[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84530-en":3,"doc-seo-84530-105":28,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},84530,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","AD-MPCC Adaptive Differentiable Model Predictive Contouring Control for Autonomous Racing","AD-MPCC introduces an Adaptive Differentiable Model Predictive Contouring Control framework for autonomous racing across varying road-surface conditions. The approach combines differentiable MPCC with online parameter estimation by fitting a parameterized Pacejka Magic Formula using regularized moving-horizon estimation with exponentially decaying weights. It further defines Diff-MPCC to adapt MPCC objective weights through long-horizon performance costs, supported by a Pacejka-informed supervised learning model trained from Diff-MPCC data. Simulations show improved safety and faster lap times over baseline controllers on single- and multi-surface tracks.","AD-MPCC: Adaptive Differentiable Model Predictive Contouring Control  \nfor Autonomous Racing  \nNam T. Nguyen 1 ,†, Binh Nguyen 1 ,†, Ahmad Amine2 ,  \nThanh Vo-Duy3 , Rahul Mangharam2 , and Truong X. Nghiem 1  \narXiv :2607 .00141v1 [ cs .RO] 30 Jun 2026  \nAbstract—This paper presents Adaptive Differentiable Model Predictive Contouring Control (AD-MPCC), a framework for autonomous racing that integrates differentiable MPCC with online parameter estimation to handle varying road-surface conditions. For online parameter estimation, we leverage a parameterized Pacejka Magic Formula together with a regularized moving-horizon estimation scheme with exponentially decaying weights to capture road interactions and update parameters in real time. Furthermore, we propose a differentiable MPCC (Diff-MPCC) framework that enables optimal adjustment of objective weights based on predefined long-horizon performance costs. To implement Diff-MPCC for online objective weight adaptation, we propose a Pacejkainformed machine learning model that is trained in a supervised manner using data generated by Diff-MPCC to tune the objective weights. Simulation results demonstrate that ADMPCC reliably ensures safety and achieves faster lap times compared to baseline controllers in both single-surface and multiple-surface scenarios.  \nI. INTRODUCTION  \nAutonomous racing pushes vehicles to operate at their physical limits while optimizing well-defined performance objectives such as lap-time minimization [1], making it a compelling testbed for advanced control methods, including imitation learning [2], reinforcement learning [3], or iterative learning control [4] . Model predictive contouring control (MPCC) [5], [6] has emerged as a standard control framework for autonomous racing. By jointly minimizing contouring and lag errors while maximizing progress along a reference path, MPCC naturally captures the trade-off between tracking accuracy and racing speed.  \nA growing body of work has sought to improve MPCC by replacing or augmenting the physics-based predictive model with data-driven models. Gaussian process models have been integrated with nominal dynamics in [7], [8], and neural networks have been used to compensate for unmodeled effects in [9], with both approaches demonstrating improved lap times over their physics-based counterparts [10] . However, the nonlinearity and nonconvexity of the learned components increase the complexity of the predictive model, complicating real-time deployment. In practice, the dominant source of  \nThis material is based upon work supported by the National Science Foundation under Award No. 2514584.  \n†These authors contributed equally to this work.  \n1Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32822, USA.  \n2Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19014, USA.  \n3CTI Lab4EV, School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi 10000, Vietnam.  \nFig. 1. The AD-MPCC architecture for autonomous racing. Purple lines and black lines represent offline training and real-time deployment, respectively. Dashed lines denote parameters and solid lines denote signals.  \nmodel uncertainty in racing arises from tire-road interactions, which are well characterized by the Pacejka tire model [11] . Rather than introducing learned residual models, directly estimating Pacejka parameters preserves simplicity and the interpretability of the vehicle dynamics based on physics. On multi-surface tracks, Pacejka parameters must be estimated in real time to ensure the predictive model’s accuracy.  \nIn addition to online parameter estimation, another challenge in autonomous racing on multi-surface tracks is that changes in the dynamic model caused by updates of the Pacejka parameters require corresponding adaptation of the MPCC objective weights to maintain safety and consistent control performance. Dif","cbCaiuZ4ve9q09ev","https://ap.wps.com/l/cbCaiuZ4ve9q09ev","pdf",2574301,1,"English","en",105,"# Introduction\n## MPCC for autonomous racing\n## Data-driven and learned model augmentation\n## Challenges with online dynamics and objective weights\n# AD-MPCC Framework\n## Differentiable MPCC (Diff-MPCC)\n## Pacejka-based online parameter estimation\n## Pacejka-informed machine learning weight tuning","[{\"question\":\"What problem does AD-MPCC address in autonomous racing?\",\"answer\":\"AD-MPCC targets autonomous racing on tracks with changing road-surface conditions, where tire-road interaction uncertainties and model updates can degrade predictive accuracy and control performance.\"},{\"question\":\"How does AD-MPCC estimate road-surface parameters online?\",\"answer\":\"It uses a parameterized Pacejka Magic Formula within a prior-regularized moving-horizon estimation scheme that applies exponentially decaying weights to emphasize recent observations for real-time updates.\"},{\"question\":\"How are MPCC objective weights adapted while driving?\",\"answer\":\"AD-MPCC employs Diff-MPCC to compute gradients of the MPCC solution with respect to objective weights via implicit optimality conditions, enabling gradient-based updates using a long-horizon performance 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problem does AD-MPCC address in autonomous racing?","Question",{"text":74,"@type":75},"AD-MPCC targets autonomous racing on tracks with changing road-surface conditions, where tire-road interaction uncertainties and model updates can degrade predictive accuracy and control performance.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does AD-MPCC estimate road-surface parameters online?",{"text":79,"@type":75},"It uses a parameterized Pacejka Magic Formula within a prior-regularized moving-horizon estimation scheme that applies exponentially decaying weights to emphasize recent observations for real-time updates.",{"name":81,"@type":72,"acceptedAnswer":82},"How are MPCC objective weights adapted while driving?",{"text":83,"@type":75},"AD-MPCC employs Diff-MPCC to compute gradients of the MPCC solution with respect to objective weights via implicit optimality conditions, enabling gradient-based updates using a long-horizon performance 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