Hierarchical nonlinear control for multi-rotor asymptotic stabilization based on zero-moment direction

Abstract

We consider the hovering control problem for a class of multi-rotor aerial platforms with generically oriented propellers. Given the intrinsically coupled translational and rotational dynamics of such vehicles, we first discuss some assumptions for the considered systems to reject torque disturbances and to balance the gravity force, which are translated into a geometric characterization of the platforms that is usually fulfilled by both standard models and more general configurations. Hence, we propose a control strategy based on the identification of a zero-moment direction for the applied force and the dynamic state feedback linearization around this preferential direction, which allows to asymptotically stabilize the platform to a static hovering condition. Stability and convergence properties of the control law are rigorously proved through Lyapunov-based methods and reduction theorems for the stability of nested sets. Asymptotic zeroing of the error dynamics and convergence to the static hovering condition are then confirmed by simulation results on a star-shaped hexarotor model with tilted propellers.

On local-global hysteresis-based hovering stabilization of the DarkO convertible UAV

“…We propose in this section two control design strategies for stabilizing a hovering position. The first one is inspired by the nonlinear stabilizer presented in [20] and provides a large region of attraction, and the second one is based on the linearized dynamics and allow for more effective gain tuning in the final approaching phase. The two controllers are united via a hybrid mechanism that allows retaining the steady-state performance of the linearized design with the large region of attraction guaranteed by the nonlinear design.…”

“…We illustrate in this section a nonlinear dynamic control law inspired by the result of [20]. For the nonlinear control law of [20] to be applicable, matrices F and M reported in (3) must allow defining a so-called zero moment direction ū ∈ R 4 ensuring |F ū| = 1 and M ū = 0, and a right inverse M r of M satisfying M M r = I and F M r = 0.…”

“…We illustrate in this section a nonlinear dynamic control law inspired by the result of [20]. For the nonlinear control law of [20] to be applicable, matrices F and M reported in (3) must allow defining a so-called zero moment direction ū ∈ R 4 ensuring |F ū| = 1 and M ū = 0, and a right inverse M r of M satisfying M M r = I and F M r = 0. In our case, it is immediate to see that the zero-moment direction ū = √ 2 2af [ 1 1 0 0 ] ⊤ satisfies the required conditions, whereas the fact that rank(F ) = 2 (so that ker F has dimension 2) makes it impossible to find a right inverse M r of M completely contained in ker F .…”

“…Performing a Schur complement, this minimization is well obtained by solving the following semi-definite program: leading to κ = 39.7. With this optimality-based selection, the nonlinear dynamic design of [20] can be effectively applied by obtaining responses that are almost indistinguishable from the fully decoupled case F M r = 0. Note that a similar approach, essentially neglecting the extra terms acting on the translational dynamics is also suggested in the survey paper [4].…”

“…As a final remark, as compared to the solution proposed in [20], to partially take into the saturation effects highlighted in Remark 1, the error feedback interconnection of the outer loop in [20] has been augmented with a simple error governor strategy never allowing the translational position error e p entering [20, eqn. (22)] to exceed the maximum value of 3 meters.…”