Theory and practice for autonomous formation flight of quadrotors via distributed robust sliding mode control protocol with fixed-time stability guarantee

A detailed theoretical design and technological implementation aspects are presented in this paper to address the aerial formation control problem of networked quadrotors with a fixed-time stability property. The control algorithm is embedded in a distributed fashion onboard each quadrotor along with a leader-follower scheme. The dynamics of the vehicles are subject to disturbances and nonlinearities. Given the communication topology within the graph, a Distributed Fixed-Time Consensus Observer (DFCO) is designed for the followers that are not all directly informed of the leader's states. An output-feedback control is employed in the position-loop to ensure robust and velocity-free control where only the position of the quadrotors is measurable. Then, inspired by the homogeneity theory, a novel Homogeneous Nonsingular Terminal Sliding Function (HNTSF) that guarantees Global Asymptotic Stability (GAS) in the bi-limit approximation is designed for the position states. Subsequently, a Fixed-time Distributed Non-switching Nonsingular Formation Control Protocol (FDNNFCP) is proposed for the position-loop of each follower aircraft. Also, a Trajectory Tracking Controller (TTC) is designed for the leader. A Modified Robust Homogeneous-based Continuous Twisting Control (MRHCTC) with improved performance is developed to stabilize the attitude-loop. Considering the overall feedback system, the presented work provides a rigorous stability analysis through the bi-limit homogeneity theory and Lyapunov theorem. Moreover, Processor-In-the-Loop (PIL) simulations, ROS/Gazebo implementation, and outdoor flight experiments are conducted to characterize the control performance. Compared with relevant and recent literature on finite-time/fixed-time controllers besides the well-known Proportional-Integral-Derivative (PID) controller, the proposed control approach achieves superior performance in practice since: (i) Convergence-time of the quadrotors to the formation does not depend on their initial positions; (H) Chattering issue of switching and discontinuous control approaches is mitigated; (Hi) Null steady-state error is ensured along with improved robustness.