Vehicle Drift Emergence: Continuous Evolution from Grip Driving to the Handling Limit via Boundary Exploration Learning Model Predictive Control

Abstract

Automated drift controllers commonly track a prescribed drift equilibrium, sideslip reference, or trajectory. These formulations establish how to execute drift, whereas the continuous transition from grip driving to drift near the handling limit remains unresolved. This paper defines drift emergence in a repetitive lap time minimization task, where neither the controller objective nor the reward contains an explicit drift reference. A boundary exploration learning model predictive controller (BE-LMPC) constructs an empirical safe set and a locally shifted terminal cost from completed laps. By iteratively improving spatial speed allocation under a fixed global speed bound, the controller progressively explores larger sideslip and yaw rate envelopes while preserving recoverability. As lap performance improves, sustained sideslip and pronounced yaw motion emerge while the rear axle approaches saturation. Analysis shows that, when external conditions vary smoothly, the transition from tire adhesion to sliding does not itself cause abrupt changes in tire force or vehicle state. The combined-slip Fiala model satisfies this continuity condition at the transition. At a tire road friction coefficient of 0.6, lap time decreases from 49.95 s on Lap~3 to 25.50 s on Lap~12, with drift first emerging on Lap~11. Lap~12 reaches 16.5$^\circ$ sideslip and 0.894 rear axle utilization. In contrast, no drift is detected for friction coefficients from 0.8 to 1.2; at 1.2, a similar peak speed is achieved with only 0.483 rear axle utilization. These results characterize drift as a conditional continuation of limit handling that emerges when increasing performance demand approaches the available tire capacity, rather than as a separately prescribed motion mode.