The Elimination of Singularity to Track Aerial Objects Using a 3-DOF Pedestal

Tracking aerial objects using conventional 2-DOF pedestals requires excessive angular acceleration and velocity in the joints for some trajectories that pass through singular points, which is referred to as singularity. In this research, a 3-DOF redundant pedestal is proposed to solve such a problem. The redundant DOF increases the maneuverability and overall performance of the pedestal and makes it possible to pass through the conventional singularities in two-degree-of-freedom structures without the need to generate high speeds and accelerations in the movement axes of the pedestal. The challenge faced by the proposed three-degree-of-freedom pedestal is the lack of a unique solution to solve the inverse kinematics problem of this pedestal. In this article, to solve the problem of inverse kinematics of the pedestal with redundant three degrees of freedom, two optimization-based algorithms regarding limited joint velocities and limited joint accelerations are proposed and compared with the conventional quasi-inverse Jacobi method. In the limited joint velocities approach, a cost function of tracking error and joint velocities is formed and minimized. In the limited joint acceleration, on the other hand, joint velocities and accelerations are the elements that form the cost function. The criteria used to compare these methods are Integral of Squared Amplitude (ISA), Integral of Absolute Amplitude (IAA), Integral of Time-weighted Absolute Amplitude (ITAA), and Integral of Time-weighted Squared Amplitude (ITSA). The simulation results show the superiority of the limited joint acceleration method compared to the other two approaches.