Direct Visual Servoing Based on Discrete Orthogonal Moments

TL;DR

This work addresses fundamental robustness and convergence limitations of direct visual servoing (DVS) by introducing a DOM-based framework (DOM-VS) that uses Discrete Orthogonal Moments as global visual features. It develops three schemes—TM-VS, KM-VS, and HM-VS—together with adaptive parameter selection for KM and HM moments and an adaptive DOM order $l$, underpinned by an analytically derived interaction matrix. The approach is validated through extensive simulations and real-robot experiments, showing that Hahn moment-based HM-VS delivers superior convergence speed and robustness to noise and occlusions, outperforming DVS, DCT-VS, and PGM-VS baselines. The results indicate meaningful practical impact for robust, large-domain visual servoing in 2-D and 3-D environments, with HM-VS offering the best overall performance among the proposed methods.

Abstract

This paper proposes a new approach to achieve direct visual servoing (DVS) based on discrete orthogonal moments (DOMs). DVS is performed in such a way that the extraction of geometric primitives, matching, and tracking steps in the conventional feature-based visual servoing pipeline can be bypassed. Although DVS enables highly precise positioning, it suffers from a limited convergence domain and poor robustness due to the extreme nonlinearity of the cost function to be minimized and the presence of redundant data between visual features. To tackle these issues, we propose a generic and augmented framework that considers DOMs as visual features. By using the Tchebichef, Krawtchouk, and Hahn moments as examples, we not only present the strategies for adaptively tuning the parameters and order of the visual features but also exhibit an analytical formulation of the associated interaction matrix. Simulations demonstrate the robustness and accuracy of our approach, as well as its advantages over the state-of-the-art. Real-world experiments have also been performed to validate the effectiveness of our approach.

Figures (33)

• Figure 1: Plots of normalized polynomials ($N=512$, $n={0,1,...,5}$). (a) Tchebichef polynomials. (b) Krawtchouk polynomials ($p=0.25$). (c) Krawtchouk polynomials ($p=0.75$). (d) Hahn polynomials ($a=0, b=0$). (e) Hahn polynomials ($a=7680, b=2560$). (f) Hahn polynomials ($a=2560, b=7680$).
• Figure 2: Example of calculating the Krawtchouk moment parameters ($N=M=128$). (a) Example image (assuming the initial image is the same as the desired image). (b) Surface plots of the 0th, 2nd, and 4th order Krawtchouk moment operators (${}^\alpha p = 0.5074$ and ${}^\beta p = 0.4812$).
• Figure 3: Example of calculating the Hahn moment parameters ($N=M=128$). (a) Surface plots of the 0th, 2nd, and 4th order Hahn moment operators for the origin image (${}^{\alpha}a=5, {}^{\alpha}b=6, {}^{\beta}a=7$ and ${}^{\beta}b=6$). (b) Surface plots of the 0th, 2nd, and 4th order Hahn moment operators for the transformed image(${}^{\alpha}a=175, {}^{\alpha}b=127, {}^{\beta}a=198$ and ${}^{\beta}b=136$).
• Figure 4: Surface plots of the 0th, 2nd, and 4th order Tchebichef moment operators ($N=M=128$). (a) Calculation result of the original image. (b) Calculation result of the transformed image.
• Figure 5: VS loss landscape on an x/y translation motion around the desired pose. (a) Desired image. (b)-(e) Images of the boundary position in the x,y direction. (f) TM-VS. (g) KM-VS. (h) HM-VS.