Friction-Aware Speed Planning with Gaussian Process Uncertainty and Chance-Constrained Model Predictive Control

Preprint, 2026

This paper presents a friction‑aware speed‑control framework that provides probabilistic braking guarantees on collision avoidance under uncertain road friction conditions. Road friction is modeled as a spatial Gaussian Process (GP) whose nonstationary variance reflects perception confidence, enabling an adaptive representation of friction ahead of the vehicle. Under a Gaussian friction assumption, we derive an analytic one‑sided chance constraint that ensures stopping within a prescribed distance at a specified risk level. This chance constraint is incorporated into a spatial‑domain model predictive controller (MPC) as a terminal feasibility condition on the distance beyond the prediction horizon, while safety within the horizon is enforced conservatively by constraining acceleration using GP‑based lower bounds on available friction. The resulting MPC formulation is computationally efficient and transparent, which facilitates its integration into AEB and ACC functionalities.
Validation through 1,000‑run Monte Carlo simulations shows that the empirical hit rate (safety‑requirement violations) matches the prescribed risk level. The behavior depends on how friction uncertainty is modeled: with spatially uniform uncertainty the controller is mildly conservative, while spatially varying friction uncertainty yields behavior close to the nominal risk. Additional ACC scenarios with a snow–ice transition show that hit rates depend strongly on the assumed lead‑vehicle friction model (highlighting the need to model lead braking capability correctly), whereas perception quality and occlusion have relatively minor effects.