Abstract: Due to the design of invariant visual features，spherical image-based visual servoing (IBVS) can obtain good motion decoupling characteristics． But calculation of feature Jacobian matrix depends on unknown 3D distance of each observed target point． For the problem of online estimating the unknown 3D parameters in spherical IBVS， a nonlinear projective distance observation algorithm is proposed with persistency of excitation (PE) lemma． In this paper，kinematics of spherical features is firstly analysed with the unified projection model; then，an update law of states of vision system is designed with PE lemma，online observation of 3D distances is realized by exploiting the known camera motion and the measured image features． Furthermore， stability analysis of the observer is proposed． Simulative results show that the proposed algorithm can effectively realize the online estimation of 3D distances，and has a better estimation accuracy and dynamic characteristics compared with the indirect estimation method based on depth observation． Meanwhile， the dynamic convergence characteristics of spherical IBVS control can be effectively improved． 

Key words: visual servoing, feature Jacobian, persistency of excitation lemma, nonlinear observation