AD-MPCC: Adaptive Differentiable Model Predictive Contouring Control for Autonomous Racing

// method overview

How it works

AD-MPCC combines two components operating at each time step:

Online Parameter Estimation — a prior-regularized moving-horizon estimator (MHE) with exponentially decaying weights rapidly updates Pacejka tire parameters to capture surface transitions in real time.
Differentiable MPCC — compute the sensitivity of the MPCC solution w.r.t. objective weights via the implicit function theorem (IFT) to find optimal MPCC weights.
Pacejka-informed ML — a Pacejka-informed machine learning model trained offline to approximate these optimal weights from a 5-dimensional input, enabling real-time weight adaptation.

// simulation results

Single-Surface Scenario

All four controllers are evaluated on a uniform road surface with μ_max = 1.2 for 10 laps. Diff-MPCC and AD-MPCC achieve approximately 11 s faster lap times than the baseline MPCC by adapting the objective weights online, while AD-MPCC further maintains the smallest mean lateral offset (0.926 m), demonstrating a better safety–speed trade-off.

MPCC

A-MPCC

Diff-MPCC

AD-MPCC (ours)

Avg. Lap Time

seconds · ↓ lower is better

MPCC

75.57 s

A-MPCC

75.62 s

Diff-MPCC

64.08 s

AD-MPCC

64.89 s

Avg. Longitudinal Speed

m/s · ↑ higher is better

MPCC

11.38

A-MPCC

11.41

Diff-MPCC

13.59

AD-MPCC

13.50

Avg. Lateral Offset

meters · ↓ lower is better

MPCC

1.953 m

A-MPCC

1.815 m

Diff-MPCC

1.040 m

AD-MPCC

0.926 m

View exact numbers as a table

Controller	Avg. Lap Time (s)	Avg. v_x (m/s)	Avg. Lateral Offset (m)	Avg. Comp. Time (ms)
MPCC	75.57	11.38	1.953	20.45
A-MPCC	75.62	11.41	1.815	21.21
Diff-MPCC	64.08	13.59	1.040	23.56
AD-MPCC	64.89	13.50	0.926	24.18

Multi-Surface Scenario

The track surface varies from μ_max = 0.7 to 1.2 across different sections. Only AD-MPCC successfully completes the lap by jointly updating Pacejka parameters and MPCC weights in real time, while MPCC, A-MPCC, and Diff-MPCC all crash at the first slippery segment (μ_max = 0.75) due to insufficient adaptation.

MPCC

✕ Crashed at μ = 0.75

A-MPCC

✕ Crashed at μ = 0.75

Diff-MPCC

✕ Crashed at μ = 0.75

AD-MPCC (ours)

✓ Completed the lap

Lap time 74.9 s

Avg. v_x 11.65 m/s

Lateral offset 1.069 m

// citation

BibTeX

@misc{nguyen2026admpccadaptivedifferentiablemodel, title={AD-MPCC: Adaptive Differentiable Model Predictive Contouring Control for Autonomous Racing}, author={Nam T. Nguyen and Binh Nguyen and Ahmad Amine and Thanh Vo-Duy and Rahul Mangharam and Truong X. Nghiem}, year={2026}, eprint={2607.00141}, archivePrefix={arXiv}, primaryClass={cs.RO}, url={https://arxiv.org/abs/2607.00141}, }

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