Dynamics and Nonlinear Control of a Quadcopter with Passive Elastic Joints: Modeling, Simulation, and Experimental Validation

The conventional dynamic model of most quadrotors in use today assumes a perfectly rigid frame, and the corresponding control systems are designed accordingly. However, as rotor spans increase and design constraints push toward ever-lighter structures, that assumption may no longer hold. In this study, we examine the simplest flexible-arm extension: a quadrotor whose four rotor arms are each connected to the base by passive viscoelastic joints, allowing each arm to rotate in a plane perpendicular to the base plane. We derive a complete nonlinear dynamic model via the Euler-Lagrange equations and develop a unique control architecture that explicitly compensates for the arms’ elastic response. Numerical simulations demonstrate superior disturbance rejection compared to a rigid-frame benchmark. Finally, experimental validation on a modified five-degree-of-freedom test platform confirms the accuracy of the model and the effectiveness of the control strategy, highlighting the practical feasibility of passive arm flexibility in quadrotor systems.