The configuration of the MUAV system can be given by
It is obvious that q is the generalized coordinate of the MUAV system.
The MUAV system is composed of two single rigid bodies, the quadrotor, and the manipulator.
With these matrix parameters, the MUAV system model can be finally obtained in the form of
Considering the limitations of the Lyapunov's stability theory for complicated nonlinear systems, in this section, Lyapunov exponent method is applied to analyze the dynamic stability of the MUAV system in the case of manipulator movements.
When designing manipulator controller with different expected manipulator joint angle, the joint torque T4 in step (iv) of the MUAV dynamic modeling changes, which makes the dynamic model changes as well.
Simulation results illustrate that the coupling between the manipulator and the quadrotor will affect the dynamic stability of the MUAV, and the coupling compensation can reduce the influence.
Caption: Figure 3: Lyapunov exponents spectrum of the MUAV ([a.sub.d] = 0).
Caption: Figure 4: Lyapunov exponents spectrum of the MUAV ([a.sub.d] = sina).
So dynamic stability researches of UAVs especially MUAVs are very necessary and important to ensure that the whole system is safe and reliable.
Well-developed mud cracks (polygons 6 inches or more in diameter) have also been observed in the overlying Toroweap Formation, and marine fossils typical of normal marine conditions occur in the Muav, Redwall, and Kaibab Limestones.
Channeled surfaces exist along the Muav-Temple Butte contact where the Temple Butte Formation fills depressions (old river channels) in the Muav Limestone (Fig.