Coordination and Geometric Optimization via Distributed Dynamical Systems

By Jorge Cortés, Francesco Bullo. SIAM Journal of Control and Optimization, 2003

502 citations recorded by the source corpus.

This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems. The resulting dynamical systems promise to be of use in coordination problems for networked robots; in this setting the distributed control laws correspond to local interactions between the robots. The technical approach relies on concepts from computational geometry, nonsmooth analysis, and the dynamical system approach to algorithms.

Subfields: Computer Networks and Communications, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/f30ae49fd8a92620f85f4796efc9023a7f068e50

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Citations in the corpus

Finite-time stability of multi-agent system in disturbed environment (2012, background): “These dynamical network systems cover a very broad spectrum of applications including cooperative control of unmanned air vehicles (UAVs) [3], autonomous underwater vehicles (AUVs) [4], distributed sensor networks [ 5 ], air and ground transportation systems [6], swarms of air and space vehicle form”
Stability of multiagent systems with time-dependent communication links (2005, background): “Our interest in multi-agent systems is motivated by the emergence of several applications including formation flying of unmanned aerial vehicles (UAVs), cooperative robotics [2]–[4] and sensor networks [5], [6].”
Motion Coordination with Distributed Information (2007, unknown): “neighbor _ pi = Ln(@ smVi(P ))(P ) Voronoi neighbors HSP Incenter Voronoi congurations [ 23 ]”
Consensus of Linear Multi-Agent Systems by Distributed Event-Triggered Strategy (2016, unknown): “One reason is the multi-agent systems can be potentially applied in such broad areas as spacecraft formation flying [1], distributed sensor networks [2], and cooperative surveillance [3].”
Notes on averaging over acyclic digraphs and discrete coverage control (2006, background): “Given a locally Lipschitz function f : R → R and a vector field X, let L̃Xf(x) denote its set-valued Lie derivative with respect to X (see [Cortés and Bullo, 2005].”
Roadmap-Based Path Planning - Using the Voronoi Diagram for a Clearance-Based Shortest Path (2008, background): “A highly interesting research on the utilization of computational geometry methods for coordination problems in dynamic systems was conducted by Cort es and Bullo [12].”
Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems (2011, background): “…interest in various scienti ﬁ c communities due to broad applications in many areas including formation control [11], [42], distributed sensor networks [7], [8], ﬂ ocking [30], [32], distributed computation [25], and synchronization of cou-Manuscript pled chaotic oscillators [2], [9], [39].”
Minimax and maximin space-filling designs: some properties and methods for construction (2017, unknown): “Voronoï tessellation (Cortés and Bullo, 2005, 2009).”
Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective (2009, background): “There is an active research effort underway in the control and dynamical systems community to study these systems and lay out a foundation for their analysis and synthesis [6, 7, 9, 26].”
Distributed Control of Robotic Networks (2009, background): “The following result characterizes the smoothness properties of the spherepacking multicenter function, see [Cortés and Bullo, 2005].”
Esaim: Control, Optimisation and Calculus of Variations Spatially-distributed Coverage Optimization and Control with Limited-range Interactions (unknown): “In our previous work [7, 8], we studied distributed algorithms for deployment and optimal coverage problems using tools from computational geometry, nonsmooth analysis and geometric optimization.”
Finite-time convergent gradient flows with applications to network consensus (2006, background): “Previous work on motion coordination of multi-agent systems has proposed cooperative algorithms based on gradient flows to achieve tasks such as cohesiveness [11, 14, 20], deployment [8, 9] and consensus [15, 16, 17], The distributed algorithms in these works achieve the desired coordination task ov”
Learning Coverage Control of Mobile Sensing Agents in One-Dimensional Stochastic Environments (2010, background): “Cortes and Bullo [2] designed and analyzed a collection of such distributed control laws for mobile sen ors whose closed-loop systems are nonsmooth gradient Jongeun Choi (corresponding author) is with the Department of Mechanical Engineering, Michigan State University jchoi@egr.”
Consensus problems in networks of agents with switching topology and time-delays (2004, background): “…to broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control [1]–[5], ﬂocking [6]–[8], distributed sensor networks [9], attitude alignment of clusters of satellites, and congestion control in communication networks [10].”
Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks (2008, unknown): “More importantly, note that the proposed protocol (30) is different from the protocols given in [22], [32] since (30) is”
Coverage control for mobile sensing networks (2002, background): “For example, in the vector quantization and signal processing literature [14], it is known that for bimodal distribution density functions, the solution to the gradient ﬂow reaches local minima where the number of generators allocated to the two region of maxima are not optimally partitioned.”
Design of computer experiments: space filling and beyond (2011, unknown): “Recent methods suggested for purely geometric problems, see, e.g., Cort´es and Bullo (2009), could be transferred to more statistically-based space-ﬁlling criteria.”
Consensus in multi‐agent systems with communication constraints (2012, background): “Distributed coordination of multi-agent systems has received increasing attention in recent years, due to its potential in understanding various animal group behaviors such as flocking and swarms [1–3], and also due to its wide applications in coordination and control of distributed sensor networks,”