An Analytical Solution to the Inverse Kinematic Problem, Dynamic Modeling, and Control of a 3 DOF Pedestal for Track Flying Targets

In this paper, a three DOF (Degree Of Freedom) aerial target tracking pedestal that covers the entirety of the 3D threat space is introduced. The conventional two DOF tracking pedestals cannot track some trajectories due to having singular points in their workspace. The extra DOF in a three DOF tracking pedestal overcomes this problem. Moreover, the redundant DOF reduces the needed joint velocity and acceleration in the tracking process and makes the whole structure more maneuverable. The challenging matter in utilizing such a redundant pedestal is that the Inverse Kinematic Problem (IKP) has infinite sets of solutions. An analytical solution is proposed to handle this problem which results in a single set of solutions. Furthermore, the dynamic model of the pedestal is derived using the Euler-Lagrange method, and the verification is performed using mechanical design software. Finally, to demonstrate the effectiveness of the proposed pedestal in tracking aerial targets with unknown trajectories, a PID controller and an LQR controller are utilized in simulations. The results yield that tracking any complex trajectory is attainable using conventional controllers.