Formation control of under-actuated multi-robot vehicle systems based on high-order fully actuated systems approach

In this paper, a formation control problem of three-dimensional (3D) under-actuated multi-robot vehicle systems with nonholonomic constraint is investigated. First, the nonlinear dynamic model is transformed into an Euler-Lagrangian-like system that satisfies the full-actuation condition. Then, by using the high-order fully actuated systems (HOFAs) approach, the general control law of the under-actuated multi-robot vehicle systems is designed and the linear closed-loop system is obtained. The nonlinear system formation control problem is converted into a formation control problem of linear closed-loop system. According to the formation control requirements and objectives, designing the final formation controller using a rigid graph theory approach allows the under-actuated multi-robot vehicle systems to accurately converge to the desired formation. Lyapunov-based stability analysis shows the error function theoretically converges to zero eventually. Simulation results confirm the effectiveness of the formation control law.