Rendezvous Guidance on Circular Path for Fixed-Wing UAV

Abstract

This paper presents a guidance method to enable a fixed-wing UAV to rendezvous with a reference point that moves on a circular path. The guidance law creates a lateral acceleration command based on the phase difference from the moving point and the side-bearing angle with respect to the center of the circle. The stability of the guidance law and the effect of velocity control are provided with linear analyses. The feasibility and performance of the proposed method are demonstrated through simulations and actual flight tests.

Appendix

This section describes how the artificial reference point was generated for the flight test described in Sect. 5. The reference point moves along a circular path. It should be created such that a following UAV can fly along with it. Also, considering the aerial docking scenario, the reference point is defined somewhere behind the leading UAV, which is also affected by the wind. Therefore, in this work, the artificial reference point is generated based on the UAV flight speed and the wind condition as well.

Figure 

Fig. 17

Reference point generation

17 shows a diagram to explain the details on how to generate the moving reference point on a circular path considering the characteristics of UAV behavior in the presence of wind.

Considering the reference point as a virtual aircraft, it is subjected to the vector relation

$${V}_{T} = {V}_{T_{{{\text{air}}}}} + {V}_{{{\text{wind}}}} ,$$

(30)

where ${V}_{T}$ is the inertial velocity of the reference point, ${V}_{{{\text{wind}}}}$ is the wind velocity, and ${V}_{T_{{{\text{air}}}}}$ the relative velocity of the reference point with respect to the wind. The wind velocity is estimated onboard the flight control computer [18].

The magnitude of ${V}_{T_{{{\text{air}}}}}$ should be chosen considering the UAV flight speed. With the given radius and the center of the circle, the instantaneous position of the reference point is determined by

$$p_{{T_{N} }} = p_{N_{c}} + R\cos \lambda_{T} ,\,\,\,\,\,\,\,\,p_{{T_{E} }} = p_{E_{c}} + R\sin \lambda_{T} ,$$

(31)

where $\lambda_{T}$ is the phase angle from the reference north axis. The angular rate is governed by

$$\frac{d}{dt}\lambda_{T} = \pm \frac{{V_{T} }}{R},$$

(32)

where (+) sign is for the clockwise rotation, and (–) sign is for the counter-clockwise rotation. From this phase angle, $\lambda_{T}$ is numerically updated by

$$\lambda_{T_{{{\text{new}}}}} = \lambda_{T} \pm \left( {\frac{{V_{T} }}{R}} \right)\Delta t,$$

(33)

where $\Delta t$ is the incremental time interval.

The remaining task is to determine $V_{T}$. From the vector relation, we have

$$V_{T_{{{\text{air}}}}} \cos \psi_{T} + V_{{{\text{wind}}}_{N}} = V_{T} \cos \psi_{T_{c}} ,\,\,\,\,\,\,\,V_{T_{{{\text{air}}}}} \sin \psi_{T} + V_{{{\text{wind}}}_{E}} = V_{T} \sin \psi_{T_{c}} .$$

(34)

Eliminating $\psi_{T}$ leads to the following expression

$$V_{T} = (V_{\text{wind}_{N}} \cos \psi_{T_{c}} + V_{{{\text{wind}}}_{E}} \sin \psi_{T_{c}} ) + \sqrt {(V_{{{\text{wind}}_{N}}} \cos \psi_{T_{c}} + V_{{{\text{wind}}}_{E}} \sin \psi_{T_{c}} )^{2} - V_{{{\text{wind}}}}^{2} + V_{{T}^{2}_{{{\text{air}}}} }} .$$

(35)

It is noted that $V_{T} = V_{{T}_{\text{air}}}$ is obtained for no wind conditions, as expected. Finally, from the diagram $\psi_{{T}_{c}}$ is determined by

$$\psi_{{T}_{c}} = \lambda_{T} - 2\pi \pm \frac{\pi }{2}.$$

(36)