Limit-aware trajectory planning with coupled longitudinal, lateral, and yaw dynamics

Near-limit trajectory planning for autonomous vehicles is fundamentally constrained by vehicle dynamic capabilities. However, existing approaches seldom incorporate fully coupled longitudinal, lateral, and yaw dynamics, limiting accuracy and safety margins in extreme manoeuvres. This study proposes a real-time trajectory planning framework that combines vehicle motion envelope modelling and online optimisation under envelope constraints. Specifically, the generalised acceleration envelope, defined as the feasible boundary of the vehicle's coupled longitudinal, lateral, and yaw accelerations under dynamic constraints, is constructed using a double-track vehicle model with longitudinal and lateral load transfer. For real-time planning, a multiple shooting formulation is adopted in the Frenet frame, where the fitted analytical envelope embedded as a dynamic constraint. The proposed approach is applicable to various vehicle configurations and is particularly beneficial for high-centre-of-gravity vehicles under near-limit conditions, where load transfer effects are more significant. The proposed method is validated through co-simulations, as well as full-scale vehicle experiments. The maximum double lane change (DLC) safe passing speed was improved by 28.57% over the decoupled planning baseline and 7.14% over the coupled planning baseline with a friction ellipse constraint. Experimental results demonstrate that the proposed method improves safety of autonomous vehicles in aggressive driving conditions.