Real-Time Multidimensional Vehicle Dynamic Stability Domain Calculation and Its Application in Intelligent Vehicles

Vehicle stability is fundamental to the safe operation of intelligent vehicles, and real-time, high-accuracy calculation of the stability domain is crucial for maintaining control across the full range of driving conditions. Because the real stability domain is difficult to parameterize accurately and is shaped by multiple driving factors including vehicle-dynamics parameters and environmental conditions, existing approaches fail to capture the multidimensional couplings between time-varying driving inputs and the resulting stability boundaries. Moreover, these methods remain overly conservative owing to algorithmic limitations and cautious design assumptions, thereby restricting dynamic performance in complex scenarios. To address these limitations, this paper introduces a multidimensional vehicle dynamic stability region calculation framework under time-varying driving conditions and apply it into path tracking controller of intelligent vehicle. Sum-of-squares programming (SOSP) is enhanced with iterative shape functions to have a more precise description of the stability domain across discrete operating conditions. A feature analysis of the driving factors including key vehicle parameters and road conditions that influence stability-domain variation is conducted based on the SOSP. A multi-input-multi-output neural network is then used to continuously maps time-dependent driving factors to their stability-domain characteristics. Furthermore, a linear interpolation is adopted to parametrically represent the stability-domain boundary. Verification on a hardware-in-the-loop (HiL) platform demonstrates that the proposed method accurately captures the stability-domain characteristics in time-varying environments subject to multiple factors. Furthermore, the path-tracking controller equipped with the proposed model computes the stability-domain boundary in real time, improves maneuverability by limiting unnecessary interventions, and markedly reduces maximum tracking error.