This document summarizes outcomes, conclusions, and suggestions of the Long Program “Mathematical Challenges and Opportunities for Autonomous Vehicles”, organized by the Institute of Pure and Applied Mathematics (IPAM) from September 14 to December 18, 2020. Due to the COVID-19 pandemic, the long program was hosted fully virtually. This white paper also includes findings and discussions from two Reunion Workshops held in person at Lake Arrowhead in June 5-10, 2022 and June 11-16, 2023. During the second Reunion Workshop in June 2023, the participants discussed to summarize (1) key findings from the long program and reunion workshops, (2) what followup has occurred since the original long program, and (3) how this community can contribute to challenges in the development, deployment, and operation of autonomous vehicles in society.

Autonomous vehicle (AV) research and development has achieved a similar status in terms of resources invested, societal excitement, and media coverage as space travel and exploration. At the same time, AV research is not rocket science; it is more complicated: while in itself, an AV is no more complex than a spacecraft, it must reliably interact and communicate with many other agents, particularly humans both inside and outside of the vehicle, much of it in a decentralized fashion. Hence, AVs, and their impact on us humans and our transportation systems, incur some of the most complicated science and engineering challenges that society will face in the near future. At the same time, there is some disconnect across the various research communities: professional product development is highly opaque, and public expectations and media communications have frequently been inaccurate or exaggerated.

Operation and Performance of Automated Vehicles

Cars in the future (even those designed to be autonomous) will likely build upon existing industry-wide vehicle architectures for data and control. Therefore, research in the area of vehicle automation must build on these industry standards and be compatible with accepted vehicle platforms. However, many research questions are still unanswered and there is room for improvement and innovation in developing reliable, safe, and efficient automated driving systems as outlined below.

• Modeling for autonomous driving
• Deep learning in autonomous driving
• Co-design of AVs individually and in systems
• Safety

Human Aspects of Automated Driving

For the foreseeable future, humans will continue to be involved in the operation of automated vehicles. Therefore, there is a need to understand how humans will interact with, and use, automated driving systems. Some aspects that will need to be considered include how human drivers will drive in the proximity of AVs, as well as how the human operator will (1) interact with the vehicle, and (2) share control of the driving tasks with the AV. These aspects of human interactions with automated driving systems will need to be understood to enable safe and efficient deployment in an automated future. The following subtopics were discussed in the program.

• Human interaction with automation
• AVs and land use/urban design
• How to test AV safety with human agents

Technical Systems Interactions for Automated Driving

The adoption of autonomous vehicles will not simply mean that humans that drive their cars manually will immediately vanish from the road. Rather, increasing vehicle automation and connectivity will fundamentally change the traffic patterns on our roads and also affect how safe our roads are. Thus, one major concern is ensuring that Connected and Automated Vehicles (CAV) will improve safety and enhance the overall traffic flow.

• Understanding and predicting how connectivity and automation will influence traffic flow

  Mixed traffic streams remain a significant area of interest in terms of understanding and predicting how connectivity and automation will influence traffic flow. The major research areas can be divided into (1) modeling and simulation of vehicle agents and (2) changes in design and operation of the transportation network.

• Leveraging autonomy and connectivity to improve traffic operations

Societal Impacts of Automated Driving

While it is widely believed that roads with autonomous vehicles are likely to be the norm in a “reasonably near” future, the way we get to this future and how it evolves involves a number of tradeoffs and decisions.  This discussion focuses on the need for the research, development and policy-making community to explicitly consider the societal impacts of a future with AVs. In particular, a key question is how we can quantitatively frame relevant discussions with a focus on the societal impact.

• Lessons from ride-hailing
• Impact of AI

In conclusion, autonomous vehicles are on their way to revolutionize how we think about transportation systems. However, before they are ubiquitous, a wide range of technical challenges must be addressed and resolved as more and higher automated vehicles are being deployed on our roadways. These problems range from control of individual vehicles to how they interact with surrounding vehicles and pedestrians to how they meet the needs of larger geographic regions.  Good mathematical models serving as “what-if machines”, simulations, measurements, and guarantees of performance are also needed in order for society and decision makers to think clearly about often-competing goals and objectives.

Automation of transportation, combined with its surrounding research needs, is a fantastic area for interdisciplinary research that spans the whole pipeline from mathematical foundations, over academic areas like engineering, computer science, and also social sciences, to industry, public stakeholders, etc. The IPAM long program, with participants from many of these fields, has shown that a productive interplay of all these areas is possible, and existing collaboration of participants have demonstrated that great outcomes can result from these interactions. The authors of this white paper would like to stress these significant opportunities for cross-disciplinary research with high broader and societal impact, and also to the opportunities for cross-disciplinary programs and initiatives, to funding agencies, public stakeholders, and education and research institutions. We hope that we can all help shape a successful transition to a better, safer, more efficient, more fair, and more enjoyable, future of transportation.

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