Feedback delay compensation of a visual servoing system using a piecewise continuous and current estimator-based observer

Turkish Journal of Electrical Engineering & Computer Sciences http://journals.tubitak.gov.tr/elektrik/ Turk J Elec Eng & Comp Sci (2017) 25: 3738 – 3751 c TÜBİTAK ⃝ doi:10.3906/elk-1606-160 Research Article Feedback delay compensation of a visual servoing system using a piecewise continuous and current estimator-based observer Abdeldafia MOHAMMED1 , Haoping WANG2,∗, Yang TIAN1 School of Automation, Nanjing University of Science and Technology, Nanjing, P.R. China 2 Sino-French International Joint Laboratory of Automatic and Signal Processing (LaFAS), School of Automation, Nanjing University of Science and Technology, Nanjing, P.R. China 1 Received: 11.06.2016 • Accepted/Published Online: 30.05.2017 • Final Version: 05.10.2017 Abstract: In this paper, a piecewise continuous current estimator-based observer is proposed to estimate a plant’s states using sampled and delayed measurements. The advantage of the proposed technique is simple in terms of analysis and design. Moreover, the proposed observer can compensate the time delay when the delay equals the sampling period. Comprehensive stability analysis of the designed observer is performed. In addition, to assess the efficiency and effectiveness of the proposed observer, a numerical comparative study with a Kalman filter-based observer is established and the simulation results are demonstrated. Key words: Piecewise continuous systems, sampled and delayed measurements, piecewise continuous current estimator 1. Introduction A visual servoing system (VSS) is a kind of system that uses vision data as a feedback signal to control an object’s motion [1]. It comprises a controller, robots, and a vision system. During the last two decades, VSSs have been broadly used to increase the accuracy and the flexibility of robotic systems [2,3]. VSSs can be utilized in many applications such as building automation (surveillance), games (soccer robots), and industrial zones (cooperative). Nonetheless, VSSs are facing a great challenge due to the use of visual information in the feedback channel. The time delay in the feedback channel occurs by image acquisition, image processing, and information transmission [4,5]. The time delay is well known to be a resource of instability and degrades the system’s performance. Generally, the sensors that are based on vision have a larger sampling period than the other types of sensors due to the restricted constraints the vision sensors have in communication and snapshot speed [6–8]. In the literature, various control design methods were presented to handle systems with time delay. In [9– 11] researchers studied the delay problem by utilizing standard analysis methods from robust control, and good control performances were observed. The analysis of the problem was investigated under the assumption that the time delay in the feedback channel is less than one sampling period. However, the control performance will be affected by increasing the sampling period, and it might be ineffective, particularly in high-speed dynamical systems. On the other hand, designs of nondelay state observers for systems with the above-mentioned problems have been proposed in several approaches such as a continuous approach, which designs a continuous time ∗ Correspondence: 3738 MOHAMMED et al./Turk J Elec Eng & Comp Sci observer based on the continuous time plant model. The weakness of this approach is the neglect of the sampling of the output and the closed-loop system stability is assured only under a small sampling period [12–14]. Based on the hybrid systems approach a piecewise continuous observer was proposed in [15,16]. The benefit of this approach is that it takes into account sampling and delay and is simpler compared with other approaches. Based on the continuous-time Lyapunov–Krasovskii approach, the Lyapunov–Krasovskii observer was proposed in [17]. The advantage of this approach is the robust stability in the case of uncertainties in the system parameters and sampling period. The disadvantage of this approach is an imperative solution of complex linear matrix inequalities. This work proposes a different approach to the observer design based on a piecewise continuous system and current estimator, and the observer gain is selected based on a linear matrix inequality (LMI) to guarantee the stability of the dynamics error. In this approach, the solution of complex linear matrix inequalities is not compulsory. This paper considers the delay in the feedback channel from sampled and delayed measurement. The goal is to design the observer based on the piecewise continuous system and current estimator to estimate the nondelay continuous state. The main contributions of this work are as follows: 1) it compensates the time delay in a feedback channel with a simpler estimator structural design than the aforesaid approaches; 2) it estimates the nondelayed continuous state from the sampled and delayed measurement; 3) with respect to the existing results, accuracy and fast computation are achieved when the time delay is equal to the sampling period. In order to demonstrate the performance superiority of the proposed observer, a comparison with the Kalman filter-based approach proposed in [13,14] has been performed. The rest of this paper is organized as follows: in Section 2, the problem formulation and introduction to the plant are given. Section 3 presents the piecewise continuous system and observer design. In Section 4, the observer dynamics and stability are presented. In Section 5, an overview of the Kalman filter-based observer is provided. The numerical simulation example is demonstrated in Section 6. Finally, concluding remarks and recommendations for future work are given in Section 7. 2. Problem formulation The VSS structure considered in this paper is shown in Figure 1. In our study, the only available plant information is obtained through the digital sensor (camera), which introduces time delay as a consequence of image acquisition, image processing, and visual information transmission. The digital sensor determines the object position to be manipulated and delivers it in a sampled and delayed form (see Figure 2). Figure 1. The VSS structure considered. 3739 MOHAMMED et al./Turk J Elec Eng & Comp Sci Figure 2. The real output and its measurement. The system dynamics is linear time-invariant (LTI) and it can be described as follows: { ẋ(t) = Ax(t) + Bu(t) y(t) = Cx(t) , (1) where u(t) ∈ ℜr is the control input and x(t) ∈ ℜn is the state, y(t) ∈ ℜm is the output of the plant, and A ∈ ℜn×n , B ∈ ℜn×r , C ∈ ℜm×n are constant matrices. It is assumed that the system in Eq. (1) is observable. Digital sensor information can be specified by: Y (t) = y ∗ (t − d), (2) where Y (t) is the digital sensor output and represents the visual information of the object position, which is used to estimate the position and velocity of the moving object, and ∗ represents sampling with the known and constant perio (...truncated)