Finite-Time Quadcopter Tracking Using a Barrier Function-Based Nonlinear Control Approach

A barrier function-based real-sliding control approach is presented, which incorporates a sequential finite-time convergence strategy to prove six degree-of-freedom (6-DOF) quadrotor helicopter (quadcopter) state regulation, without the requirement for a priori path-planning or constrained flight trajectories. To achieve the result, the 6-DOF quadcopter dynamics are re-cast as a set of three dynamic subsystems through strategic definitions of auxiliary sliding error variables. The sliding error dynamics are then formulated for each of the three subsystems, resulting in a pair of highly input-coupled error system equations for each of the three subsystems. By leveraging the finite-time convergence properties of barrier functions, a hierarchical control gain selection procedure is utilized to sequentially drive the sliding variables of each subsystem to a bounded region of the origin in finite time. A rigorous Lyapunov-based stability analysis is used to prove that finite-time bounded regulation is achieved of the complete 6-DOF quadcopter state, where the bounding region can be made arbitrarily small through judicious control gain selection. A detailed numerical simulation is provided to demonstrate the performance of the proposed barrier function-based control law as compared to a standard sliding mode control law.