Rigid formation control of nonlinear systems using null space behavior control framework based on rotation matrix constraints

This paper proposes an improved null-space behavior control algorithm based on rotation matrix constraints for nonlinear systems. We take the kinematic model of unmanned aerial vehicles (UAVs) as an example. First, the UAV mathematical model is incorporated into the mission design of null-space behavior control (NSBC) to ensure that the mission instructions satisfy the system’s motion constraints, overcoming the limitations of the classical NSBC method, which relies on the single integrator model. Second, a formation controller was designed for each agent, which utilizes a self-updating estimator that tracks the expected speed after merging under disturbance conditions. Finally, numerical simulations indicate that the proposed algorithm can form a rigid formation.