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3DIOC: Direct Data-Driven Inverse Optimal Control for LTI Systems 3DIOC:LTI 系统的直接数据驱动反向最优控制
Pub Date : 2024-09-17 DOI: arxiv-2409.10884
Chendi Qu, Jianping He, Xiaoming Duan
This paper develops a direct data-driven inverse optimal control (3DIOC)algorithm for the linear time-invariant (LTI) system who conducts a linearquadratic (LQ) control, where the underlying objective function is learneddirectly from measured input-output trajectories without system identification.By introducing the Fundamental Lemma, we establish the input-outputrepresentation of the LTI system. We accordingly propose a model-freeoptimality necessary condition for the forward LQ problem to build a connectionbetween the objective function and collected data, with which the inverseoptimal control problem is solved. We further improve the algorithm so that itrequires a less computation and data. Identifiability condition andperturbation analysis are provided. Simulations demonstrate the efficiency andperformance of our algorithms.
本文针对进行线性二次方(LQ)控制的线性时不变(LTI)系统开发了一种直接数据驱动的反最优控制(3DIOC)算法,该算法的基本目标函数直接从测量的输入输出轨迹中学习,无需系统识别。相应地,我们提出了前向 LQ 问题的无模型最优必要条件,从而在目标函数和收集的数据之间建立联系,并以此求解反向最优控制问题。我们进一步改进了算法,使其所需的计算量和数据量更少。我们还提供了可识别性条件和扰动分析。仿真证明了我们算法的效率和性能。
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引用次数: 0
Leveraging Symmetry to Accelerate Learning of Trajectory Tracking Controllers for Free-Flying Robotic Systems 利用对称性加速学习自由飞行机器人系统的轨迹跟踪控制器
Pub Date : 2024-09-17 DOI: arxiv-2409.11238
Jake Welde, Nishanth Rao, Pratik Kunapuli, Dinesh Jayaraman, Vijay Kumar
Tracking controllers enable robotic systems to accurately follow plannedreference trajectories. In particular, reinforcement learning (RL) has shownpromise in the synthesis of controllers for systems with complex dynamics andmodest online compute budgets. However, the poor sample efficiency of RL andthe challenges of reward design make training slow and sometimes unstable,especially for high-dimensional systems. In this work, we leverage the inherentLie group symmetries of robotic systems with a floating base to mitigate thesechallenges when learning tracking controllers. We model a general trackingproblem as a Markov decision process (MDP) that captures the evolution of boththe physical and reference states. Next, we prove that symmetry in theunderlying dynamics and running costs leads to an MDP homomorphism, a mappingthat allows a policy trained on a lower-dimensional "quotient" MDP to be liftedto an optimal tracking controller for the original system. We compare thissymmetry-informed approach to an unstructured baseline, using Proximal PolicyOptimization (PPO) to learn tracking controllers for three systems: theParticle (a forced point mass), the Astrobee (a fullyactuated space robot), andthe Quadrotor (an underactuated system). Results show that a symmetry-awareapproach both accelerates training and reduces tracking error after the samenumber of training steps.
跟踪控制器能使机器人系统准确地跟踪计划的参考轨迹。特别是,强化学习(RL)在为具有复杂动力学特性和最低廉在线计算预算的系统合成控制器方面大有可为。然而,RL 的采样效率低和奖励设计的挑战使得训练速度缓慢,有时甚至不稳定,尤其是对于高维系统。在这项工作中,我们利用具有浮动基底的机器人系统固有的李群对称性来缓解学习跟踪控制器时遇到的这些挑战。我们将一般跟踪问题建模为马尔可夫决策过程(MDP),该过程捕捉了物理状态和参考状态的演变。接下来,我们证明了底层动力学和运行成本的对称性会导致 MDP 同构,这种映射允许将在低维 "商 "MDP 上训练的策略提升为原始系统的最优跟踪控制器。我们将这种考虑对称性的方法与非结构化基线进行了比较,使用近端策略优化(PPO)来学习三个系统的跟踪控制器:Particle(受迫点质量)、Astrobee(全致动太空机器人)和Quadrotor(欠致动系统)。结果表明,对称感知方法既能加快训练速度,又能在相同训练步数后减少跟踪误差。
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引用次数: 0
Data-driven Dynamic Intervention Design in Network Games 网络游戏中数据驱动的动态干预设计
Pub Date : 2024-09-17 DOI: arxiv-2409.11069
Xiupeng Chen, Nima Monshizadeh
Targeted interventions in games present a challenging problem due to theasymmetric information available to the regulator and the agents. This noteaddresses the problem of steering the actions of self-interested agents inquadratic network games towards a target action profile. A common startingpoint in the literature assumes prior knowledge of utility functions and/ornetwork parameters. The goal of the results presented here is to remove thisassumption and address scenarios where such a priori knowledge is unavailable.To this end, we design a data-driven dynamic intervention mechanism that reliessolely on historical observations of agent actions and interventions.Additionally, we modify this mechanism to limit the amount of interventions,thereby considering budget constraints. Analytical convergence guarantees areprovided for both mechanisms, and a numerical case study further demonstratestheir effectiveness.
由于监管者和代理的信息不对称,在博弈中进行有针对性的干预是一个具有挑战性的问题。本论文探讨了如何在二次网络博弈中引导自利代理的行动向目标行动轮廓靠拢的问题。文献中一个常见的出发点是假设事先知道效用函数和/或网络参数。为此,我们设计了一种数据驱动的动态干预机制,该机制完全依赖于对代理行动和干预的历史观察。此外,我们还修改了该机制,以限制干预的数量,从而考虑到预算约束。我们为这两种机制提供了分析收敛保证,并通过数值案例研究进一步证明了它们的有效性。
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引用次数: 0
Optimal Investment under the Influence of Decision-changing Imitation 改变决策的模仿影响下的最优投资
Pub Date : 2024-09-17 DOI: arxiv-2409.10933
Huisheng Wang, H. Vicky Zhao
Decision-changing imitation is a prevalent phenomenon in financial markets,where investors imitate others' decision-changing rates when making their owninvestment decisions. In this work, we study the optimal investment problemunder the influence of decision-changing imitation involving one leading expertand one retail investor whose decisions are unilaterally influenced by theleading expert. In the objective functional of the optimal investment problem,we propose the integral disparity to quantify the distance between the twoinvestors' decision-changing rates. Due to the underdetermination of theoptimal investment problem, we first derive its general solution using thevariational method and find the retail investor's optimal decisions under twospecial cases of the boundary conditions. We theoretically analyze theasymptotic properties of the optimal decision as the influence ofdecision-changing imitation approaches infinity, and investigate the impact ofdecision-changing imitation on the optimal decision. Our analysis is validatedusing numerical experiments on real stock data. This study is essential tocomprehend decision-changing imitation and devise effective mechanisms to guideinvestors' decisions.
决策变化模仿是金融市场中的一种普遍现象,即投资者在做出自己的投资决策时模仿他人的决策变化率。在这项工作中,我们研究了决策改变模仿影响下的最优投资问题,该问题涉及一位领先专家和一位散户投资者,后者的决策受到领先专家的单方面影响。在最优投资问题的目标函数中,我们提出了积分差异来量化两个投资者决策改变率之间的距离。由于最优投资问题的不确定性,我们首先用变量法推导出其一般解,并在边界条件的两种特殊情况下求得散户投资者的最优决策。我们从理论上分析了当改变决策的模仿的影响接近无穷大时最优决策的渐近特性,并研究了改变决策的模仿对最优决策的影响。我们的分析通过实际股票数据的数值实验得到了验证。这项研究对于理解决策改变模仿和设计有效机制以指导投资者决策至关重要。
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引用次数: 0
To What Extent do Open-loop and Feedback Nash Equilibria Diverge in General-Sum Linear Quadratic Dynamic Games? 在一般和线性二次动态博弈中,开环和反馈纳什均衡点在多大程度上存在分歧?
Pub Date : 2024-09-17 DOI: arxiv-2409.11257
Chih-Yuan Chiu, Jingqi Li, Maulik Bhatt, Negar Mehr
Dynamic games offer a versatile framework for modeling the evolvinginteractions of strategic agents, whose steady-state behavior can be capturedby the Nash equilibria of the games. Nash equilibria are often computed infeedback, with policies depending on the state at each time, or in open-loop,with policies depending only on the initial state. Empirically, open-loop Nashequilibria (OLNE) are often more efficient to compute, while feedback Nashequilibria (FBNE) encode more complex interactions. However, it remains unclearexactly which dynamic games yield FBNE and OLNE that differ significantly andwhich do not. To address this problem, we present a principled comparison studyof OLNE and FBNE in linear quadratic (LQ) dynamic games. Specifically, we provethat the OLNE strategies of an LQ dynamic game can be synthesized by solvingthe coupled Riccati equations of an auxiliary LQ game with perturbed costs. Theconstruction of the auxiliary game allows us to establish conditions underwhich OLNE and FBNE coincide and derive an upper bound on the deviation betweenFBNE and OLNE of an LQ game.
动态博弈为模拟策略代理不断演化的互动提供了一个通用框架,博弈的纳什均衡状态可以捕捉策略代理的稳态行为。纳什均衡通常是通过反馈或开环计算出来的,前者的政策取决于每次的状态,后者的政策只取决于初始状态。从经验上看,开环纳什均衡(OLNE)的计算效率通常更高,而反馈纳什均衡(FBNE)则编码了更复杂的互动。然而,哪些动态博弈产生的 FBNE 和 OLNE 有显著差异,哪些没有差异,目前还不清楚。为了解决这个问题,我们对线性二次(LQ)动态博弈中的 OLNE 和 FBNE 进行了原则性比较研究。具体来说,我们证明了 LQ 动态博弈的 OLNE 策略可以通过求解具有扰动成本的辅助 LQ 博弈的耦合里卡蒂方程来合成。通过构建辅助博弈,我们可以建立 OLNE 和 FBNE 重合的条件,并推导出 LQ 博弈中 FBNE 和 OLNE 之间偏差的上限。
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引用次数: 0
Three Degree-of-Freedom Soft Continuum Kinesthetic Haptic Display for Telemanipulation Via Sensory Substitution at the Finger 三自由度软连续体感触觉显示器,通过手指感觉替代实现遥控操作
Pub Date : 2024-09-17 DOI: arxiv-2409.11606
Jiaji Su, Kaiwen Zuo, Zonghe Chua
Sensory substitution is an effective approach for displaying stable hapticfeedback to a teleoperator under time delay. The finger is highly articulated,and can sense movement and force in many directions, making it a promisinglocation for sensory substitution based on kinesthetic feedback. However,existing finger kinesthetic devices either provide only one-degree-of-freedomfeedback, are bulky, or have low force output. Soft pneumatic actuators havehigh power density, making them suitable for realizing high force kinestheticfeedback in a compact form factor. We present a soft pneumatic handheldkinesthetic feedback device for the index finger that is controlled using aconstant curvature kinematic model. changed{It has respective position andforce ranges of +-3.18mm and +-1.00N laterally, and +-4.89mm and +-6.01Nvertically, indicating its high power density and compactness. The averageopen-loop radial position and force accuracy of the kinematic model are 0.72mmand 0.34N.} Its 3Hz bandwidth makes it suitable for moderate speed hapticinteractions in soft environments. We demonstrate the three-dimensionalkinesthetic force feedback capability of our device for sensory substitution atthe index figure in a virtual telemanipulation scenario.
感官替代是在时间延迟的情况下向远程操作员显示稳定触觉反馈的有效方法。手指具有高度铰接性,可以感知多个方向的运动和力量,因此是基于动觉反馈进行感觉替代的理想位置。然而,现有的手指动觉设备要么只能提供单自由度反馈,要么体积庞大,要么力输出较低。软气动致动器具有较高的功率密度,因此适合在小巧的外形中实现高力度的动觉反馈。我们介绍了一种用于食指的软气动手持式动觉反馈装置,该装置采用恒定曲率运动学模型进行控制。它的位置和力程分别为横向+-3.18毫米和+-1.00牛顿,纵向+-4.89毫米和+-6.01牛顿,这表明它具有高功率密度和小巧的特点。运动模型的平均开环径向位置和力精度分别为 0.72mm 和 0.34N。}其 3Hz 的带宽使其适用于软环境中的中速触觉交互。我们展示了该设备的三维触觉力反馈能力,可在虚拟远程操控场景中对索引图进行感官替代。
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引用次数: 0
Pose estimation of CubeSats via sensor fusion and Error-State Extended Kalman Filter 通过传感器融合和误差状态扩展卡尔曼滤波器估算立方体卫星的姿态
Pub Date : 2024-09-17 DOI: arxiv-2409.10815
Deep Parikh, Manoranjan Majji
A pose estimation technique based on error-state extended Kalman that fusesangular rates, accelerations, and relative range measurements is presented inthis paper. An unconstrained dynamic model with kinematic coupling for athrust-capable satellite is considered for the state propagation, and apragmatic measurement model of the rate gyroscope, accelerometer, and anultra-wideband radio are leveraged for the measurement update. The error-stateextended Kalman filter framework is formulated for pose estimation, and itsperformance has been analyzed via several simulation scenarios. An applicationof the pose estimator for proximity operations and scaffolding formation ofCubeSat deputies relative to their mother-ship is outlined. Finally, theperformance of the error-state extended Kalman filter is demonstrated usingexperimental analysis consisting of a 3-DOF thrust cable satellite mock-up,rate gyroscope, accelerometer, and ultra-wideband radar modules.
本文提出了一种基于误差状态扩展卡尔曼的姿态估计技术,该技术融合了角速率、加速度和相对距离测量。在状态传播方面,考虑了具有推力能力的卫星的无约束动态模型与运动耦合,在测量更新方面,利用了速率陀螺仪、加速度计和超宽带无线电的实用测量模型。为姿态估计制定了误差状态扩展卡尔曼滤波框架,并通过几个模拟场景对其性能进行了分析。概述了姿态估计器在立方体卫星副手相对于母船的接近操作和脚手架形成中的应用。最后,利用由 3-DOF 推力电缆卫星模型、速率陀螺仪、加速度计和超宽带雷达模块组成的实验分析,展示了误差状态扩展卡尔曼滤波器的性能。
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引用次数: 0
Distributed Perception Aware Safe Leader Follower System via Control Barrier Methods 通过控制障碍方法实现分布式感知安全领导者追随者系统
Pub Date : 2024-09-17 DOI: arxiv-2409.11394
Richie R. Suganda, Tony Tran, Miao Pan, Lei Fan, Qin Lin, Bin Hu
This paper addresses a distributed leader-follower formation control problemfor a group of agents, each using a body-fixed camera with a limited field ofview (FOV) for state estimation. The main challenge arises from the need tocoordinate the agents' movements with their cameras' FOV to maintain visibilityof the leader for accurate and reliable state estimation. To address thischallenge, we propose a novel perception-aware distributed leader-follower safecontrol scheme that incorporates FOV limits as state constraints. A ControlBarrier Function (CBF) based quadratic program is employed to ensure theforward invariance of a safety set defined by these constraints. Furthermore,new neural network based and double bounding boxes based estimators, combinedwith temporal filters, are developed to estimate system states directly fromreal-time image data, providing consistent performance across variousenvironments. Comparison results in the Gazebo simulator demonstrate theeffectiveness and robustness of the proposed framework in two distinctenvironments.
本文讨论的是一组代理的分布式领导者-追随者编队控制问题,每个代理都使用一个固定在身体上的摄像头,并使用有限的视场(FOV)进行状态估计。主要的挑战来自于需要根据摄像机的视场协调代理的运动,以保持领导者的可见度,从而进行准确可靠的状态估计。为了应对这一挑战,我们提出了一种新颖的感知型分布式领导者-追随者安全控制方案,该方案将 FOV 限制作为状态约束。我们采用了基于控制障碍函数(CBF)的二次方程程序来确保由这些约束条件定义的安全集的前向不变性。此外,还开发了新的基于神经网络和双边界框的估计器,并结合时间滤波器,直接从实时图像数据中估计系统状态,从而在各种环境中提供一致的性能。Gazebo 模拟器中的比较结果表明了所提出的框架在两种不同环境中的有效性和鲁棒性。
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引用次数: 0
Online 4D Ultrasound-Guided Robotic Tracking Enables 3D Ultrasound Localisation Microscopy with Large Tissue Displacements 在线 4D 超声引导机器人跟踪实现了大组织位移下的三维超声定位显微镜检查
Pub Date : 2024-09-17 DOI: arxiv-2409.11391
Jipeng Yan, Shusei Kawara, Qingyuan Tan, Jingwen Zhu, Bingxue Wang, Matthieu Toulemonde, Honghai Liu, Ying Tan, Meng-Xing Tang
Super-Resolution Ultrasound (SRUS) imaging through localising and trackingmicrobubbles, also known as Ultrasound Localisation Microscopy (ULM), hasdemonstrated significant potential for reconstructing microvasculature andflows with sub-diffraction resolution in clinical diagnostics. However, imagingorgans with large tissue movements, such as those caused by respiration,presents substantial challenges. Existing methods often require breath holdingto maintain accumulation accuracy, which limits data acquisition time and ULMimage saturation. To improve image quality in the presence of large tissuemovements, this study introduces an approach integrating high-frame-rateultrasound with online precise robotic probe control. Tested on amicrovasculature phantom with translation motions up to 20 mm, twice theaperture size of the matrix array used, our method achieved real-time trackingof the moving phantom and imaging volume rate at 85 Hz, keeping majority of thetarget volume in the imaging field of view. ULM images of the moving crosschannels in the phantom were successfully reconstructed in post-processing,demonstrating the feasibility of super-resolution imaging under large tissuemotions. This represents a significant step towards ULM imaging of organs withlarge motion.
通过定位和跟踪微气泡进行超分辨率超声(SRUS)成像,也称为超声定位显微镜(ULM),在临床诊断中以亚衍射分辨率重建微血管和血流方面已显示出巨大的潜力。然而,对组织运动较大的器官(如呼吸引起的运动)进行成像是一项巨大的挑战。现有的方法通常需要屏住呼吸以保持累积精度,这就限制了数据采集时间和超低成像饱和度。为了在组织运动较大的情况下提高图像质量,本研究引入了一种将高帧率超声与在线精确机器人探头控制相结合的方法。在平移运动达 20 毫米(是所用矩阵阵列孔径大小的两倍)的微血管模型上进行了测试,我们的方法实现了对移动模型的实时跟踪和 85 Hz 的成像容积速率,将大部分目标容积保持在成像视野内。在后处理过程中,我们成功地重建了模型中移动横通道的超分辨图像,证明了在大组织运动下进行超分辨成像的可行性。这标志着我们向大运动器官的超分辨成像迈出了重要一步。
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引用次数: 0
Sample Complexity Bounds for Linear System Identification from a Finite Set 从有限集合识别线性系统的样本复杂性界限
Pub Date : 2024-09-17 DOI: arxiv-2409.11141
Nicolas Chatzikiriakos, Andrea Iannelli
This paper considers a finite sample perspective on the problem ofidentifying an LTI system from a finite set of possible systems usingtrajectory data. To this end, we use the maximum likelihood estimator toidentify the true system and provide an upper bound for its sample complexity.Crucially, the derived bound does not rely on a potentially restrictivestability assumption. Additionally, we leverage tools from information theoryto provide a lower bound to the sample complexity that holds independently ofthe used estimator. The derived sample complexity bounds are analyzedanalytically and numerically.
本文从有限样本的角度探讨了利用轨迹数据从有限的可能系统集合中识别 LTI 系统的问题。为此,我们使用最大似然估计器来识别真实系统,并为其样本复杂度提供了一个上限。至关重要的是,推导出的上限并不依赖于潜在的可限制性假设。此外,我们还利用信息论工具提供了样本复杂度的下限,该下限与所使用的估计器无关。我们对推导出的样本复杂度边界进行了分析和数值计算。
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引用次数: 0
期刊
arXiv - EE - Systems and Control
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