390 research outputs found
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 to
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
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