International Journal of Innovative Computing, Information and Control ICIC International c ⃝2019 ISSN 1349-4198 Volume 15, Number 5, October 2019 pp. 1881–1900 STRUCTURE FROM MOTION RECOVERY FOR MONOCULAR VISION SYSTEMS: A ROBUST NONLINEAR OBSERVER-BASED APPROACH Zoubaida Mejri 1,3 , Lilia Sidhom 1,2 and Afef Abdelkrim 1,3 1 Research Laboratory L.A.R.A in Automatic Control National Engineering School of Tunis (ENIT) University of Tunis El Manar BP 37, Le Belv´ ed` ere, Tunis 1002, Tunisia zoubaida.mejri@enit.utm.tn; lilia.Sidhom@enib.rnu.tn; afef.a.abdelkrim@ieee.org 2 National Engineering School of Bizerte (ENIB) University of Carthage BP 66, Campus Universitaire Menzel Abderrahman 7035, Bizerte, Tunisia 3 National Engineering School of Carthage (ENICarthage) University of Carthage 45 Rue des Entrepreneurs, Charguia II, Tunis 2035, Tunisia Received February 2019; revised June 2019 Abstract. This paper deals with the estimation structure and motion of a moving object with time varying velocities viewed by a moving camera problem, in which the object motion is assumed to be on a ground plane. The problem focuses on the dynamics of a relative motion model based on a moving camera and a moving object where disturbances and uncertainties are diagnosed. To treat this problem, the Nonlinear Unknown Input Sliding Mode Observer (NUISMO) is proposed with feedback injection term in addition to giving a proof of its convergence. Lacking information about the nature of model nonlinearities except that is upper bound and its boundary can be generated in real time. The object velocities are considered as an unknown input to the perspective dynamical system. This approach allows decoupling the state object estimation from its velocities that behaves also as a disturbance input. Several simulation results are performed to show the effectiveness of the proposed approach compared to a Nonlinear Unknown Input Observer (NUIO) in the presence of measurement noise. Keywords: Structure from motion estimation, Measurement noise, Unknown input observer, Sliding mode, Uncertain nonlinearity, Disturbances 1. Introduction. In robotics and computer vision fields, the well-known problem of Structure from motion and Motion from Motion which is referred to as trajectory tri- angulation [1,2] and is termed to SaMfM [3], is yet addressed today [4-8]. Given one dynamic object that moves throughout a video sequence and given its 2-D tracked fea- tures, the aim of the SaMfM is to recover the structure and motion that is represented respectively by the three-dimensional structure of the scene (the Euclidean coordinates) and its motion relative to the camera. SaMfM is often required for numerous applica- tions, for instance, augmented reality, autonomous navigation, video-based surveillance, vision-based robotic applications and object recognition, among others. The interest of solving the SaMfM problem can be explained for example in a practical case by a robotic arm equipped with camera and taking hold of objects moving on a conveyor. Thus, this robot can estimate its own coordinate and motion while sensing its environment which is DOI: 10.24507/ijicic.15.05.1881 1881