Efficient Three Dimensional Formation Control for Unmanned Aerial Vehicles in GPS-Denied Environments

This paper considers the control problem for leader-follower unmanned aerial vehicles (UAVs) to maintain a three-dimensional (3D) formation in GPS-denied environments. The controller derivation is based on a 3D dynamics model that uses the distance, azimuth and elevation angles, defined in a local spherical coordinate frame, to describe the relative motion between two UAVs. To ease the derivation process and to generate an efficient controller that does not demand considerable onboard computational resources, this paper employs a design process that integrates the feedback linearization approach, a linear-quadratic regulator (LQR), and the differential flatness method. The proposed controller is tested in a simulated environment where the follower UAV is commanded to follow a predefined 3D formation with respect to the leader UAV that tracks a circular orbit with intermittently varying desired airspeed and orbit radius. The simulation result shows that the controller is able to drive the follower UAV to quickly converge to and maintain the desired formation only using the relative distance and orientation information in a GPS-denied environment. The proposed controller also shows its comparable performance in comparison to an existing Backstepping controller on the basis of converging speed, steady-state error, overshoot, and computational efficiency.