This is a nonlinear problem and is typically solved on a mainframe computer using a Newton gradient algorithm. With our distributed iterative relaxation technique, it is possible to solve these nonlinear calculations over a distributed network. Most importantly, the iterative solution only requires that neighboring nodes communicate with each other, thus greatly reducing the inter-nodal communication requirements. When controlling multiple robotic vehicles, the mechanical analog to the electrical network is that voltage becomes force, current becomes velocity, inductors become mass, resistors become dampers, and capacitors become springs. Virtual dampers and springs between vehicles can be used to artificially specify the impedance between nodes, and the real power at each node is the energy stored in each vehicle.
Reactive power is the power associated with one vehicle pushing another vehicle.
When each vehicle wants to determine it's own vector force and velocity, it will communicate with neighboring vehicles and solve the power flow problem using the distributed iterative relaxation technique. The resulting vehicle formations will depend on the virtual dampers and springs and specified real and reactive powers. Both the variable structure control design and self-organizing communication network will be tested on up to 20 miniature robotic vehicles. We will also simulate the algorithms for numbers larger than 20. This also will be tested on up to 20 miniature robotic vehicles, and simulated for numbers larger than 20.