Quadrotor Attitude Control using Incremental Nonlinear Dynamics Inversion
Given the large flight envelope of vertical take-off and landing vehicles, and the nonlinear nature of multirotor aircraft, especially in aggressive maneuvering, nonlinear control strategies are often considered. Yet, most available solutions are model dependent and thus require a precise knowledge of the system dynamics, including the hard to model aerodynamics. This paper proposes a sensor-based approach to the problem. It considers a recent strategy based on incremental control and Nonlinear Dynamics Inversion (NDI), the Incremental Nonlinear Dynamics Inversion (INDI), to solve the attitude control problem of quadrotors. The INDI general formulation is presented, and then applied considering the attitude stabilization of a quadrotor. In order to apply the INDI solution to this case study, a linear predictor for the angular acceleration is provided. Simulation results demonstrate the robustness of this sensor-based approach to model-parameter uncertainties and wind disturbances. An analysis is also done regarding the tuning of INDI parameters and its sensitivity to the chosen sampling time.
Robust Flight Control Using Incremental Nonlinear Dynamic Inversion and Angular Acceleration Prediction
This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of angular accelerations eliminates sensitivity to model mismatch, greatly increasing the robust performance of the system compared with conventional nonlinear dynamic inversion. However, angular accelerations are not readily available. Furthermore, it is shown that angular acceleration feedback is sensitive to sensor measurement time delays. Therefore, a linear predictive filter is proposed that predicts the angular accelerations, solving the time delay and angular acceleration availability problem. The predictive filter uses only references and measurements of angular rates. Hence, the proposed control method makes incremental nonlinear dynamic inversion practically available using conventional inertial measurement units.
Graphs of polyhedra; polyhedra as graphs
Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and inconsistency that pervade much of the literature dealing with polyhedra more general than the convex ones.