Elsevier

Control Engineering Practice

Volume 6, Issue 2, 1 February 1998, Pages 219-225
Control Engineering Practice

Design of an H filter-based robust visual servoing system

https://doi.org/10.1016/S0967-0661(98)00010-0Get rights and content

Abstract

This paper is concerned with the performance evaluation of the H filter for the 2-D visual servoing of a moving target. The efficacy of the H filter is validated experimentally in comparison with the Kalman filter, using an eye-in-hand coordinated robot manipulator system. The H filter can provide a powerful tool for solving vision-based control problems in robotics, just as the Kalman filter can.

Introduction

By integrating control and vision, a robotic system can move appropriately in a dynamically changing working space. Tracking and grasping of a moving object by a robot manipulator is a typical example of this category of problem in real situations. The combination of robot control with computer vision could become extremely important, when dealing with a robotic system working in uncertain and dynamic environments. Recent research efforts in this direction have been well covered collected in (Hutchinson et al., 1996) (see also the references therein).

In the visual servoing in particular, a powerful estimation algorithm taken from systems and control theory plays an important role, since dynamic image scenes have to be processed. The Kalman filter is a popular algo rithm, and it has been frequently utilized, not only in the visual servoing (Hutchinson et al., 1996) but also in the implementation of computer vision (Matthies et al., 1989). At the present time, the Kalman filter is accepted as a basic, standard tool for active/dynamic vision (Blake and Yuille, 1992).

The combination of Linear Quadratic (LQ) control with the Kalman filter gives the well-known Linear Quadratic Gaussian (LQG) theory, which was mainly developed during the 60s and 70s. Since the 80s, however, a great move has occurred, from the LQG theory to the H theory (Doyle et al., 1989). The H theory provides the capability to handle model uncertainties in a more practical way. While the LQG theory considers the effects of uncertainty in a stochastic framework, the H theory treats them in a functional analytic framework. Further, it gives a certain min-max optimal solution to deal with the disturbances caused by uncertainties (Basar and Bernhard, 1991). It has been shown that the H theory can be regarded as a natural generalization of the LQG theory (Doyle et al., 1989).

Recently, the H theory has been successfully applied to visual feedback control (Ogura et al., 1994), where the emphasis was on the control aspect. Although the corresponding estimation theory in an H setting has been developed (Nagpal and Khargonekar, 1991; Shaked and Theodor, 1992), not much work has been done on the use of the H filter in robotics and/or vision research (Fujita et al., 1993, Fujita et al., 1995 ). The superiority of the H filter over the existing estimation algorithms is theoretically convincing in some respects, since the model uncertainties can be handled more adequately (Nagpal and Khargonekar, 1991; Shaked and Theodor, 1992). Hence, an experimental validation of its efficacy presents quite a challenge in the present situation.

The purpose of this paper is to validate the performance of the H filter experimentally, using an eye-in-hand coordinated robot manipulator system. An empirical comparison is made, using the H filter and the Kalman filter, for an estimation problem arising in visual servoing. The experimental results reveal the po tential efficacy of the H filter. As in an important earlier paper (Papanikolopoulos et al., 1993), two-dimensional (2-D) visual servoing of a moving target is considered in the experiments. The development of the H filter will lead to another powerful tool for the solution of vision-based control problems in robotics, in the same way as the Kalman filter is already widely accepted.

The rest of the paper is organized as follows. In Section 2, the configuration for the experiments with visual servoing is introduced. The modeling of the visual servoing system is presented in Section 3. The control strategies and the estimation problem involved in applying the H filter are described in Section 4. Section 5presents the Algorithm of the H filter. In Section 6, experimental results are presented. The efficacy of the H filter is discussed, in comparison with the Kalman filter. Finally, in Section 7, the paper is summarized.

Section snippets

Eye-in-hand systems

A variety of configurations for experiments involving visual servoing have been proposed, depending on the design goals or the experimental setups of the robot and the camera concerned. This paper considers a standard eye-in-hand configuration, where the manipulator carries the camera on its end-effector. Then, the goal is to control the robot motion, such that the camera tracks a moving target.

For the performance evaluation of the H filter in visual servoing, the eye-in-hand coordinated robot

Preliminaries

The main objective of this paper is to introduce a powerful new estimation algorithm in this field. Under the following assumption, attention is restricted to 2-D visual servoing, in order to discuss the robustness against disturbances for the linear system of the planar model (e.g. (Kelly, 1996)) of the visual servoing.

Assumption (Fig. 2(A)): The target moves in a plane, called A, and the camera moves in another plane, called B. The target moving plane, A, runs parallel to the camera moving

Estimation-based visual servoing

Consider an ideal system, where these is no acceleration of the relative motion, and in which there are no disturbances; i.e.,x̃k+1=Ax̃k+Buk+Eq̃kwith vk=0. Assume the model of the motion of target q̃k as follows:q̃k+1=q̃k(q̃k=0=q0).The objectives of the visual servoing are (i) stability of the closed-loop system (internal stability), (ii) the regulated output vector ξk(=x̃k)→0(k→∞). Notice that, if ξk=0 can be achieved, then the positions and the orientation (pose) of the center of mass of the

H Filter: algorithm

Given the system (24), (25), and (26), consider first the following cost function:J:=k=0zek+1ẑek+12k=0σvk2k=0σwk+12.If the inequality J<0 is satisfied for all (σvk,σwk)≠0, thenk=0zek+1ẑek+12k=0σvk2+k=0σwk+12<1for all nonzero (σvk,σwk). The implication of the above inequality is quite important. Recall that σvkandσwk are not specific signals, but belong to the classes of unknown-but-bounded signals. Hence the inequality shows that the level of the estimation error

Experimental results and discussions

The numerical design of the H filter has been under taken, using the computer-aided design environments stated in Section 2. The selection of each design parameter is carefully considered, essentially on the basis of its physical meaning. Almost all, since each design parameter is the weighting factor for its magnitude of the signal, the design process is intuitively tractable. After some iterations using the computing environments, the final design parameters selected, as well as the system

Conclusions

The work described in this paper has validated the performance of the H filter experimentally, using an eye-in-hand coordinated robot manipulator system. An empirical comparison has been made between the H filter and the Kalman filter, for the estimation problems arising in visual servoing. The experimental results have shown the efficacy of the H filter. Therefore, the H filter can provide a powerful tool for the solution of vision-based control problems in robotics, just like the Kalman

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