Problem:
Cooperation among a collection of vehicles performing a shared task using intervehicle com- munication to coordinate their actions. Tools from graph theory are useful to model communication network and its topology to formation stabilities
Methodology:
by using double integrator dinamics, I used graph theory to model the communication of 6 vehicles then the laplacian was found. The eigenvalues of the laplacian prove the system to be marginally stable. Using the feedback control law I was able to construct a controller that updated the position and velocity matrices to ensure a hexagon formation.
This procedure was modeled using matlab and the results proved the designed controller ensures a hexagon formation for the 6 vehicles while they update position and velocity through communication.
Simulation:
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