Challenged by urbanization and increasing travel needs, existing transportation systems need new mobility paradigms. In this article, we present the emerging concept of autonomous mobility-on-demand, whereby centrally orchestrated fleets of autonomous vehicles provide mobility service to customers. We provide a comprehensive review of methods and tools to model and solve problems related to autonomous mobility-on-demand systems. Specifically, we first identify problem settings for their analysis and control, from both operational and planning perspectives. We then review modeling aspects, including transportation networks, transportation demand, congestion, operational constraints, and interactions with existing infrastructure. Thereafter, we provide a systematic analysis of existing solution methods and performance metrics, highlighting trends and trade-offs. Finally, we present various directions for further research. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.

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