We describe a new subdivision scheme for unstructured tetrahedral meshes. Previous tetrahedral schemes based on generalizations of box splines have encoded arbitrary directional preferences in their associated subdivision rules that were not reflected in tetrahedral base mesh. Our method avoids this choice of preferred directions resulting a scheme that is simple to implement via repeated smoothing. In an extended appendix, we analyze this tetrahedral scheme and prove that the scheme generates C 2 deformations everywhere except along edges of the tetrahedral base mesh. Along edges shared by four or more tetrahedra in the base mesh, we present strong evidence that the scheme generates C 1 deformations.
Robotic multi-agent systems can efficiently handle spatially distributed tasks in dynamic environments. Problem instances of particular interest and generality are the dynamic vehicle routing problem and the dynamic traveling repairman problem. Operational policies for robotic fleets solving these two problems take decisions in an online setting with continuously arriving dynamic demands to optimize system time and efficiency. They can be classified along several lines. First, some require a model of the demand, e.g., based on historical information, while others work model-free. Second, they are designed for different operating conditions from light to heavy system load. Third, they work in a time-invariant or time-varying setting. We present a novel class of model-free operational policies for time-varying demands, with performance independent of the load factor and applicable to any number of dimensions, a combination of properties not achieved by any other operational policy in the literature. The underlying principle of the introduced policies is to send available robots to recent realizations of the stochastic process that generates service requests. In simple terms, the strategies rely on sending more than one robot for every service request arriving to the system. This leads to an advantage in scenarios where demand is non-uniformly distributed and correlated in space an time. We provide theoretical stability and performance guarantees for both the time-invariant and the time-varying cases as well as for correlated demand. We verify our theoretical results numerically. Finally, we apply our operational policy to the problem of mobility-on-demand fleet operation and demonstrate that it outperforms model-based and complex algorithms across all load ranges despite of its simplicity.
In a mobility-on-demand system, travel requests are handled by a fleet of shared vehicles in an on-demand fashion. An important factor that determines the operational efficiency and service level of such a mobility-on-demand system is its operational policy that assigns available vehicles to open passenger requests and relocates idle vehicles. Previously described operational policies are based on control theoretical approaches, most notably on receding horizon control. In this work, we employ reinforcement learning techniques to design an operational policy for a mobility-on-demand system. In particular, we propose a cascaded learning framework to reduce the number of state-action pairs which allows for more efficient learning. We train our model using the AMoDeus simulation environment and real taxi trip travel data from the city of San Francisco. Finally, we demonstrate that our reinforcement learning based operational policy for mobility-on-demand systems outperforms state-of the art fleet operational policies that are based on conventional control theoretical approaches.
Despite recent breakthroughs, the ability of deep learning and reinforcement learning to outperform traditional approaches to control physically embodied robotic agents remains largely unproven. To help bridge this gap, we created the "AI Driving Olympics" (AI-DO), a competition with the objective of evaluating the state of the art in machine learning and artificial intelligence for mobile robotics. Based on the simple and well specified autonomous driving and navigation environment called "Duckietown," AI-DO includes a series of tasks of increasing complexity -from simple lane-following to fleet management. For each task, we provide tools for competitors to use in the form of simulators, logs, code templates, baseline implementations and low-cost access to robotic hardware. We evaluate submissions in simulation online, on standardized hardware environments, and finally at the competition event. The first AI-DO, AI-DO 1, occurred at the Neural Information Processing Systems (NeurIPS) conference in December 2018. The results of AI-DO 1 highlight the need for better benchmarks, which are lacking in robotics, as well as improved mechanisms to bridge the gap between simulation and reality.
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