Friction-Aware MPC with Lateral-Slip Constraint Back-Off

This research project develops and evaluates a friction-aware linear Model Predictive Controller (MPC) for vehicle path following and stability under reduced tire-force capacity. The controller is evaluated against a nonlinear five-state combined-slip vehicle model and compared with both a fixed nominal MPC and a no-ESC baseline.

The reproducible MATLAB/Simulink research code and frozen numerical results are available here: GitHub repository

Manuscript status: the journal-neutral master manuscript is complete and the scientific results are frozen. Remaining pre-submission work is limited to author metadata/confirmations and target-journal formatting.

The final controller uses a 4.4° internal lateral-slip back-off while performance is evaluated against a separate physical lateral-slip criterion of 5°. The prediction-model tire-force-capacity factor is matched to the simulated road/plant capacity for the tested scenarios. This project does not claim online friction estimation, nonlinear MPC, formal robust MPC, or friction-dependent constraint scheduling.

Research question

A fixed nominal MPC can track well when the tire-force capacity is high, yet lose stability margin when the available force capacity is reduced. The central question is whether a capacity-aware prediction model combined with a modest constraint back-off can preserve lateral-slip and sideslip margins without abandoning path-following performance.

Final controller configuration

Setting	Final value
Main operating speed	50 km/h
Sampling period	0.01 s
Prediction horizon	20
Control horizon	5
Manipulated variables	Steering, front-wheel torque, rear-wheel torque
MPC internal lateral-slip bound	±4.4°
Physical lateral-slip evaluation criterion	±5°
Longitudinal-slip criterion	±0.1
Vehicle-sideslip criterion	±0.1 rad
Tested tire-force-capacity factors	μ = 1.0, 0.7, 0.4

For the tested capacity levels, the prediction-model factor is set as mu_MPC = mu_road. This is a controlled simulation assumption using known scenario capacity, not an online road-friction estimator.

50 km/h tracking comparison

Path-following comparison at 50 kilometers per hour — **Figure 1. Path-tracking RMSE at 50 km/h.** Website visualization generated directly from the frozen Table 01 results for No ESC, fixed nominal MPC, and the final proposed MPC at μ = 1.0, 0.7, and 0.4.

μ	Controller	Path RMSE	Max path error	Max lateral slip	Max β	All monitored criteria
1.0	Fixed MPC	0.603 m	1.780 m	4.990°	0.0399 rad	Pass
1.0	Proposed MPC	0.695 m	2.101 m	4.394°	0.0367 rad	Pass
0.7	Fixed MPC	1.107 m	3.084 m	8.936°	0.1098 rad	Fail
0.7	Proposed MPC	1.352 m	3.408 m	4.416°	0.0494 rad	Pass
0.4	Fixed MPC	5.396 m	16.719 m	26.199°	0.4305 rad	Fail
0.4	Proposed MPC	2.196 m	3.806 m	4.416°	0.0635 rad	Pass

At μ = 0.4, the proposed controller reduces path RMSE by approximately 59.3%, maximum path error by 77.2%, maximum lateral slip by 83.1%, and maximum vehicle sideslip by 85.3% relative to the fixed MPC.

The result also exposes an important tradeoff: at μ = 1.0 and μ = 0.7, the proposed controller does not minimize path RMSE. Its design deliberately gives up some nominal tracking performance to retain stability margin as available tire-force capacity decreases.

Stability under reduced tire-force capacity

Vehicle stability metrics under reduced tire-force capacity — **Figure 2. Maximum lateral-slip response versus tire-force capacity.** The 5° physical evaluation criterion is shown explicitly. The proposed controller remains below it in the tested μ = 0.7 and μ = 0.4 cases, where the fixed nominal MPC does not.

Plant-parameter mismatch

Robustness is tested by changing the nonlinear plant only: vehicle mass is increased by 10% and front/rear cornering stiffness is reduced by 10%, while the MPC prediction model remains nominal.

Friction-aware MPC response under vehicle mass and cornering-stiffness mismatch — **Figure 3. Combined plant-parameter mismatch.** The proposed MPC preserves all monitored criteria under the tested +10% mass and −10% cornering-stiffness mismatch.

Mismatch metric	Result
Path RMSE	0.900 m
Maximum path error	2.653 m
Maximum lateral slip	4.902°
Maximum longitudinal slip	0.00697
Maximum vehicle sideslip β	0.0416 rad

The 4.902° peak lateral slip is close to the 5° physical evaluation limit, so this should be interpreted as a successful tested robustness case, not as a formal robust-stability guarantee.

80.5 km/h stress test

A second scenario increases the vehicle speed to 80.5 km/h at μ = 1.0. This is a simulation stress test using the same path-following architecture; it is not presented as an FMVSS 126 compliance maneuver.

High-speed vehicle control comparison at 80.5 kilometers per hour — **Figure 4. Maximum lateral slip in the 80.5 km/h stress test.** The proposed MPC is the only tested configuration below the 5° lateral-slip criterion; the table below reports the associated tracking and sideslip results.

Controller	Path RMSE	Max lateral slip	Max β	All monitored criteria
No ESC	0.932 m	7.609°	0.1104 rad	Fail
Fixed MPC	0.898 m	5.028°	0.0642 rad	Fail
Proposed MPC	0.952 m	4.418°	0.0565 rad	Pass

Computational timing

Desktop Simulink profiling for the proposed MPC controller — **Figure 5. Desktop sampling-budget utilization.** The website visualization is generated from the corrected timing table. The profiling measures the proposed MPC hierarchy in desktop simulation and should not be interpreted as embedded WCET or certified real-time performance.

Timing metric	Result
Mean MPC hierarchy time per sample	0.171 ms
Standard deviation	0.00476 ms
Maximum run-average time	0.176 ms
Mean sampling utilization	1.71%
Mean timing margin	9.829 ms
Sampling interval	10 ms

Control effort

Metric	Fixed MPC	Proposed MPC
Maximum steering	8.646°	7.828°
RMS steering	3.903°	3.751°
Maximum steering rate	409.852°/s	410.587°/s
Maximum wheel torque	83.331 N·m	67.761 N·m
RMS wheel torque	36.584 N·m	32.997 N·m
Maximum torque rate	114.894 N·m/s	88.783 N·m/s

Relative to the fixed MPC, the proposed controller reduces maximum steering magnitude by about 9.5%, maximum wheel torque by 18.7%, and maximum torque rate by 22.7%. Peak steering rate increases slightly, by about 0.18%, so no claim of improved peak steering-rate smoothness is made.

Reproducibility

The frozen study package was validated in MATLAB R2022b Update 4 with Simulink, Model Predictive Control Toolbox, Control System Toolbox, and Symbolic Math Toolbox. The repository contains the final Simulink model, path data, proposed/fixed/no-ESC scenario scripts, robustness and high-speed tests, corrected timing/control-effort scripts, frozen CSV tables, and publication-figure generator.

The numerical source of truth is the frozen result tables and verified-results file included with the research-code package. Older exploratory 4.7°, 4.9°, 5°, and 6° tuning experiments are intentionally excluded from the public-facing project.

Scope and limitations

The controller is evaluated entirely in simulation. The project does not provide experimental vehicle validation, hardware-in-the-loop validation, embedded timing certification, formal robust-stability guarantees, online friction estimation, nonlinear MPC, stochastic/tube MPC, or regulatory compliance testing. The 80.5 km/h scenario is a stress test, and the parameter-mismatch study is an empirical robustness evaluation.

The research manuscript package identifies the manuscript authors as Mohammad-Hossein Fakouri and Mohsen Ghaffari. The website page reports only technical results supported by the frozen pre-submission package and does not infer unconfirmed contribution roles.