Nonlinear Multibody Dynamics of a Powered Parafoil Vehicle Using Kane’s Equations: Directional Asymmetry and Dutch-Roll

Abstract

Directional asymmetry and Dutch-roll are critical phenomena observed during powered parafoil vehicle (PPV) flight tests, complicating stable flight and leading to obvious lateral–directional biases in autopilot tracking. However, existing PPV models typically neglect propeller counter-torque (PCT), resulting in limited research on directional asymmetry. Moreover, conventional Newton–Euler formulations require explicit treatment of internal constraint forces, complicating analytical linearization and local stability analysis. To address these issues, first, this paper develops a nonlinear 9-degree-of-freedom (9-DOF) PPV model using Kane’s equations with quasi-velocities. This multibody dynamic model provides a compact and structurally consistent basis for linearization and stability analysis. Subsequently, the mechanism analysis shows that PCT shifts the coupled roll–yaw equilibrium and is the primary physical source of the observed directional asymmetry. In addition, the Dutch-roll mode is identified as the dominant oscillatory mode governing the lateral–directional stability of the PPV. The modal analysis further indicates that increasing thrust and directional control inputs reduce the Dutch-roll damping ratio. On this basis, a damping-ratio-based flight envelope is constructed. Furthermore, numerical simulations and flight-test comparisons demonstrate that the proposed model captures the principal PPV dynamic responses. The simulation results also support the mechanism analysis of directional asymmetry and the Dutch-roll.