A novel 1D trifocal tensor-based control for differential-drive robots

Abstract

This paper presents an image-based approach to perform visual control for differential-drive robots. We use for the first time the elements of the 1D trifocal tensor directly in the control law. The visual control utilizes the usual teach-by showing strategy without requiring any a prior knowledge of the scene and does not need any auxiliary image. The main contribution of the paper is that the proposed two-steps control law ensures total correction of both position and orientation without switching to any other visual constraint rather than the 1D trifocal tensor. The paper exploits the sliding mode control technique in a square system, ensuring stability and robustness for the closed loop. The good performance of the control system is proven via simulations.I. INTRODUCTION An interesting research field is concerned about visual servoing for mobile robots, which can allow them to improve their navigation capabilities in a single robot task or in cooperative tasks. A way to face the problem of extracting information from images is by using a geometric constraint relating features from such images. Nowadays, two geometric constraints have been well exploited to control mobile robots, epipolar geometry and the homography model. [6]. However, these geometric constraints have both serious drawbacks. Epipolar geometry is ill-conditioned with short baseline and with planar scenes. The homography model is not well defined if there is no dominant planes in the scene or with large baselines.In order to overcome the drawbacks of the typical geometric constraints, we propose a novel approach based on the 1D trifocal tensor. This tensor completely describes the relative geometry of three views and it is independent of the observed scene [7]. The effectiveness of applying the trifocal tensor to recover location information has been proved in [8] and [9]. The first work uses conventional cameras and artificial landmarks on a plane while the second one uses both conventional and omnidirectional cameras. Both of these works propose the trifocal tensor to be used for initialization of bearing-only SLAM algorithms. A recent work [10] presents a visual control for mobile robots based on the elements of a 2D trifocal tensor constrained to a planar motion. This work shows good performance reaching the target location, however the stability properties of the controller are not very clear.We propose in this paper an image-based approach to perform visual servoing for differential-drive robots. The visual control is performed using the value of the elements of the 1D trifocal tensor directly in the control law. The approach utilizes the usual teach-by showing strategy without requiring any a prior knowledge of the scene and does not need any auxiliary image. We propose a two-steps control law, the first step performs position correction and the second one corrects orientation. In the first step a tracking problem is solved by using sliding mode control. This controller is designed using the well known methodology for a square ...

Visual Servoing of Nonholonomic Mobile Robots: A Review and a Novel Perspective

“…It is not limited by the scenes because it has rich information from three views, which can avoid the drawbacks of epipolar geometry and homography. Becerra and Sagüés [64] used the 1D trifocal tensor to regulate the mobile robot. And the path following problem is solved by using 1D trifocal tensor [65].…”

Adaptive dynamic surface control for vision-based stabilization of an uncertain electrically driven nonholonomic mobile robot

“…[6], a switching control scheme based on the epipolar geometry and homography was proposed, which took advantage of both models avoiding the drawbacks of each one and allowing a smooth motion of robot. Another feasible way to overcome the drawbacks of these two geometric constraints is to use trifocal tensor, 7,8 which Vision-based pose stabilization of an uncertain mobile robot describes the relative geometry of three views completely and is independent of the observed scene. Recently, Zhang et al 9 proposed a hybrid vision-based stabilization strategy based on a motionestimation technique, which can be applied in both planar and non-planar scenes and required no matrix estimation or decomposition.…”