Distributed Control of Robotic Networks
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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