Simplified Aerodynamic Modeling of a Bird Robot Using the DeNOC Matrices

Abstract

To design an efficient flapping wing aerial vehicle, a simplified aerodynamic model of a bird robot is presented in this paper. A bird robot was divided into three modules, namely, main body, right wing, and left wing. The main body of the bird was considered as spheroidal prolate, and the wings as rigid plate with airfoil cross-section. The robotic bird was considered as tree-type multibody system, where the main body is parent and wings are children. Each wing was connected to the main body using a two-degree-of-freedom (DoF) joint, which provides twisting and flapping motions to the wings. The kinematic configuration of the bird model was represented using the modified Denavit–Hartenberg (DH) parameters. The flapping and twisting of the wings generate both lift and forward thrust for the bird flight. The equations of motion of the robotic bird were derived using the DeNOC matrices. The constant drag and lift coefficients were considered for the main body of robotic bird; however, variable drag and lift coefficients were used for the aerodynamic modeling of the wings. The sinusoidal trajectory was considered as the desired joint motion for twisting and flapping of the wings. A proportional-derivative (PD) controller was used for the force forward simulation of the robotic bird. A relation between the flapping frequency and lift force on the main body was established.