Controlled Lagrangians control for a quadrotor helicopter

Energy-based Hamiltonian approach in H∞ controller design for n-degree of freedom mechanical systems

“…, q n ] T ∈ R n is the position vector,q ∈ R n is the velocity vector, M(q) = M T (q) > 0 ∈ R n×m is the inertia matrix, C(q,q) is the coriolis and centripental forces vector, B(q) ∈ R n is the potential forces vector, G(q) ∈ R n×m is the input coupling matrix and u ∈ R m is the applied torque vector. In fact, there exist a variety of systems with the structure of Equation (3) such as quadrotor (Zheng, Zhu, Zuo, & Yan, 2015), wheeled inverted pendulum (Delgado & Kotyczka, 2016) and many other mechanical systems.…”