Distributed Control of Robotic Networks A Mathematical Approach to Motion Coordination Algorithms The entire book is freely available for download. The latest version of the book is from March 10, 2009 Copyright You are allowed to freely download, share, print, or photocopy the book. You are not allowed to modify, sell, or claim authorship of any part of the book. We thank you for any feedback information, including suggestions, evaluations, error descriptions, or comments about teaching or research uses Download bib entry [entry.bib]

complete book [PDF]

chapter by chapter [see below] Book contents Chapter 1: An introduction to distributed algorithms [PDF] Elementary concepts and notation Distance functions Matrix theory

State machines and dynamical systems Stability and attractivity notions Invariance principles Notions and results for set-valued systems Notions and results for time-dependent systems

Graph theory Connectivity notions Weighted digraphs Distances on digraphs and weighted digraphs Graph algorithms Algebraic graph theory

Distributed algorithms on synchronous networks Physical components and computational models Complexity notions Broadcast and BFS tree computation Leader election Shortest-paths tree computation

Linear distributed algorithms Linear iterations on synchronous networks Averaging algorithms Convergence speed of averaging algorithms Algorithms defined by tridiagonal Toeplitz and tridiagonal circulant matrices

Notes

Proofs

Exercises Chapter 2: Geometric models and optimization [PDF] Basic geometric notions Polygons and polytopes Nonconvex geometry Geometric centers Voronoi and range-limited Voronoi partitions

Proximity graphs Spatially distributed proximity graphs Proximity graphs over tuples of points Spatially distributed maps

Geometric optimization problems and multicenter functions Expected-value multicenter functions Worst-case and disk-covering multicenter functions Sphere-packing multicenter functions

Notes

Proofs

Exercises Chapter 3: Robotic network models and complexity notions [PDF] A model for synchronous robotic networks Physical components Control and communication laws Agree and pursuit control and communication law

Robotic networks with relative sensing Kinematics notions The physical components Relative-sensing control laws Equivalence between communication and relative-sensing laws

Coordination tasks and complexity notions Coordination tasks Complexity notions Invariance under rescheduling

Complexity of direction agreement and equidistance

Notes

Proofs

Exercises Chapter 4: Connectivity maintenance and rendezvous [PDF] Problem statement

Connectivity maintenance algorithms Enforcing range-limited links Enforcing network connectivity Enforcing range-limited line-of-sight links and network connectivity

Rendezvous algorithms Averaging control and communication law Circumcenter control and communication laws Correctness and complexity of circumcenter laws Circumcenter law in nonconvex environments

Simulation results

Notes

Proofs

Exercises Chapter 5: Deployment [PDF] Problem statement

Deployment algorithms Geometric-center laws Geometric-center laws with range-limited interactions Correctness and complexity of geometric-center laws

Simulation results

Notes

Proofs

Exercises Chapter 6: Boundary estimation and tracking [PDF] Event-driven asynchronous robotic networks

Problem statement Linear interpolations for boundary estimation Network model and boundary estimation task

Estimate update and cyclic balancing law Single-robot estimate update law Cooperative estimate update law Cyclic balancing algorithm for equidistance task Correctness of the estimate update and cyclic balancing law

Simulations results

Notes

Proofs

Exercises References [PDF] Indices [PDF]