# Computational issues in autonomous control of unmanned air vehicles

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In this work, we investigate just a few of the many computational issues involved in achieving autonomous control of unmanned air vehicles (UAVs). Of the many techniques used for UAV control, this research is vision based. We seek autonomous control and obstacle avoidance using a sequence of images from a camera. With the use of a camera, one part of this process is image processing, but it is not discussed here. We instead investigate several of the 'post processing of the image' issues. Image processing seeks to determine the flow of the image in the image plane. Using two consecutive images, image motion vectors are computed for a given collection of pixel position vectors.

We describe two methods used to recover the linear and angular velocity that the UAV (camera) underwent between the two camera frames. The only information needed is the pixel position vectors, the image motion vectors, and the speed of the UAV. The two methods discussed are the continuous eight-point algorithm and a direct minimization of a cost function. Without access to real data taken from a camera undergoing a known motion, we test the algorithms on random synthetic data and compare the results to the initial known linear and angular velocity.

The linear and angular velocity signals being computed may be noisy; as such, we also investigate a nonlinear observer to filter the possible noisy signal and test this observer on the equations of motion of a rigid body undergoing rotations and translations. As solving the observer equations involves numerical integration, we also investigate variable step-size selection methods for implicit integration schemes. The minimization of an efficiency function is the basis for the selection of the step-sizes for implicit Runge-Kutta and Runge-Kutta-Nyström methods. The methods are tested on three well-known examples from the literature.

Finally, we consider the topic of obstacle avoidance. A novel approach based on Lyapunov theory is used to steer a UAV away from obstacles detected by the camera. We test the algorithm on a UAV simulation evolving in a two-dimensional space.