Iterative Pose Estimation for a Planar Object Using Virtual Sphere

This article proposed an iterative pose estimation for the planar object to deal with the pose ambiguity in the
Perspective n Points
(PnP) problem. Specifically, by utilizing the unit virtual sphere, the PnP pose estimation problem can be performed as a minimization of the error function with three independent transitional parameters, referred to as the coupling position. Then, Levenberg–Marquardt (LM) optimization algorithm is applied to acquire the coupling position of the first local minimum. Furthermore, the coupling position is represented as the two Euler angles and the vector length, which are combined with the planar points to compute the second local minimum approximation as the initialization of the second LM algorithm. Consequently, once the global coupling position in the two local minimum is decided by the lower error, the orientation and position are directly decoupled by using the singular value decomposition. It is shown that the designed pose estimation is able to achieve prescribed performance for locating and distinguishing two local minimum, and meanwhile guarantee the superior computation behavior under the pose ambiguity for the planar object. Finally, numerical simulation and physical experiment are conducted to validate the effectiveness of the proposed method, compared with the state-of-the-art PnP methods.