Thesis title: Modeling and Control for Multi-Quadrotor Cooperative Load Transportation
This research addresses the problem of a cooperative transportation system consisting of multiple quadrotors carrying a slung load. It presents a comprehensive methodology that encompasses the entire development process, from mathematical modeling to controller synthesis. Two distinct mathematical models are developed: one based on the Udwadia–Kalaba formulation and another based on an embedded Lagrangian formulation defined directly on the configuration manifold. For effective cooperative load transport, reliable models of individual agents, as well as their coupled behavior, are essential. The Udwadia-Kalaba formulation allows one to first model the full dynamics of each subsystem, including actuators dynamics, saturations, delays, and external disturbances, and then impose the constraint forces in closed form. To guarantee the safety and effectiveness of the transportation system, the control laws must account for factors such as load distribution, swing control, and collision avoidance, possibly incorporating coupling effects between the dynamics of rigid payload, flexible cables, and multiple quadrotors into control system design. The embedded Lagrangian formulation provides a compact representation of the coupled dynamics, making it particularly suitable for controller synthesis. Moreover, it admits analytical linearization along reference trajectories, thereby enabling the systematic design of linear controllers. Two different control strategies are proposed. In the first, a time-varying LQR is designed based on the linearized dynamics of the coupled system, with feasible quadrotor trajectories generated by exploiting the system differential flatness. To reduce dependence on an accurate model of the constrained dynamics and to eliminate the need for additional sensing or estimation algorithms, a second control strategy is proposed, in which the agents are controlled to maintain a fixed formation. The control scheme employs a cascade architecture, where the payload is treated as an external disturbance acting on the formation. Robustness against unmodeled constraint forces is achieved by utilizing INDI-based inner loops. An obstacle avoidance strategy for the entire formation–payload system is also proposed, in which a Control Barrier Function (CBF) acts on the virtual leader to generate safe trajectories. Additional CBFs are implemented at the quadrotor level to prevent inter-agent collisions. Simulation results confirm the effectiveness of the proposed approaches, while the formation controller has been experimentally validated using Parrot Bebop 2 quadrotors and a motion capture system.