GTP-SLAM: Game-Theoretic Priors for Simultaneous Localization and Mapping in Multi-Agent Scenarios

Robots operating in complex, multi-player settings must simultaneously model the environment and the behavior of human or robotic agents who share that environment. Environmental modeling is often approached using Simultaneous Localization and Mapping (SLAM) techniques; however, SLAM algorithms usually neglect multi-player interactions. In contrast, a recent branch of the motion planning literature uses dynamic game theory to explicitly model noncooperative interactions of multiple agents in a known environment with perfect localization. In this work, we fuse ideas from these disparate communities to solve SLAM problems with game theoretic priors. We present GTP-SLAM, a novel, iterative best response-based SLAM algorithm that accurately performs state localization and map reconstruction in an uncharted scene, while capturing the inherent game-theoretic interactions among multiple agents in that scene. By formulating the underlying SLAM problem as a potential game, we inherit a strong convergence guarantee. Empirical results indicate that, when deployed in a realistic traffic simulation, our approach performs localization and mapping more accurately than a standard bundle adjustment algorithm across a wide range of noise levels.Comment: 6 pages, 3 figure

Towards Dynamic Causal Discovery with Rare Events: A Nonparametric Conditional Independence Test

Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links, between random variables in a dynamic setting, that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel statistical independence test on data collected from time-invariant dynamical systems in which rare but consequential events occur. In particular, we exploit the time-invariance of the underlying data to construct a superimposed dataset of the system state before rare events happen at different timesteps. We then design a conditional independence test on the reorganized data. We provide non-asymptotic sample complexity bounds for the consistency of our method, and validate its performance across various simulated and real-world datasets, including incident data collected from the Caltrans Performance Measurement System (PeMS). Code containing the datasets and experiments is publicly available

Multi-Hypothesis Interactions in Game-Theoretic Motion Planning

We present a novel method for handling uncertainty about the intentions of non-ego players in dynamic games, with application to motion planning for autonomous vehicles. Equilibria in these games explicitly account for interaction among other agents in the environment, such as drivers and pedestrians. Our method models the uncertainty about the intention of other agents by constructing multiple hypotheses about the objectives and constraints of other agents in the scene. For each candidate hypothesis, we associate a Bernoulli random variable representing the probability of that hypothesis, which may or may not be independent of the probability of other hypotheses. We leverage constraint asymmetries and feedback information patterns to incorporate the probabilities of hypotheses in a natural way. Specifically, increasing the probability associated with a given hypothesis from $0$ to $1$ shifts the responsibility of collision avoidance from the hypothesized agent to the ego agent. This method allows the generation of interactive trajectories for the ego agent, where the level of assertiveness or caution that the ego exhibits is directly related to the easy-to-model uncertainty it maintains about the scene.Comment: For associated mp4 file, see https://youtu.be/x7VtYDrWTW

Solving finite production rate model with scrap and multiple shipments using algebraic approach

This paper solves a finite production rate (FPR) model with scrap and multiple shipments using an algebraic method. Classic FPR model assumes a continuous inventory issuing policy to satisfy demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated production-inventory system, multiple shipment policy is practically used in lieu of a continuous issuing policy and generation of defective items during production run is inevitable. In this study, it is assumed that all defective items are scrap and the perfect quality items can only be delivered to customers if the whole lot is quality assured at the end of the production run. A conventional approach for solving the FPR model is the use of differential calculus on the long-run average cost function with the need to prove optimality first. This paper demonstrates that optimal lot size and its overall costs for the aforementioned FPR model can be derived without derivatives. As a result, it enables students or practitioners who have little knowledge of calculus to understand and to handle with ease the real-life FPR model

Poemas chineses

Apresentamos aqui três versões de dois poemas de Li Po. Durante o trabalho, deparamo-nos com a delicada tarefa de transpor a estrutura sintética dos poemas, o que nos levou à extrema concisão no processo de tradução. A visualidade ideogrâmica e a riqueza imagética da poesia chinesa foram aspectos fundamentais que exigiram bastante cuidado de nossa parte, incluindo o próprio universo cifrado e simbólico dos poemas

The Computation of Approximate Generalized Feedback Nash Equilibria

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and sufficient conditions for (local) GFNE solutions at the trajectory level, which enable the development of efficient numerical methods for their computation. Specifically, we propose a Newton-style method for finding game trajectories which satisfy the necessary conditions, which can then be checked against the sufficiency conditions. We show that the evaluation of the necessary conditions in general requires computing a series of nested, implicitly-defined derivatives, which quickly becomes intractable. To this end, we introduce an approximation to the necessary conditions which is amenable to efficient evaluation, and in turn, computation of solutions. We term the solutions to the approximate necessary conditions Generalized Feedback Quasi Nash Equilibria (GFQNE), and we introduce numerical methods for their computation. In particular, we develop a Sequential Linear-Quadratic Game approach, in which a locally approximate LQ game is solved at each iteration. The development of this method relies on the ability to compute a GFNE to inequality- and equality-constrained LQ games, and therefore specific methods for the solution of these special cases are developed in detail. We demonstrate the effectiveness of the proposed solution approach on a dynamic game arising in an autonomous driving application

Solving finite production rate model with scrap and multiple shipments using algebraic approach

This paper solves a finite production rate (FPR) model with scrap and multiple shipments using an algebraic method. Classic FPR model assumes a continuous inventory issuing policy to satisfy demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated production-inventory system, multiple shipment policy is practically used in lieu of a continuous issuing policy and generation of defective items during production run is inevitable. In this study, it is assumed that all defective items are scrap and the perfect quality items can only be delivered to customers if the whole lot is quality assured at the end of the production run. A conventional approach for solving the FPR model is the use of differential calculus on the long-run average cost function with the need to prove optimality first. This paper demonstrates that optimal lot size and its overall costs for the aforementioned FPR model can be derived without derivatives. As a result, it enables students or practitioners who have little knowledge of calculus to understand and to handle with ease the real-life FPR model

Dynamic Tolling in Arc-based Traffic Assignment Models

Tolling in traffic networks offers a popular measure to minimize overall congestion. Existing toll designs primarily focus on congestion in route-based traffic assignment models (TAMs), in which travelers make a single route selection from their source to destination. However, these models do not reflect real-world traveler decisions because they preclude deviations from a chosen route, and because the enumeration of all routes is computationally expensive. To address these limitations, our work focuses on arc-based TAMs, in which travelers sequentially select individual arcs (or edges) on the network to reach their destination. We first demonstrate that marginal pricing, a tolling scheme commonly used in route-based TAMs, also achieves socially optimal congestion levels in our arc-based formulation. Then, we use perturbed best response dynamics to model the evolution of travelers' arc selection preferences over time, and a marginal pricing scheme to the social planner's adaptive toll updates in response. We prove that our adaptive learning and marginal pricing dynamics converge to a neighborhood of the socially optimal loads and tolls. We then present empirical results that verify our theoretical claims.Comment: 18 pages, 4 figures, 2 tables. arXiv admin note: text overlap with arXiv:2304.0470

Incorporating machine reliability issue and backlogging into the EMQ model - Part I: Random breakdown occurring in backorder filling time

This study is concerned with determination of the optimal replenishment policy for economic manufacturing quantity (EMQ) model with backlogging and machine reliability issue. Classic EMQ model does not consider nonconforming items generated during a production cycle, nor does it deal with the machine breakdown situation. It is noted that in manufacturing system when back-ordering is permitted, a random machine failure can take place in either backorder filling time or in on-hand inventory piling period. The first phase of this study examines the aforementioned practical issues by incorporating rework process of defective items, scrap and random machine failure taking place specifically in backorder satisfying time into the EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall production-inventory costs. Mathematical modelling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. Theorem on conditional convexity of total cost function is proposed and proved. The optimal lot size for such a real-life imperfect manufacturing system is derived. A numerical example is given to demonstrate its practical usage