Formation control algorithms for unmanned vehicles are proposed and developed based on the concept of tensegrity structures to solve the cooperative control problems. The tensegrity concept, which is enhanced by virtualising the strings and bars of the tensegrity grid, is used to establish the relationship between isolated vehicles that forms a formation topology and to develop mathematical algorithms in characterising the interaction control forces among the vehicles. The simple form of tensegrity mathematics significantly simplified the design of the formation control algorithm and its computation procedure while optimising the corresponding formation topology. The formation is proved to be exponentially stable by the Lyapunov stability theory, if all the vehicles are driven to their equilibrium under the regulation of interaction control forces among them. The control force is dynamically redefined as a non linear tension force based on tensegrity's virtual string which demonstrates better performance in compensating the external disturbance forces to maintain a firm formation while allowing flexible shape transformation to achieve obstacle avoidance. A decentralized scheme is also proposed to simplify the mathematical analysis of the complex formation control problem, in addition to solving the scalable formation problem by decomposing the formation system into an ensemble of vehicle subsystems. By defining the applied interaction force as a bounded energy exogenous input to the subsystem, a H∞ robust controller, which is formulated by solving a LMI optimisation problem, stabilises each subsystem in the formation by regulating its applied tension force. This H∞ controller provides robustness to the scalable multi-vehicle formation system and improves its overall performance by attenuating the formation error propagation. This algorithm is extended for the formation flight of multiple Aerosonde UAVs to verify the effectiveness of the proposed algorithm using 3D formation stability results. The LMI-based H∞ autopilot was developed to regulate the related induced forces and thus stabilises all the individual UAVs in the formation. Simulation results demonstrated the stability and effectiveness of the proposed tensegrity-based formation control strategy for a diverse range of multi-UAV formation achieving, maintaining, transforming and manoeuvring scenarios.