Organizations: School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. · Department of Advanced Energy, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, 277-8561, Japan. · Faculty of Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China.
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 Lap3 to 25.50 s on Lap12, with drift first emerging on Lap11. Lap12 reaches 16.5∘ 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.
Figures & tables
Figure 1: Planar three-degree-of-freedom single-track model with vehicle sideslip angle β .
Figure 2: Continuous grip-to-drift evolution. (a) Normalized Fiala lateral force (top) and incremental cornering stiffness (bottom) for χx=0 , 0.5, and 0.8; open circles mark sliding onset. (b) (β,r) trajectories through the critical corner for Laps 3, 5, 7, and 9 through 12 at μ=0.6 . Open circles linked by the dashed line identify the fixed location s/L=0.467 , marked by a star on the inset track. Gray dotted lines denote the ∣β∣ and ∣r∣ thresholds. The inset track is rotated and reflected for display.
Figure 3: BE-LMPC framework for repetitive lap-time improvement under a fixed vehicle model and global speed bound. Recoverable laps update the empirical safe set, and the recovery rule expands the sideslip and yaw-rate bounds. The demand-to-capacity ratio characterizes the resulting grip or drift response.
Vehicle parameters
Controller parameters
Parameter
Symbol
Value
Parameter
Symbol
Value
Vehicle mass
m
3.2kg
Power regularization
vϵ
0.50m/s
Yaw moment of inertia
Iz
0.04kgm2
Prediction horizon
N
25
CG-to-axle distances
lf/lr
0.16/0.17 m
Control period
Ts
0.05s
CG height
h
0.08m
Global speed bound
vmax
10.0m/s
Cornering stiffness/load
cαf/cαr
2.3/2.3 rad -1
Maximum steering angle
δmax
0.41rad
Table 1: Principal vehicle and controller parameters
Test
Condition
Purpose
Main case
BE-LMPC, μ=0.6
Evaluate lap-wise evolution from grip to drift
Friction sweep
μ=0.6 , 0.8, 1.0, 1.2
Identify friction conditions associated with emergence
Method comparison
BE-LMPC, grip constraint, fixed envelope
Isolate the effects of boundary exploration and drift freedom
Table 2: Simulation test matrix
Figure 4: Lap-wise drift emergence at μ=0.6 . (a) Lap times for Laps 3 through 12; blue and red bars denote grip and drift, respectively, and labels give the envelope level. (b) Track trajectories for grip Lap 10 and first-drift Lap 11; red segments satisfy the joint criterion. The map is rotated and reflected for display. (c) Threshold-normalized sideslip and rear-axle utilization with the envelope level; R and X denote accepted and rejected laps.
Figure 5: State and control responses for grip Lap 10 and first-drift Lap 11 at μ=0.6 : (a) speed, (b) sideslip angle, (c) yaw rate, (d) steering angle, and (e) longitudinal acceleration. Gray dotted lines mark the steering constraint. In (e), dotted and solid curves denote acmd and realized ax , respectively. Light-red shading marks intervals satisfying the joint drift criterion.
Varied parameter
Values
First drift lap
βth / ( ∘ )
6, 8, 10, 12
11, 11, 11, 11
ρth
0.75, 0.82, 0.90
9, 11, –
Td / s
0.20, 0.30, 0.50
10, 11, 12
Table 3: Effect of drift-criterion parameters on the first detected drift lap
Figure 6: Effect of tire-road friction on drift emergence. (a) Lap-wise outcomes: recoverable grip (open circles), recoverable drift (filled squares), and rejection (crosses). (b) Final-lap maximum sideslip and rear-axle utilization normalized by their thresholds; the hatched region satisfies both criteria. (c) Final recoverable lap time (solid circles, left axis) and peak speed (dashed triangles, right axis).
μ
First drift lap
Final recoverable lap
Lap time (s)
Max. ∣β∣ / ( ∘ )
Max. ρr
Final state
0.6
11
12
25.50
16.49
0.894
Drift
0.8
–
12
25.25
12.66
0.699
Limit grip
1.0
–
12
25.20
11.50
0.572
Limit grip
1.2
–
12
25.10
10.82
0.483
Limit grip
Table 4: Quantitative drift-emergence results under different friction conditions
Figure 7: Comparison at μ=0.6 of BE-LMPC, grip-constrained sideslip, and a fixed envelope. (a) Lap-time convergence; the dash-dotted vertical line marks the first BE-LMPC drift lap. (b) Final-lap sideslip and rear-utilization criterion plane; the hatched region satisfies both thresholds. (c) Lap outcomes: recoverable grip (open circles), recoverable drift (filled squares), and rejection (crosses). (d) Final trajectories with an enlargement at the location of maximum path separation.
In Formula 1, drivers optimize racing lines within tire grip limits to minimize lap times; however, in rally racing, drivers intentionally break traction to drift on loose surfaces. This maneuver rapidly aligns the vehicle for corner exits, ultimately reducing lap time. Autonomously executing such maneuvers formulates a complex dual-objective control problem: stabilizing highly nonlinear drift dynamics while strictly minimizing lap time. Addressing this challenge motivates the development of advanced Minimum-Lap-Time (MLT) drift control architectures. This paper proposes a planning-control framework specifically designed for MLT drifting scenario. First, we formulate an optimal control problem to generate a MLT drift planning trajectory, which is used as prior data to train a deep reinforcement learning drift controller. Given that drifting involves extremely large sideslip angles and is therefore challenging to learn directly, a Track-guided Reinforcement Learning (TgRL) drift control method is proposed to enable progressive training in a step-by-step manner, from drift control policy, to drift corner policy, and finally to a comprehensive drift race policy. The reward function incorporates both an instant reward term and an end reward term derived from the Minimum-Lap-Time objective. Simulation results demonstrate that the proposed framework enables the agent to learn a drift racing policy that not only ensures vehicle motion control performance but also effectively reduces lap time.
Sheng Zhao, Bolin Zhao, Xiaodong Wu +1
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China · School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798, Singapore
Real-world collision avoidance is a core motivation for studying the dynamics and control of high sideslip drifting in vehicles, yet the practical benefit of such maneuvers has so far primarily been tested in scenarios explicitly engineered to require drifting. In this work, we explore the question of if and when drifting may be optimal for safety in real-world winter driving conditions. We present a drift-capable nonlinear model predictive control (MPC) system designed to handle scenarios grounded in crash fatality data and deploy the controller in a high fidelity simulator across road departure and oncoming vehicle collision avoidance scenarios. The controller naturally initiates and sustains drifting maneuvers to stay on the road when hitting a patch of ice on the rear axle and to avoid an oncoming vehicle that has slid into its lane. Comparisons with a benchmark electronic stability control (ESC) system demonstrate how a drift-capable controller can trade off stability for controllability to precisely maneuver through dangerous winter driving scenarios. A Monte Carlo study over random ice patches further shows that the drift-capable controller achieves lower median lane error than ESC across several speeds, while revealing that drifting emerges predominantly at higher speeds.
Autonomously controlling and handling a vehicle at and beyond its stability limit is a mathematically and computationally demanding task. Prior demonstrations of automated drifting have been limited to research platforms with instantaneous torque delivery and independently actuated wheels, leaving their applicability to production vehicles with actuator latencies and mechanically coupled axles uncertain. To overcome these issues, we design a predictor to compensate for powertrain delays, develop a revised control formulation to accommodate higher actuation latencies as well as a differential coupling on the driven axle, and introduce brake-based velocity stabilization. This paper presents the controller framework, the model extensions, and real-world experimental results. We observe that our controller enables a production sports car with a combustion engine to robustly sustain circular and figure-eight drifts, limiting lateral error to 1.1 m and sideslip overshoot to 0.06 rad despite actuator delays exceeding 250 ms, while mitigating oscillations and maintaining stable path and sideslip tracking. In conclusion, our results establish that autonomous drifting is feasible on production-ready vehicles, opening pathways to advanced safety systems capable of stabilizing cars in scenarios where traditional control fails.
Frederik Werner, Till Heintzenberg, Markus Lienkamp +1
Professorship of Autonomous Vehicle Systems, TUM School of Engineering and Design, Technical University of Munich, 85748 Garching, Germany; Munich Institute of Robotics and Machine Intelligence (MIRMI)