Visual Servoing with Trifocal Tensor

Abstract

In this paper, a trifocal tensor-based approach is developed for 6 degrees-of-freedom visual servoing. The trifocal tensor model among the current, desired, and initial views is introduced to describe the geometric relationship. Then, the tensor elements are refined to construct the visual feedback without resorting to explicit estimation of the camera pose. Based on the extracted tensor features, an adaptive controller is designed to drive the camera to a desired pose and compensate for the unknown distance scale factor. Moreover, Lyapunovbased techniques are exploited to analyze the system stability and convergence domain. Simulation results are provided to demonstrate the effectiveness of the developed approach.

Trifocal tensor-based 6-DOF visual servoing

“…Consider the vision model presented in Figure 1, if the reference frame F * coincides with the frame F d or F c , then the calculation of trifocal tensor will be degenerated by using (3) (see Appendix A). Existing works (Shademan and Jägersand, 2010; Zhang et al, 2018) usually use the current, desired, and initial views to define the trifocal tensor. However, under this configuration, the aforementioned degeneration case occurs easily, typically at the beginning of the servo where the current view is coincident with the initial one, and hence it is numerically troublesome to estimate the trifocal tensor (Becerra et al, 2014).…”

“…Fourth, instead of designing the control law similar to the typical proportional controller as in Shademan and Jägersand (2010), an adaptive regulation control law is designed in this paper, and the theoretical analysis of the system stability and convergence domain is presented. A preliminary version of this paper was presented in Zhang et al (2018). Compared with Zhang et al (2018), a generation strategy for the reference view is introduced to ensure that the trifocal tensor can be estimated stably, and more rigorous and detailed Lyapunov-based analysis is presented to show the almost global asymptotic convergence of the system errors instead of local stability result given in Zhang et al (2018).…”

“…A preliminary version of this paper was presented in Zhang et al (2018). Compared with Zhang et al (2018), a generation strategy for the reference view is introduced to ensure that the trifocal tensor can be estimated stably, and more rigorous and detailed Lyapunov-based analysis is presented to show the almost global asymptotic convergence of the system errors instead of local stability result given in Zhang et al (2018). In addition, to evaluate the proposed approach thoroughly, different simulations and experiments are conducted.…”