Safe operating envelope generation using phase portraits for a tractor-semitrailer combination

Paper in proceeding, 2026

Articulated heavy vehicles are prone to jackknifing and trailer swing on low‑friction roads, yet conventional control systems rely on fixed slip thresholds that may be inadequate. This study presents a phase‑portrait method to generate state‑dependent Safe Operating Envelopes (SOEs) for a tractor‑semitrailer combination. A nonlinear single‑track model is developed, and its five‑dimensional dynamics are decoupled into two robust 2D phase planes, while preserving coupling through kinematic relations. Equilibrium points are classified by the Jacobian eigenvalues, and global stability is assessed using finite-time largest Lyapunov exponents. Tire slip limits are overlaid, and the intersection of the basin of attraction with the safe and efficient region defines the SOE. Parametric sweeps of steering angle, road friction, longitudinal slip, and vehicle speed demonstrate how each parameter influences the safe operating region of the tractor and the trailer. The resulting SOEs provide an adaptive foundation for real‑time stability and slip control.