Constrained Dynamics of an Aerial Manipulator Interacting With Flexible Cantilever Beams

Abstract

Aerial manipulation poses complex challenges for aircraft design, modeling, and control, especially when dealing with nonlinear continuous systems. This article explores the coupled dynamics of a fully actuated aerial vehicle when interacting with a cantilever beam undergoing large deflections, focusing on achieving a more accurate model and identifying the challenges involved in this task. The analysis can be applied to prolonged interactions, such as tree branch deflection or long reach manipulation. Based on the Udwadia–Kalaba formulation, the presented model follows a relatively simple and systematic approach for imposing constraints without Lagrange multipliers. The resulting constrained equation of motion is obtained in closed form and captures the essential characteristics of the interaction: kinematic constraints and geometric nonlinearities. Furthermore, simulation and experiments demonstrate the feasibility and performance limitations of using a linear motion controller and how end-effector configuration can affect stability.