About

Dr. Madhur Behl is an Associate Professor in the department of Computer Science at the University of Virginia and an Amazon Scholar. His research spans robotics, autonomous systems, and cyber-physical systems, with a focus on physical AI, autonomous driving, and high-speed decision making.

Research topics

• Computer Science
• Meteorology
• Geography
• Engineering
• Artificial Intelligence
• Environmental science
• Geology
• Machine Learning
• Cartography
• Oceanography
• Civil engineering
• Simulation
• Geotechnical engineering
• Telecommunications
• Transport engineering

Selected publications

• BARTé: Composite Bézier Curves for Racing Trajectory Estimation

  Journal of Intelligent & Robotic Systems · 2026-03-27

  articleOpen accessSenior author

  Accurate opponent trajectory prediction remains a significant challenge in autonomous racing, where vehicles often execute aggressive maneuvers and sudden acceleration changes. Transformer-based architectures like Motion Transformer (MTR) have shown promise for vehicle trajectory prediction in structured environments such as highways and urban roads. However, they, along with LSTM-enhanced methods like MixNet, face limitations in predicting trajectories under the extreme dynamics of autonomous racing, often leading to increased errors and computational inefficiencies. To address these challenges, we propose two novel methods. First, BézierMixNet extends MixNet by utilizing Bézier curves to more accurately represent trajectories through a combination of reference paths. Second, we introduce BARTé, which employs Composite Bézier Curves to achieve both computational efficiency and high prediction accuracy in dynamic racing scenarios. Our methods are evaluated on extensive datasets from the DeepRacing Formula One simulation and real-world data from the Indy Autonomous Challenge. Compared to state-of-the-art models, BARTé reduces average displacement error by approximately 4%, longitudinal error by 48% while reducing computation time by 90%, demonstrating significant advantages for high-speed autonomous racing.

  PublisherDOI

• Probabilistic Collision Risk Estimation Through Gauss-Legendre Cubature and Non-Homogeneous Poisson Processes

  IEEE Robotics and Automation Letters · 2026-05-11

  articleOpen accessSenior author

  Overtaking in high-speed autonomous racing demands precise, real-time estimation of collision risk; particularly in wheel-to-wheel scenarios where safety margins are minimal. Existing methods for collision risk estimation either rely on simplified geometric approximations, like bounding circles, or perform Monte Carlo sampling which leads to overly conservative motion planning behavior at racing speeds. We introduce the Gauss–Legendre Rectangle (GLR) algorithm, a principled two-stage integration method that estimates collision risk by combining Gauss–Legendre with a non-homogeneous Poisson process over time. GLR produces accurate risk estimates that account for vehicle geometry and trajectory uncertainty. In experiments across 446 overtaking scenarios in a high-fidelity Formula One racing simulation, GLR outperforms five state-of-the-art baselines achieving an average error reduction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$77\%$</tex-math></inline-formula> and surpassing the next-best method by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$52\%$</tex-math></inline-formula>, all while running at 1000 Hz. The framework is general and applicable to broader motion planning contexts beyond autonomous racing.

  PublisherOA PDFDOI

• HALO: Fault-Tolerant Safety Architecture For High-Speed Autonomous Racing

  ACM Transactions on Cyber-Physical Systems · 2026-05-02

  articleOpen accessSenior author

  The field of high-speed autonomous racing has seen significant advances in recent years, with the rise of competitions such as RoboRace and the Indy Autonomous Challenge providing a platform for researchers to develop software stacks for autonomous race vehicles capable of reaching speeds in excess of 170 mph. Ensuring the safety of these vehicles requires the software to continuously monitor for different faults and erroneous operating conditions during high-speed operation, with the goal of mitigating any unreasonable risks posed by malfunctions in sub-systems and components. This paper presents a comprehensive overview of the HALO safety architecture, which has been implemented on a full-scale autonomous racing vehicle as part of the Indy Autonomous Challenge. The paper begins with a failure mode and criticality analysis of the perception, planning, control, and communication modules of the software stack. Specifically, we examine three different types of faults - node health, data health, and behavioral-safety faults. To mitigate these faults, the paper then outlines HALO safety archetypes and runtime monitoring methods. Finally, the paper demonstrates the effectiveness of the HALO safety architecture for each of the faults, through real-world data gathered from autonomous racing vehicle trials during multi-agent scenarios.

  PublisherOA PDFDOI

• BARTé: Composite Bézier Curves for Racing Trajectory Estimation

  2025-02-26

  preprintOpen accessSenior author

  Accurate opponent trajectory prediction remains a significant challenge in autonomous racing, where vehicles often execute aggressive maneuvers and sudden acceleration changes. Transformer-based architectures like Motion Transformer (MTR) have shown promise for vehicle trajectory prediction in structured environments such as highways and urban roads. However, they, along with LSTM-enhanced methods like MixNet, face limitations in predicting trajectories under the extreme dynamics of autonomous racing, often leading to increased errors and computational inefficiencies. To address these challenges, we propose two novel methods. First, BézierMixNet extends MixNet by utilizing Bézier curves to more accurately represent trajectories through a combination of reference paths. Second, we introduce BARTé, which employs Composite Bézier Curves to achieve both computational efficiency and high prediction accuracy in dynamic racing scenarios. Our methods are evaluated on extensive datasets from the DeepRacing Formula One simulation and real-world data from the Indy Autonomous Challenge. Compared to state-of-the-art models, BARTé reduces average displacement error by approximately 4%, longitudinal error by 48% while reducing computation time by 90%, demonstrating significant advantages for high-speed autonomous racing.

  PublisherOA PDFDOI

• Trajectory-to-Action Pipeline (TAP): Automated Scenario Description Extraction for Autonomous Vehicle Behavior Comparison

  ArXiv.org · 2025-02-27

  preprintOpen accessSenior author

  Scenario Description Languages (SDLs) provide structured, interpretable embeddings that represent traffic scenarios encountered by autonomous vehicles (AVs), supporting key tasks such as scenario similarity searches and edge case detection for safety analysis. This paper introduces the Trajectory-to-Action Pipeline (TAP), a scalable and automated method for extracting SDL labels from large trajectory datasets. TAP applies a rules-based cross-entropy optimization approach to learn parameters directly from data, enhancing generalization across diverse driving contexts. Using the Waymo Open Motion Dataset (WOMD), TAP achieves 30% greater precision than Average Displacement Error (ADE) and 24% over Dynamic Time Warping (DTW) in identifying behaviorally similar trajectories. Additionally, TAP enables automated detection of unique driving behaviors, streamlining safety evaluation processes for AV testing. This work provides a foundation for scalable scenario-based AV behavior analysis, with potential extensions for integrating multi-agent contexts.

  PublisherOA PDFDOI

• Foreword for ICCPS’24 Special Issue

  ACM Transactions on Cyber-Physical Systems · 2025-10-08

  article1st authorCorresponding

  Cyber-physical systems (CPS) research continues to advance the integration of computation, communication, and control into safety-critical and large-scale infrastructures. The ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS), held as part of CPS-IoT Week, has long been a premier venue for disseminating these advances and fostering interdisciplinary dialogue. This special issue contains a selection of original papers, which extend earlier results presented at the 15th ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS) that took place in Hong Kong from May 13–16, 2024, as part of CPS-IoT Week 2024. They cover different aspects of CPS research, reflecting both methodological rigor and practical impact.

  PublisherDOI

• DBF-MA: A Differential Bayesian Filtering Planner for Multi-Agent Autonomous Racing Overtakes

  ArXiv.org · 2025-09-26

  preprintOpen accessSenior author

  A significant challenge in autonomous racing is to generate overtaking maneuvers. Racing agents must execute these maneuvers on complex racetracks with little room for error. Optimization techniques and graph-based methods have been proposed, but these methods often rely on oversimplified assumptions for collision-avoidance and dynamic constraints. In this work, we present an approach to trajectory synthesis based on an extension of the Differential Bayesian Filtering framework. Our approach for collision-free trajectory synthesis frames the problem as one of Bayesian Inference over the space of Composite Bezier Curves. Our method is derivative-free, does not require a spherical approximation of the vehicle footprint, linearization of constraints, or simplifying upper bounds on collision avoidance. We conduct a closed-loop analysis of DBF-MA and find it successfully overtakes an opponent in 87% of tested scenarios, outperforming existing methods in autonomous overtaking.

  PublisherOA PDFDOI

• DKMGP: A Gaussian Process Approach to Multi-Task and Multi-Step Vehicle Dynamics Modeling in Autonomous Racing

  arXiv (Cornell University) · 2024-11-20

  preprintOpen accessSenior author

  Autonomous racing is gaining attention for its potential to advance autonomous vehicle technologies. Accurate race car dynamics modeling is essential for capturing and predicting future states like position, orientation, and velocity. However, accurately modeling complex subsystems such as tires and suspension poses significant challenges. In this paper, we introduce the Deep Kernel-based Multi-task Gaussian Process (DKMGP), which leverages the structure of a variational multi-task and multi-step Gaussian process model enhanced with deep kernel learning for vehicle dynamics modeling. Unlike existing single-step methods, DKMGP performs multi-step corrections with an adaptive correction horizon (ACH) algorithm that dynamically adjusts to varying driving conditions. To validate and evaluate the proposed DKMGP method, we compare the model performance with DKL-SKIP and a well-tuned single-track model, using high-speed dynamics data (exceeding 230kmph) collected from a full-scale Indy race car during the Indy Autonomous Challenge held at the Las Vegas Motor Speedway at CES 2024. The results demonstrate that DKMGP achieves upto 99% prediction accuracy compared to one-step DKL-SKIP, while improving real-time computational efficiency by 1752x. Our results show that DKMGP is a scalable and efficient solution for vehicle dynamics modeling making it suitable for high-speed autonomous racing control.

  PublisherOA PDFDOI

• Bringing AI up to speed – autonomous auto racing promises safer driverless cars on the road

  2024-02-14

  article1st authorCorresponding
  PublisherDOI

• Deep Dynamics: Vehicle Dynamics Modeling With a Physics-Constrained Neural Network for Autonomous Racing

  IEEE Robotics and Automation Letters · 2024-04-15 · 31 citations

  articleSenior author

  Autonomous racing is a critical research area for autonomous driving, presenting significant challenges in vehicle dynamics modeling, such as balancing model precision and computational efficiency at high speeds ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;$</tex-math></inline-formula> 280 km/h), where minor errors in modeling have severe consequences. Existing physics-based models for vehicle dynamics require elaborate testing setups and tuning, which are hard to implement, time-intensive, and cost-prohibitive. Conversely, purely data-driven approaches do not generalize well and cannot adequately ensure physical constraints on predictions. This paper introduces Deep Dynamics, a physics-constrained neural network (PCNN) for autonomous racecar vehicle dynamics modeling. It merges physics coefficient estimation and dynamical equations to accurately predict vehicle states at high speeds. A unique Physics Guard layer ensures internal coefficient estimates remain within their nominal physical ranges. Open-loop and closed-loop performance assessments, using a physics-based simulator and full-scale autonomous Indy racecar data, highlight Deep Dynamics as a promising approach for modeling racecar vehicle dynamics.

  PublisherDOI

Frequent coauthors

• Jonathan L. Goodall

  50 shared

• Rahul Mangharam

  36 shared

• Benjamin D. Bowes

  University of Virginia

  31 shared

• Mohamed M. Morsy

  State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering

  30 shared

• Jeffrey M. Sadler

  Oklahoma State University

  29 shared

• Truong X. Nghiem

  15 shared

• Faria Tuz Zahura

  Government of the United States of America

  8 shared

• Arsalan Heydarian

  Engineering Systems (United States)

  6 shared

Education

• Ph.D., Electrical and Systems Engineering

  University of Pennsylvania

  2015

• M.S., Electrical and Systems Engineering

  University of Pennsylvania

  2012

• B.S., ECE

  PEC University of Technology

  2009

Awards & honors

• NSF CAREER Award
• first place in the DOE Cleantech Prize (2016)
• winner of the World Embedded Software Contest (2011)
• multiple Outstanding Researcher Awards from the University o…