Stability of load lifting by a quadrotor under attitude control delay

We propose a control law for stabilization of a quadrotor-load system, and provide conditions on the control law's gains that guarantee exponential stability of the equilibrium. The system is composed of a load and an unmanned aerial vehicle (UAV) attached to each other by a cable of fixed length, which behaves as a rigid link under tensile forces; and the control input is composed of a three dimensional force requested to the UAV, which the UAV provides with or without delay. Given the proposed control law, we analyze the stability of the equilibrium in two separate parts. In the first, the system is modeled assuming that the UAV provides the requested control input without delay, and we verify that the equilibrium is exponentially stable. In the second part, the UAV is modeled as possessing an attitude inner loop, and we provide a lower bound on the attitude gain for which exponential stability of the equilibrium is preserved. An integral action term is also included in the control law, which compensates for battery drainage or model mismatches, such as an unknown load mass. We present experiments for different scenarios that demonstrate and validate the robustness of the proposed control law.