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Markov chain-based stochastic strategies for robotic surveillance

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arXiv 2020年

作者： Duan, Xiaoming Bullo, Francesco Department of Mechanical Engineering Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where the efficiency is defined with respect to relevant underlying performance metrics. We first start by reviewing the basics of Markov chains, which is the primary motion model for stochastic robotic surveillance. Then two main criteria regarding the speed and unpredictability of surveillance strategies are discussed. The central objects that appear throughout the treatment is the hitting times of Markov chains, their distributions and expectations. We formulate various optimization problems based on the concerned metrics in different scenarios and establish their respective properties. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Stochastic strategies for robotic surveillance as stackelberg games

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arXiv 2020年

作者： Duan, Xiaoming Paccagnan, Dario Bullo, Francesco Mechanical Engineering Department the Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This paper studies a stochastic robotic surveillance problem where a mobile robot moves randomly on a graph to capture a potential intruder that strategically attacks a location on the graph. The intruder is assumed to be omniscient: it knows the current location of the mobile agent and can learn the surveillance strategy. The goal for the mobile robot is to design a stochastic strategy so as to maximize the probability of capturing the intruder. We model the strategic interactions between the surveillance robot and the intruder as a Stackelberg game, and optimal and suboptimal Markov chain based surveillance strategies in star, complete and line graphs are studied. We first derive a universal upper bound on the capture probability, i.e., the performance limit for the surveillance agent. We show that this upper bound is tight in the complete graph and further provide suboptimality guarantees for a natural design. For the star and line graphs, we first characterize dominant strategies for the surveillance agent and the intruder. Then, we rigorously prove the optimal strategy for the surveillance agent. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Robust Implicit Networks via Non-Euclidean Contractions

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arXiv 2021年

作者： Jafarpour, Saber Davydov, Alexander Proskurnikov, Anton V. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States Department of Electronics and Telecommunications Politecnico di Torino Turin Italy Institute for Problems in Mechanical Engineering Russian Academy of Sciences St. Petersburg Russia

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are equivalent to infinite-depth weight-tied feedforward networks. While implicit models show improved accuracy and significant reduction in memory consumption, they can suffer from ill-posedness and convergence instability. This paper provides a new framework, which we call Non-Euclidean Monotone Operator Network (NEMON), to design well-posed and robust implicit neural networks based upon contraction theory for the non-Euclidean norm ∞. Our framework includes (i) a novel condition for well-posedness based on one-sided Lipschitz constants, (ii) an average iteration for computing fixed-points, and (iii) explicit estimates on input-output Lipschitz constants. Additionally, we design a training problem with the well-posedness condition and the average iteration as constraints and, to achieve robust models, with the input-output Lipschitz constant as a regularizer. Our ∞ well-posedness condition leads to a larger polytopic training search space than existing conditions and our average iteration enjoys accelerated convergence. Finally, we evaluate our framework in image classification through the MNIST and the CIFAR-10 datasets. Our numerical results demonstrate improved accuracy and robustness of the implicit models with smaller input-output Lipschitz bounds. Code is available at https://***/davydovalexander/Non-Euclidean_Mon_Op_Net. Copyright © 2021, The Authors. All rights reserved.

关键词： Computation theory

The Kinematics of Tracked Vehicles via the Power Dissipation Method

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arXiv 2020年

作者： Dixit, Anushri Burdick, Joel Anushri Dixit is with Control and Dynamical Systems California Institute of Technology PasadenaCA91125 United States Mechanical and Civil Engineering California Institute of Technology PasadenaCA91125 United States

This paper develops a new quasi-static modeling framework for tracked robots based on the power dissipation method. Given a set of track speeds, this method predicts the vehicle’s instantaneous rigid body motion. We introduce three specific models: a model for tracked operation on flat ground, a model for vehicle motion when the track’s grouser tips touch the ground, and a model for operation on stairs. Experiments show that these models predict tracked vehicle motion more accurately than existing kinematic models, and predict phenomena which are not captured by other models. These novel models provide a basis for new feedback control approaches. Copyright © 2020, The Authors. All rights reserved.

关键词： Tracked vehicles

From Bipedal Walking to Quadrupedal Locomotion: Full-Body Dynamics Decomposition for Rapid Gait Generation

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From Bipedal Walking to Quadrupedal Locomotion: Full-Body Dy...

IEEE International Conference on Robotics and Automation (ICRA)

作者： Wen-Loong Ma Aaron D. Ames department of mechanical engineering California Institute of Technology Pasadena CA faculty of the department of Control and Dynamical Systems California Institute of Technology Pasadena CA

ISBN: (数字)9781728173955

ISBN: (纸本)9781728173962

This paper systematically decomposes a quadrupedal robot into bipeds to rapidly generate walking gaits and then recomposes these gaits to obtain quadrupedal locomotion. We begin by decomposing the full-order, nonlinear and hybrid dynamics of a three-dimensional quadrupedal robot, including its continuous and discrete dynamics, into two bipedal systems that are subject to external forces. Using the hybrid zero dynamics (HZD) framework, gaits for these bipedal robots can be rapidly generated (on the order of seconds) along with corresponding controllers. The decomposition is achieved in such a way that the bipedal walking gaits and controllers can be composed to yield dynamic walking gaits for the original quadrupedal robot - the result is the rapid generation of dynamic quadruped gaits utilizing the full-order dynamics. This methodology is demonstrated through the rapid generation (3.96 seconds on average) of four stepping-in-place gaits and one diagonally symmetric ambling gait at 0.35 m/s on a quadrupedal robot - the Vision 60, with 36 state variables and 12 control inputs - both in simulation and through outdoor experiments. This suggested a new approach for fast quadrupedal trajectory planning using full-body dynamics, without the need for empirical model simplification, wherein methods from dynamic bipedal walking can be directly applied to quadrupeds.

关键词： Legged locomotion Robot kinematics Dynamics Nonlinear dynamical systems Jacobian matrices Trajectory

FaSTrack:A Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking

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FaSTrack:A Modular Framework for Real-Time Motion Planning a...

作者： Chen, Mo Herbert, Sylvia L. Hu, Haimin Pu, Ye Fisac, Jaime Fernandez Bansal, Somil Han, Soojean Tomlin, Claire J. School of Computing Science Simon Fraser University BurnabyBCV5A 1S6 Canada Department of Mechanical and Aerospace Engineering University of California San Diego San DiegoCA92122 United States Department of Electrical Engineering Princeton University PrincetonNJ08536 United States Department of Electrical and Electronic Engineering University of Melbourne ParkvilleVIC3010 Australia Department of Electrical Engineering and Computer Sciences University of California Berkeley BerkeleyCA94704 United States Control and Dynamical Systems Program California Institute of Technology Los AngelesCA90019 United States

Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified planning model of the system. The plan is tracked by the system, represented by a more realistic, higher dimensional tracking model. We precompute the tracking error bound (TEB) due to mismatch between the two models and due to external disturbances. We also obtain the corresponding tracking controller used to stay within the TEB. The precomputation does not require prior knowledge of the environment. We demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and three different real-time trajectory planners with three different tracking-planning model pairs. © 1963-2012 IEEE.

关键词： Real time systems

Resilient control under Quantization and Denial-of-Service: Co-designing a Deadbeat controller and Transmission Protocol

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arXiv 2021年

作者： Liu, Wenjie Sun, Jian Wang, Gang Bullo, Francesco Chen, Jie State Key Lab of Intelligent Control and Decision of Complex Systems The School of Automation Beijing Institute of Technology Beijing100081 China State Key Lab of Intelligent Control and Decision of Complex Systems The School of Automation Beijing Institute of Technology Beijing100081 China Beijing Institute of Technology Chongqing Innovation Center Chongqing401120 China Department of Control Science and Engineering Tongji University Shanghai201804 China Mechanical Engineering Department The Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This paper is concerned with the problem of stabilizing continuous-time linear time-invariant systems subject to quantization and Denial-of-Service (DoS) attacks. In this context, two DoS-induced challenges emerge with the design of resilient encoding schemes, namely, the coupling between encoding strategies of different signals, and the synchronization between the encoder and decoder. To address these challenges, a novel structure that is equipped with a deadbeat controller as well as a delicate transmission protocol for the input and output channels, co-designed leveraging the controllability index, is put forward. When both input and output channels are subject to DoS attacks and quantization, the proposed structure is shown able to decouple the encoding schemes for input, output, and estimated output signals. This property is further corroborated by designing encoding schemes as well as conditions that ensure exponential stability of the closed-loop system. On the other hand, when only the output channel is subject to network phenomenon, the proposed structure can achieve exponential stabilization without acknowledgment (ACK) signals, in contrast to existing ACK-based results. Finally, a numerical example is given to demonstrate the practical merits of the proposed approach as well as the theory. © 2021, CC BY.

关键词： Denial-of-service attack

Soft-Landing Dynamics of a Type of Four-Legged Space Lander

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SSRN

SSRN 2024年

作者： Shi, Tengfei Shi, Tengfei Yang, Yinping Zhang, Zhijuan Liu, Cuicui Liu, Caishan Ma, Daolin Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and Aerospace Engineering Southwest Jiaotong University Chengdu610031 China State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing100871 China Institute of Dynamics and Control College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology Beijing100871 China China Academy of Space Technology Beijing100094 China School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Marine Intelligent Equipment and System Ministry of Education Shanghai200240 China

Analyzing the landing dynamics response is essential for enhancing the success rate of surface explorations on Mars, the moon, or asteroids. This paper develops a comprehensive dynamics model for a space lander equipped with four sets of buffer legs, each consisting of a primary strut, two secondary struts, and a footpad, during its soft landing process. The degrees of freedom of the main body and the footpads are defined as generalized coordinates to describe the motion of the space lander. The compression force of the buffer struts is obtained by interpolating real experimental data, and the contact force between the footpad and the ground is calculated using Archimedes law for granular media. Then, the dynamical model for the lander in terms of minimal degrees of freedom can be constructed by applying the Lagrange equations of the second kind. The proposed dynamics model is validated by the experiments of a single-legged lander vertical touchdown and a four-legged lander free touchdown. Moreover, histories of buffer force, acceleration of the main body, and other key physical quantities are computed to investigate the landing process. This highly efficient and accurate dynamics model provides a method to perform extensive simulations to design and optimize a soft landing process. © 2024, The Authors. All rights reserved.

关键词： Landing

Integral control barrier function for dynamically defined control laws

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arXiv 2020年

作者： Ames, Aaron D. Notomista, Gennaro Wardi, Yorai Egerstedt, Magnus Mechanical and Civil Engineering Control and Dynamical Systems Caltech PasadenaCA91125 United States George W. Woodruff School of Mechanical Engineering Georgia Tech Atlanta United States School of Electrical and Computer Engineering Georgia Tech AtlantaGA30332 United States

This paper introduces integral control barrier functions (I-CBFs) as a means to enable the safety-critical integral control of nonlinear systems. Importantly, I-CBFs allow for the holistic encoding of both state constraints and input bounds in a single framework. We demonstrate this by applying them to a dynamically defined tracking controller, thereby enforcing safety in state and input through a minimally invasive I-CBF controller framed as a quadratic program. Copyright © 2020, The Authors. All rights reserved.

关键词： Quadratic programming