Showing papers by "Richard M. Murray published in 2003"
04 Jun 2003
TL;DR: It turns out that the connectivity of the network is the key in reaching a consensus in networks of dynamic agents, and a tight upper bound is found on the maximum fixed time-delay that can be tolerated in the network.
Abstract: In this paper, we introduce linear and nonlinear consensus protocols for networks of dynamic agents that allow the
agents to agree in a distributed and cooperative fashion.
We consider the cases of networks with communication time-delays and channels that have filtering effects.
We find a tight upper bound on the maximum fixed time-delay
that can be tolerated in the network. It turns out that the
connectivity of the network is the key in reaching a
consensus. The case of agreement with bounded inputs is
considered by analyzing the convergence of a class of nonlinear protocols. A Lyapunov function is introduced that
quantifies the total disagreement among the nodes of a
network. Simulation results are provided for agreement in networks with communication time-delays and constrained inputs.
896 citations
TL;DR: The Panel on Future Directions in Control, Dynamics, and Systems was formed in 2000 to provide a renewed vision of future challenges and opportunities in the control field along with recommendations to government agencies, universities, and research organizations to ensure continued progress in areas of importance to the industrial and defense base as mentioned in this paper.
Abstract: The Panel on Future Directions in Control, Dynamics, and Systems was formed in April 2000 to provide a renewed vision of future challenges and opportunities in the control field, along with recommendations to government agencies, universities, and research organizations to ensure continued progress in areas of importance to the industrial and defense base. The panel released a report in April 2002, the intent of which is to raise the overall visibility of research in control, highlight its importance in applications of national interest, and indicate some of the key trends that are important for continued vitality of the field. After a brief introduction, we summarize the report, discuss its applications and education and outreach, and conclude with some recommendations.
363 citations
09 Dec 2003
TL;DR: This paper gives formal definitions of nets and flocks as spatially induced graphs and define flocking and introduces the notion of framenets and describes a procedure for automatic construction of an energy function for groups of agents.
Abstract: In this paper, we provide a dynamic graph theoretic framework for flocking in presence of multiple obstacles. In particular, we give formal definitions of nets and flocks as spatially induced graphs and define flocking. We introduce the notion of framenets and describe a procedure for automatic construction of an energy function for groups of agents. The task of flocking is achieved via dissipation of this energy according to a protocol that only requires the use of local information. We show that all three rules of Reynolds are hidden in this single protocol. Three types of agents called /spl alpha/, /spl beta/, and /spl gamma/ agents are used to create flocking. Simulation results are provided that demonstrate flocking by 100 dynamic agents.
329 citations
01 Jan 2003
TL;DR: It is demonstrated that a class of directed graphs, called balanced graphs, have a crucial role in solving average-consensus problems and a group disagreement function, Lyapunov function, is proposed for convergence analysis of this agreement protocol for networks with directed graphs and switching topology.
Abstract: In this paper, we provide tools for convergence and performance analysis of an agreement protocol for a network of integrator agents with directed information flow. We also analyze algorithmic robustness of this consensus protocol for networks with mobile nodes and switching topology. A connection is established between the Fiedler eigenvalue of the graph Laplacian and the performance of this agreement protocol. We demonstrate that a class of directed graphs, called balanced graphs, have a crucial role in solving average-consensus problems. Based on the properties of balanced graphs, a group disagreement function (i.e. Lyapunov function) is proposed for convergence analysis of this agreement protocol for networks with directed graphs and switching topology.
228 citations
10 Nov 2003
TL;DR: Stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions generate smoother paths than previous methods, making them more suited to aircraft-like vehicles.
Abstract: Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed.
180 citations
01 Jan 2003
TL;DR: In this paper, the authors define flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential-geometric framework, utilizing the infinite dimensional geometry developed by Vinogradov and coworkers.
Abstract: Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft.
159 citations
TL;DR: Using tools from dynamical systems and systems identification, a segmentation and classification algorithm is developed in order to reduce a complex activity into the sequence of movemes that have generated it.
156 citations
04 Jun 2003
TL;DR: A class of triangulated graphs for algebraic representation of formations that allows one to specify a mission cost for a group of vehicles and solve tracking problems for groups of vehicles in formations using an optimization-based approach is introduced.
Abstract: We introduce a class of triangulated graphs for algebraic representation of formations that allows one to specify a mission cost for a group of vehicles. This representation plus the navigational information allows one to formally specify and solve tracking problems for groups of vehicles in formations using an optimization-based approach. The approach is illustrated using a collection of six underactuated vehicles that track a desired trajectory in formation.
155 citations
04 Jun 2003
TL;DR: The features of RoboFlag provide a number of research challenges in distributed control, sensor fusion, team-based control, and human-centered control.
Abstract: This paper provides an introduction to the RoboFlag competition and its use as a testbed for distributed control of multi-vehicle systems. The game consists of two teams of 6-10 robots and 2 people, each attempting to capture the other teams flag while defending their own. Limited sensing capability, distributed processing, and limited bandwidth communications are integral parts of the system. The features of RoboFlag provide a number of research challenges in distributed control, sensor fusion, team-based control, and human-centered control.
61 citations
09 Dec 2003
TL;DR: Low observability flight path planning of unmanned air vehicles (UAVs) in the presence of radar detection systems using the nonlinear trajectory generation (NTG) software package developed at Caltech is used.
Abstract: This paper explores low observability flight path planning of unmanned air vehicles (UAVs) in the presence of radar detection systems. The probability of detection model of an aircraft near an opponent radar depends on aircraft attitude, range, and configuration. A detection model is coupled with a simplified aircraft dynamics model. The nonlinear trajectory generation (NTG) software package developed at Caltech is used. The NTG algorithm is a gradient descent optimization method that combines three technologies: B-splines, output space collocation and nonlinear optimization tools. Implementations are formulated with temporal constraints that allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent. Illustrative examples of optimized routes for low observability are presented.
45 citations
09 Dec 2003
TL;DR: In this paper, the stability analysis problem for nonlinear systems with general linear feedback interconnections is studied, and necessary conditions for stability of a classification of interconnected systems are presented.
Abstract: This paper explores the stability analysis problem for nonlinear systems which have general linear feedback interconnections. Systems are often modeled in this manner in the study of decentralized control because many communication topologies can be modeled and analyzed using connections to graph theory. We present necessary conditions for stability of a classification of interconnected systems, and we give some examples to provide insight into this problem. These conditions are related to positive definiteness of matrices associated with the feedback interconnection, and specialize to the common case where the Laplacian matrix of a graph represents the communication topology of the system.
TL;DR: In this paper, the authors summarized the findings and recommendations of a recent panel of future directions in control, dynamics, and systems, sponsored by the US Air Force Office of Scientific Research.
09 Dec 2003
TL;DR: The focus of the paper is on obtaining conditions for the stability of the formation that can be checked in a decentralized way and shows that the method of analysis can be extended to more general cases of complicated agent dynamics, non-ideal links for information flow, etc.
Abstract: We analyze a network of dynamic agents where the topology of the network specifies the information flow between the agents. We present an analysis method for such a system for both consensus and formation stabilization problems. To consider the general features introduced by the information flow topology, we consider the case of agent dynamics being a single integrator. Then we show that the method of analysis can be extended to more general cases of complicated agent dynamics, non-ideal links for information flow, etc. We also consider the case when the topology of the network is changing over time. The focus of the paper is on obtaining conditions for the stability of the formation that can be checked in a decentralized way.
04 Jun 2003
TL;DR: A suboptimal version of the casual Viterbi estimation algorithm is considered and it is shown that a separation property does not hold between the optimal control and the Markov state estimate.
Abstract: We analyze a jump linear Markov system being stabilized using a linear controller. We consider the case when the Markov state is associated with the probability distribution of a measured variable. We assume that the Markov state is not known, but rather is being estimated based on the observations of the variable. We present conditions for the stability of such a system and also solve the optimal LQR control problem for the case when the state estimate update uses only the last observation value. In particular we consider a suboptimal version of the casual Viterbi estimation algorithm and show that a separation property does not hold between the optimal control and the Markov state estimate. Some simple examples are also presented.
04 Jun 2003
TL;DR: A model reduction approach is developed in which the number of possible configurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones in an infinite-dimensional film growth master equation.
Abstract: A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear-like structure and an often-high dimension. We develop a model reduction approach in which the number of possible configurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are derived based on a minimum and maximum time scale of interest. An analogous linear identification procedure is then presented, which computes the state and output matrices for a predetermined configuration set. These ideas are demonstrated first in a finite-dimensional model inspired by problems in surface evolution, and then in an infinite-dimensional film growth master equation.
10 Nov 2003
TL;DR: The trajectory of achieving cooperative tasks, i.e., with temporal constraints, is constructed by a nonlinear trajectory generation (NTG) algorithm, used to generate real-time trajectory for desired robot activities.
Abstract: This paper discusses a design methodology of cooperative trajectory generation for multi-robot systems. The trajectory of achieving cooperative tasks, i.e., with temporal constraints, is constructed by a nonlinear trajectory generation (NTG) algorithm. Three scenarios of multi-robot tasking are proposed at the cooperative task planning framework. The NTG algorithm is, then, used to generate real-time trajectory for desired robot activities. Given robot dynamics and constraints, the NTG algorithm first finds trajectory curves in a lower dimensional space and parameterizes the curves by a set of B-spline representations. The coefficients of the B-splines are further solved by sequential quadratic programming to satisfy the optimization objectives and constraints. The NTG algorithm has been implemented to generate real-time trajectories for a group of cooperative robots in the presence of spatial and temporal constraints. Finally, an illustrated example of cooperative task planning with temporal constraints is presented.
04 Jun 2003
TL;DR: This paper provides a systematic way to design the local controller and the system control strategy with the performance constrains and presents the connection failure tolerance problem.
Abstract: In this paper, we treat the string stability as a kind of performance of a linear multi-vehicle system with acyclic formation structures. By using a double-graph model, we can describe information flows and formulate the string stability. This paper provides a systematic way to design the local controller and the system control strategy with the performance constrains. We also present the connection failure tolerance problem and give some essential conclusions.
01 Jan 2003
TL;DR: In this article, the effect of a varying downstream boundary condition on dynamic separation control in a two-dimensional low-speed asymmetric diffuser was investigated using spanwise unsteady forcing from a single tangential actuator located directly upstream of the separation point.
Abstract: This paper presents an experimental investigation into the effect of a varying downstream boundary condition on dynamic separation control in a twodimensional low-speed asymmetric diffuser. The potential for coupling between the downstream boundary condition and the separation dynamics is relevant, for example, in using separation control to enable more aggressive serpentine aircraft inlets, where the compressor may be close to the separation point. Separation control in the experiment is obtained using spanwise unsteady forcing from a single tangential actuator located directly upstream of the separation point. The downstream boundary condition simulates the dominant quasi-steady and reflection characteristics of a compressor. Although the boundary condition affects the uncontrolled pressure recovery, the optimal forcing frequency is shown to depend only on the mass flow rate and not on either the presence, impedance, or location of the downstream boundary condition. At the conditions tested herein, we therefore conclude that the mechanism underlying dynamic separation control is local in nature, and is not influenced by global system dynamics.
04 Jun 2003
TL;DR: Using geometric concepts from observability theory for nonlinear systems, an approach for parameter estimation for linearly and nonlinearly parameterized systems is proposed and an observability check for parameters is established.
Abstract: Using geometric concepts from observability theory for nonlinear systems, we propose an approach for parameter estimation for linearly and nonlinearly parameterized systems. The proposed approach relies on extending a parameter estimation problem to a state estimation problem by introducing the parameters as auxiliary state variables. Applying tools from geometric nonlinear control theory we establish an observability check for parameters, and we construct a local observer with established speed of convergence in the observable sets of the extended system.
04 Jun 2003
TL;DR: Using tools from dynamical systems and systems identification, a segmentation and classification algorithm is developed in order to reduce a complex activity into the sequence of movemes that have generated it.
Abstract: Using tools from dynamical systems and systems identification, we develop a framework for the study of primitives for human motion, which we refer to as movemes. The objective is understanding human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. We develop a segmentation and classification algorithm in order to reduce a complex activity into the sequence of movemes that have generated it. We test our ideas on data sampled from five human subjects who were drawing figures using a computer mouse. Our experiments show that we are able to distinguish between movemes and recognize them even when they take place in activities containing an unspecified number of movemes.
01 Sep 2003
TL;DR: Simulation and experimental results are presented on the generation and implementation of optimal trajectories for the MVWT vehicles, which are nonlinear, spatially constrained and their input controls are bounded.
Abstract: The Caltech Multi-Vehicle Wireless Testbed (MVWT) is a platform designed to explore theoretical advances in multi-vehicle coordination and control, networked control systems and high confidence distributed computation. The contribution of this report is to present simulation and experimental results on the generation and implementation of optimal trajectories for the MVWT vehicles. The vehicles are nonlinear, spatially constrained and their input controls are bounded. The trajectories are generated using the NTG software package developed at Caltech. Minimum time trajectories and the application of Model Predictive Control (MPC) are investigated.
01 Sep 2003
TL;DR: It is shown that the well-posedness notion can be applied in practice so to establish if sets of actions, viewed as signals in time, can define movemes.
Abstract: We develop the study of primitives of human motion, which we refer to as movemes. The idea is to understand human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. How can we construct an alphabet of movemes from human data? In this paper we address this issue by introducing the notion of well-posednes. Using examples from human drawing data, we show that the well-posedness notion can be applied in practice so to establish if sets of actions, viewed as signals in time, can define movemes.
Proceedings Article•
01 Jan 2003
TL;DR: In this article, the authors summarized the findings and recommendations of a recent panel on Future Directions in Control, Dynamics, and Systems, sponsored by the US Air Force Office of Scientific Research.
Abstract: This paper summarizes the findings and recommendations of a recent panel on Future Directions in Control, Dynamics, and Systems, sponsored by the US Air Force Office of Scientific Research. A set of grand challenges that illustrate some of the recommendations and opportunities are provided. Finally, the paper describes two new courses being developed at Caltech that are aligned with the recommendations of the report.
15 Sep 2003
TL;DR: Some of the limits of receding horizon control are explored, including the extent to which traditional control specifications can be cast as RHC problem specifications.
Abstract: Receding horizon control allows a blending of navigation and control functions at the inner and outer loop levels and significantly enhances the ability of the control system to react to complex dynamic and environmental constraints. In this paper, we explore some of the limits of receding horizon control, including the extent to which traditional control specifications can be cast as RHC problem specifications. Simulation results for a planar flight vehicle with representative flight dynamics illustrate the main features of the proposed approach.
01 Sep 2003
TL;DR: This paper provides simulation and experimental results for stabilization and tracking of a single vehicle, and a simulation of stabilization of a six-vehicle formation, demonstrating that in all cases the control bounds and the control objective are satisfied.
Abstract: In this paper, we introduce an approach for distributed nonlinear control of multiple hovercraft-type underactuated vehicles with bounded and unidirectional inputs. First, a bounded nonlinear controller is given for stabilization and tracking of a single vehicle, using a cascade backstepping method. Then, this controller is combined with a distributed gradient-based control for multi-vehicle formation stabilization using formation potential functions previously constructed. The vehicles are used in the Caltech Multi-Vehicle Wireless Testbed (MVWT). We provide simulation and experimental results for stabilization and tracking of a single vehicle, and a simulation of stabilization of a six-vehicle formation, demonstrating that in all cases the control bounds and the control objective are satisfied.
01 Jan 2003
TL;DR: This paper considers film growth on a vicinal surface using a kinetic Monte Carlo model and indicates that a 5-state model may be sufficient for real-time roughness control.
Abstract: For closed-loop control of thin film deposition, one would like to directly control film properties such as roughness, stress, or composition, rather than process parameters like temperatures and flow rates. This requires a model of the dynamic response of film properties to changes in process conditions. Direct atomistic simulation is far too slow to be used in this capacity, but a promising approach we explore here is to derive reduced-order dynamic models from atomistic simulations. In this paper, we consider film growth on a vicinal surface using a kinetic Monte Carlo model. The temperature range spans the transition from smooth step flow to rough island growth. Proper Orthogonal Decomposition is used to extract the dominant spatial modes from the KMC simulations. Only five spatial modes adequately represent the roughness dynamics for all simulated times and temperatures, indicating that a 5-state model may be sufficient for real-time roughness control.
23 Jun 2003
01 Jan 2003
TL;DR: In this article, the stability analysis problem for nonlinear systems with general linear feedback interconnections is studied, where the Laplacian matrix of a graph represents the communication topology of the system.
Abstract: This paper explores the stability analysis problem for nonlinear systems which have general linear feedback interconnections. Systems are often modeled in this manner in the study of decentralized control because many communication topologies can be modeled and analyzed using connections to graph theory. We present necessary conditions for stability of a classiflcation of interconnected systems, and we give some examples to provide insight into this problem. These conditions are related to positive deflniteness of matrices associated with the feedback interconnection, and specialize to the common case where the Laplacian matrix of a graph represents the communication topology of the system.