Modeling, Planning and Control of UAVs

Vision-Based Loitering Over a Target for a Fixed-Wing UAV

Snapshot from simulation.

For a fixed-wing Unmanned Aerial Vehicle (UAV) equipped with a gimbaled camera, we consider the problem of tracking a visual target while simultaneously bringing the UAV to orbit on a circular trajectory centered above the target. Our objective is to achieve this kind of loitering behavior with a feedback controller that requires image+proprioceptive data only - and can therefore be used in GPS-denied environments. 

To solve the problem, we adopt an Image-Based Visual Servoing (IBVS) approach. In particular, it is first shown that regulation of the visual features plus the pan angle to a suitable set-point entails convergence to the desired kind of trajectory; then, such regulation is achieved for a simplified model of the UAV+camera system with direct yaw control; finally, the same behavior is obtained for the original UAV+camera system through backstepping. Improvements to the basic scheme are possible, including the enforcement of a desired radius for the circular trajectory, a simplified roll control technique, and the integration of an estimator to make sure that the depth of the visual target is not needed for implementation.


Basic loitering scheme

A preliminary validation of the visual loitering scheme has been performed with the aid of MATLAB simulations. The UAV is assumed to be in horizontal flight with a constant cruise speed of 10 m/s. The target on the ground is indicated by the crosshair. As expected, convergence to a circular trajectory is achieved with perfect tracking of the target. Two simulations are shown below, corresponding to different initial conditions.

Simulation 1, basic scheme, x-y trajectorySimulation 1, basic scheme, features errors.

Simulation 2, basic scheme, x-y trajectorySimulation 2, basic scheme, features errors.

Loitering with a specified radius

The desired radius can be imposed by adding a suitable feedforward term to the yaw control of the simplified UAV+camera system. To make room for this, we modify our control approach in a task-priority sense. The results are shown below, where the UAV+camera system is driven from the same initial condition to two different circular trajectories, with radius 30 (solid blue) and 15 (dashed red) m, respectively.

Enforcing a desired radius.

Using linear roll control

As an alternative to the backstepping approach, a simple linear roll controller can be used to guarantee that the original UAV+camera system tracks the simplified model. This more intuitive design is obviously much easier to implement, and offers similar performance (solid blue: using the linear roll controller; dashed red: using the backstepping roll controller).

Linear roll control vs full backstepping, featuresLinear roll control vs full backstepping, roll rate.

Using a depth estimator

The above visual loitering method (in all its versions) needs the feature depth for computing the interaction matrix. In principle, the depth could be computed from the configuration of the UAV+camera system, including the UAV cartesian coordinates, and the cartesian coordinates of the target. This is in fact the method used in the above simulations. However, our control approach has been to avoid altogether the use of cartesian information, which may be indeed unavailable. A possible solution is to estimate the depth from the evolution of the visual features during the motion, using the nonlinear observer described here. The results shown below (solid blue: using the estimated depth; dashed red: using the actual depth) confirm that the integration of such a component in our scheme is effective.

Basic scheme with depth observer, comparison in features graphs.Basic scheme with depth observer, comparison in features graphs.

Moving target

The proposed visual loitering scheme performs satisfactorily also in the case of a slowly moving target. In this simulation, the target is moving at around 0.7 m/s (-0.5 m/s along x and -0.5 m/s along y) while the UAV airspeed is 10 m/s.

Basic scheme with moving target.

Video clips

Here is a video clip showing the simulations for the basic loitering scheme (fixed target) and for the moving target case.

Simulation on an Aerosonde UAV

We present a realistic simulation which shows the performance of our visual loitering method (including all the three modifications above) on a more complete UAV model. In particular, we have used the simulator of the Aerosonde UAV included in the Aerosim Blockset (formerly available here). To this accurate simulator, which includes aerodynamic effects, we have added low level control loops aimed at improving the adherence of the model to the simplified model used for control design. In particular, airspeed and altitude hold control modes have been implemented via the control of elevator and throttle. The roll rate reference produced by the loitering controller is tracked using a linear control loop on the ailerons, while the rudder is used to achieve coordinated turn with sideslip angle close to zero.

We have performed several simulations for the case of a fixed target. The results shown below confirm that here proposed visual loitering scheme is effective even for realistic models of UAVs.

Simulation on aerosonde,  x-y trajectorySimulation on aerosonde, features errors.

To test the robustness of the proposed visual loitering method, we run the same Aerosonde simulation in the presence of perturbations. In particular, we added a zero-mean Gaussian noise with variance 0.01 on each visual feature and a constant wind of 8 m/s along the x axis (about 30% of the aircraft speed). The resulting trajectory is slightly deformed (and not centered on the target anymore), but the visual loitering scheme is still effective. The results are shown below.

Simulation on aerosonde, with noise and wind, x-y trajectorySimulation on aerosonde, with noise and wind, features errors.


[1] P. Peliti, L. Rosa, G. Oriolo and M. Vendittelli, Vision-based loitering over a target for a fixed-wing UAV, 10th IFAC Symposium on Robot Control (SYROCO 2012), Dubrovnik, Croatia, pp. 51-57, 2012. (pdf)

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