Hoberman's Twiddlestix as a paradigm for multi-vehicle formation control

In this thesis we study the problem of multi-vehicle formation control. We use the so called "Hoberman's Twiddlestix" as a paradigm to investigate problems of controller synthesis. The design of a distributed controller that drives multiple nonholonomic vehicles to achieve a Hoberman formation is the primary goal of our controller synthesis. The main tools we employ in this thesis are graph rigidity theory and nonlinear control theory. We apply graph rigidity theory to the Hoberman structure to obtain the overall distributed control structure. We employ nonlinear control theory to design the local controllers. The local controller is a switching type controller. It is shown by simulations that the overall controller reaches the control synthesis goal: to stabilize a group of non-holonomic vehicles to a formation defined only in terms of distance constraints between the vehicles.