A control Lyapunov function approach to multi-agent coordination

Ögren, Petter; Egerstedt, Magnus; Hu, Xianfeng

doi:10.1109/cdc.2001.981040

Cited by 68 publications

(83 citation statements)

References 6 publications

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“…This contradicts lim t→∞ ∑ (i, j)∈N * * q i j (t) − q i jc = d * * , ∀(i, j) ∈ N * * , i = j. Therefore q c must be an unstable equilibrium point of the closed loop system (17). Proof of Theorem 1 is completed.…”

mentioning

confidence: 89%

“…Although these guarantee a complete solution, centralized schemes require high computational power and are not robust due to the heavy dependence on a single controller. A nice application of formation control based on potential field method [3] and Lyapunov's direct method [17] to gradient climbing is recently addressed in [18]. However, the final configuration of formation cannot be foretold.…”

Section: Introductionmentioning

confidence: 99%

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Bounded Controllers for Decentralized Formation Control of Mobile Robots with Limited Sensing

Duc

2007

INT J COMPUT COMMUN

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This paper presents a constructive method to design bounded cooperative controllers that force a group of N mobile robots with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the robots. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, and are equal to infinity when a collision between any robots occurs. Smooth and p times differential jump functions are introduced and embedded into the potential functions to deal with the robot limited sensing ranges. Formation tracking is also considered.

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mentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Bounded Controllers for Decentralized Formation Control of Mobile Robots with Limited Sensing

Duc

2007

INT J COMPUT COMMUN

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“…Capitalizing on this idea and building on the methods of [55,56],Ögren et al [4] developed a provable methodology to control the shape of the formation as well as the rotation, translation and expansion of the formation (see also [64]); this was used to design control strategies for a network of vehicles to adaptively climb gradients in the sampled field and thus robustly find peaks (see Section 3.1 below for a review of the implementation of this methodology in the field). These ideas were extended further by Zhang and Leonard [65,66] to design provable control laws for cooperative level set tracking, whereby small vehicle groups could cooperate to generate contour plots of noisy, unknown fields, adjusting their formation shape to provide optimal filtering of their noisy measurements.…”

Section: Background and Historymentioning

confidence: 99%

“…Artificial potentials presented an attractive methodological basis for cooperative control of network formations [53,54,55,56,57,58] both because convergence and performance could be proved using Lyapunov stability theory (see, e.g., early work on robot navigation and obstacle avoidance [59,60]) and because control laws derived from artificial potentials resembled the distributed, cohesive and repulsive forces used to model animals that move together [61,62].…”

Section: Background and Historymentioning

confidence: 99%

Cooperative Vehicle Environmental Monitoring

Leonard

2016

Springer Handbook of Ocean Engineering

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Over the last decade, methodologies for automated cooperative control of robotic vehicles have been designed, deployed and proven to provide efficient, reliable, and sustained monitoring of the uncertain and inhospitable ocean environment. Unprecedented data sets have been collected from deployments of cooperative vehicles in the field, and both real-time and post-deployment analyses have led to new understanding of the environment. This first decade of success in cooperative vehicle environmental monitoring sets the stage for new opportunities and future gain, especially as the development of cooperative control methodologies can continue to leverage ongoing technological and scientific advances in underwater communication and sensing, energy and computational efficiency, vehicle size, speed, maneuverability and cost, and ocean modeling and prediction.Indeed, the demonstrated potential of cooperative vehicle control has led to increased demand for fleets of autonomous underwater vehicles (AUVs) for use in measuring ocean physics, biology, chemistry and geology to improve understanding of natural dynamics and human-influenced changes in the marine environment. Further, methodologies for cooperative control of robotic vehicles in the ocean are readily adaptable to applications on land, in the air and in space; likewise, there is much to be learned from developments in these other domains. The recent explosion in research on networks and complex systems, including investigation of mechanisms that explain a "collective intelligence" exhibited by animal aggregations on the move, are also being leveraged to advance design of cooperative vehicle dynamics.For environmental monitoring to be successful, physical, chemical, and biological variables must be measured across a range of spatial and temporal scales; in the ocean the monitoring strategy must also contend with a harsh, three-dimensional physical space that is highly uncertain and dynamic. Small spatial and temporal scales associated with the measured variables typically make a stationary sensor array impractical because a very large number of sensors would be needed to get sufficient resolution in space and/or time. An array of mobile sensors, however, may be very well suited to such a challenge since mobility can be exploited to dynamically distribute fewer sensors according to the spatial and temporal scales.The underlying principle of cooperative control of vehicles for environmental monitoring leverages mobility of sensors and uses an interacting dynamic among the individual sensors to yield a collective behavior that performs better than the sum of the parts. If the vehicles can communicate their state or measure the relative state of others in the team, then they can cooperate and the cooperative vehicle dynamics can provide coordinated motion of the team as a whole. The resulting vehicle network functions as a dynamically reconfigurable sensor array with a capability for high performance in environmental monitoring not available at the level of individual...

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“…For example, Lui et al [13] use Lyapunov methods and Leonard et al [14] and Olfati and Murray [15] use potential function theory to understand flocking behavior, and Ögren et al [16] uses control Lyapunov function-based ideas to analyze formation stability, while Fax and Murray [17] and Desai et al [18] employ graph theoretic techniques for the same purpose.…”

Section: Introductionmentioning

confidence: 99%

Coordination of groups of mobile autonomous agents using nearest neighbor rules

Jadbabaie

Lin

Morse

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

750

1,243

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In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors. " In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function. KeywordsCooperative control, graph theory, infinite products, multiagent systems, switched systems This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/29 provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.

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A control Lyapunov function approach to multi-agent coordination

Cited by 68 publications

References 6 publications

Bounded Controllers for Decentralized Formation Control of Mobile Robots with Limited Sensing

Bounded Controllers for Decentralized Formation Control of Mobile Robots with Limited Sensing

Cooperative Vehicle Environmental Monitoring

Coordination of groups of mobile autonomous agents using nearest neighbor rules

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