actuation constraints.

Significance and Claims
The paper claims that the proposed hierarchical framework effectively balances the competing objectives of safety and competitiveness in multi-vehicle racing. By decoupling combinatorial maneuver selection from continuous control and employing an adaptive mechanism for safety margins, the system achieves robustness to environmental variations that fixed-parameter approaches cannot match. The authors emphasize that this approach allows for "context-dependent modulation of safety margins" without sacrificing the formal guarantees provided by CBFs. The work concludes that while safety guarantees rely on the assumption of inactive slack variables in the soft formulation, the adaptive strategy significantly improves the practical applicability of MPC-CBF controllers in dynamic, interactive racing scenarios. The implementation is released as open source to support reproducibility.

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