Leveraging Control Barrier Functions for Vehicle Yaw Stability in the Sideslip-Yaw Rate Space

Abstract

This thesis presents a safety-critical braking-based control framework for vehicle yaw stabilization using a unified Control Lyapunov–Barrier Function (CLBF) formulation for advanced driver assistance systems (ADAS). The proposed controller computes the four wheel braking torques required to generate a corrective yaw moment that keeps the vehicle state inside a prescribed region defined in the sideslip–yaw rate phase plane. The control objective is posed as a constrained quadratic program(QP), enabling the simultaneous enforcement of stability. The controller was implemented in MATLAB/Simulink® using the CasADi optimization toolkit and integrated with a high-fidelity vehicle dynamics model (CarSim®). A complete driver-in-the-loop experimental setup was developed using a five degree-of freedom (5-DOF) motion simulator (SimCraft APEX5), a steering wheel interface (Logitech G29), and a three-screen immersive display. The CLBF controller was evaluated using three aggressive and stability-critical maneuvers: Sine-with-Dwell, Fishhook, and Double Lane Change (DLC). Such maneuvers provide comprehensive validation by inducing rapid lateral load transfer, large sideslip excursions, and near-spin conditions. Across all maneuvers, the controller successfully maintained the state inside the CLBF stability region and produced better coordinated braking interventions compared with conventional Electronic Stability Control (ESC). The designed road friction estimator and controller were validated under three friction scenarios; uniform low friction, step changes in friction, and split-μ conditions; demonstrating accurate tire-force estimation, friction estimation, and robust stability across varying road surfaces. Real-time feasibility was achieved by warm-starting the control inputs, linearizing the constraints, and converting the nonlinear program (NLP) into a QP, which reduced computation time from nearly one hour to approximately 5 seconds for a 3-second simulation maneuver. Furthermore, the controller was ported to a Python implementation embedded directly within CarSim®, enabling near real-time execution. Experimental results under the Double Lane Change (DLC) maneuver at a medium road friction coefficient (μ = 0.5) show that the CLBF controller significantly outperforms a conventional Electronic Stability Control (ESC) system. The proposed controller reduces peak yaw rate by up to 50%, maintains sideslip angle within 3 degrees, and ensures that the entire state trajectory remains inside the CLBF ellipse. Additionally, migrating the controller from MATLAB to Python reduced the real-time computation ratio from 2.1:1 (2.1 seconds of computation per 1 second of driving) to 1.2:1, demonstrating feasibility for embedded deployment. Overall, the results highlight the potential of CLBF-based braking control to deliver provable stability guarantees and real-time feasibility in aggressive driving scenarios. This framework offers a strong foundation for future ADAS and autonomous vehicle architectures requiring certified safety and robust yaw-stability control.