This dissertation focuses on the collaborative control of homogeneous UAV swarms. A two-level scheme is proposed by combining the high-level path planning and the low-level vehicle motion control. A decentralized artificial potential function (APF) based approach, which mimics the bacteria foraging process, is studied for the high-level path planning. The deterministic potential based approach, however, suffers from the local minima entrapment dilemma, which motivate us to fix the "flaw" that is naturally embedded. An innovative decentralized stochastic approach based on the Markov Random Filed (MRF) theory is proposed; this approach traditionally used in statistical mechanics and in image processing. By modeling the local interactions as Gibbs potentials, the movements of vehicles are then decided by using Gibbs sampler based simulated annealing (SA) algorithm.

A two-step sampling scheme is proposed to coordinate vehicle networks: in the first sampling step, a vehicle is picked through a properly designed, configuration-dependent proposal distribution, and in the second sampling step, the vehicle makes a move by using the local characteristics of the Gibbs distribution. Convergence properties are established theoretically and confirmed with simulations. In order to reduce the communication cost and the delay, a fully parallel sampling algorithm is studied and analyzed accordingly. In practice, the stochastic nature of the proposed algorithm might lead to a high traveling cost. To mitigate this problem, a hybrid algorithm is developed by combining the Gibbs sampler based method with the deterministic gradient-flow method to gain the advantages of both approaches.

The robustness of the Gibbs sampler based algorithm is also studied. The convergence properties are investigated for different types sensor errors including range-error and random-error. Error bounds are derived to guarantee the convergence of the stochastic algorithm.

In the low-level motion control module, a model predictive control (MPC) approach is investigated for car-like UAV model. Multiple control objectives, for example, minimizing tracking error, avoiding actuator/state saturation, and minimizing control effort, are easily encoded in the objective function. Two numerical optimization approaches, gradient descendent approach and dynamic programming approach, are studied to strike the balance between computation time and complexity.