Abstract: Technological advances in self-driving vehicles will soon enable the implementation of large-scale mobility-on-demand (MoD) systems. The efficient management of fleets of vehicles remains a key challenge, in particular to achieve a demand-aligned distribution of available vehicles, commonly referred to as rebalancing. In this article, we present a discrete-time model of an autonomous MoD system, in which unit capacity self-driving vehicles serve transportation requests consisting of a (time, origin, destination) tuple on a directed graph. Time delays in the discrete-time model are approximated as first-order lag elements yielding a sparse model suitable for model predictive control (MPC). The well-posedness of the model is demonstrated, and a characterization of its equilibrium points is given. Furthermore, we show the stabilizability of the model and propose an MPC scheme that, due to the sparsity of the model, can be applied even to large-scale cities. We verify the performance of the scheme in a multiagent transport simulation and demonstrate that service levels outperform those of the existing rebalancing schemes for identical fleet sizes.

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Topics: Model predictive control (57%), Scalability (50%), Directed graph (50%)

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8 results found

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Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

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30,199 Citations

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Performance and safety of Bayesian model predictive control: Scalable model-based RL with guarantees

05 Jun 2020-

Abstract: Despite the success of reinforcement learning (RL) in various research fields, relatively few algorithms have been applied to industrial control applications. The reason for this unexplored potential is partly related to the significant required tuning effort, large numbers of required learning episodes, i.e. experiments, and the limited availability of RL methods that can address high dimensional and safety-critical dynamical systems with continuous state and action spaces. By building on model predictive control (MPC) concepts, we propose a cautious model-based reinforcement learning algorithm to mitigate these limitations. While the underlying policy of the approach can be efficiently implemented in the form of a standard MPC controller, data-efficient learning is achieved through posterior sampling techniques. We provide a rigorous performance analysis of the resulting `Bayesian MPC' algorithm by establishing Lipschitz continuity of the corresponding future reward function and bound the expected number of unsafe learning episodes using an exact penalty soft-constrained MPC formulation. The efficiency and scalability of the method are illustrated using a 100-dimensional server cooling example and a nonlinear 10-dimensional drone example by comparing the performance against nominal posterior MPC, which is commonly used for data-driven control of constrained dynamical systems.

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Topics: Model predictive control (61%), Reinforcement learning (58%), Control theory (53%) ... read more

7 Citations

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Abstract: Robotic multi-agent systems can efficiently handle spatially distributed tasks in dynamic environments. Problem instances of particular interest, and generality are the dynamic traveling repairman problem, and the dynamic vehicle routing problem. Operational policies for robotic fleets solving these two problems take decisions in an online setting with continuously arriving demands to optimize service level, and efficiency, and 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, which have performance independent of the load factor, a combination of properties not achieved by other operational policies in the literature. The underlying principle of the introduced policies is to send available robots to recent service request locations. In simple terms, they 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, and time. We provide 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 its simplicity.

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Topics: Service level (53%), Multi-agent system (53%)

7 Citations

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28 Jun 2021-

Abstract: Challenged by urbanization and increasing travel needs, existing transportation systems call for 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, both from the operational and the planning perspective. 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.

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Topics: Service (business) (53%)

5 Citations

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Erotokritos Skordilis^{1}, Yi Hou^{1}, Charles Tripp^{1}, Matthew Moniot^{1} +2 more•Institutions (1)

27 May 2021-

Abstract: Mobility on demand (MoD) systems show great promise in realizing flexible and efficient urban transportation. However, significant technical challenges arise from operational decision making associated with MoD vehicle dispatch and fleet rebalancing. For this reason, operators tend to employ simplified algorithms that have been demonstrated to work well in a particular setting. To help bridge the gap between novel and existing methods, we propose a modular framework for fleet rebalancing based on model-free reinforcement learning (RL) that can leverage an existing dispatch method to minimize system cost. In particular, by treating dispatch as part of the environment dynamics, a centralized agent can learn to intermittently direct the dispatcher to reposition free vehicles and mitigate against fleet imbalance. We formulate RL state and action spaces as distributions over a grid partitioning of the operating area, making the framework scalable and avoiding the complexities associated with multiagent RL. Numerical experiments, using real-world trip and network data, demonstrate that this approach has several distinct advantages over baseline methods including: improved system cost; high degree of adaptability to the selected dispatch method; and the ability to perform scale-invariant transfer learning between problem instances with similar vehicle and request distributions.

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Topics: Reinforcement learning (53%), Modular design (50%)

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31 results found

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01 Mar 2004-

Abstract: Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

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Topics: Conic optimization (62%), Convex optimization (59%), Nonlinear programming (57%) ... read more

33,299 Citations

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Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

... read more

30,199 Citations

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Abstract: We consider n points (nodes), some or all pairs of which are connected by a branch; the length of each branch is given. We restrict ourselves to the case where at least one path exists between any two nodes. We now consider two problems. Problem 1. Constrnct the tree of minimum total length between the n nodes. (A tree is a graph with one and only one path between every two nodes.) In the course of the construction that we present here, the branches are subdivided into three sets: I. the branches definitely assignec~ to the tree under construction (they will form a subtree) ; II. the branches from which the next branch to be added to set I, will be selected ; III. the remaining branches (rejected or not yet considered). The nodes are subdivided into two sets: A. the nodes connected by the branches of set I, B. the remaining nodes (one and only one branch of set II will lead to each of these nodes), We start the construction by choosing an arbitrary node as the only member of set A, and by placing all branches that end in this node in set II. To start with, set I is empty. From then onwards we perform the following two steps repeatedly. Step 1. The shortest branch of set II is removed from this set and added to

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Topics: Ternary tree (60%), Tree (data structure) (54%), Longest path problem (52%) ... read more

21,172 Citations

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Abstract: It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for 2^{b} quanta, b=1,2, \cdots, 7 , are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.

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Topics: Quantization (signal processing) (58%), Quantum (53%)

9,657 Citations

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01 Jan 1982-

Abstract: It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for 2^{b} quanta, b=1,2, \cdots, 7 , are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.

... read more

Topics: Quantization (signal processing) (58%), Quantum (53%)

9,602 Citations