Bilateral Control System of Flexible Master-Slave Arms with Random Delay Using Kalman Filter

Teleoperation technologies for robotic systems are important for enabling human skills to be provided to remote locations. In recent years, these technologies have attracted much attention. Furthermore, these technologies are expected to be useful in general environments such as houses and offices without requiring special equipment. Therefore, teleoperation technologies should be realized by using existing communication networks, such as local area networks (LAN), wide area networks (WAN), and wireless LANs. In this study, a bilateral control system is investigated as one type of teleoperation technology. This system consists of a rigid master arm, a flexible slave arm, and a communication network, which causes random delay. The flexible slave arm tracks the rigid master arm. For this purpose, signals such as state signals and observation signals are transmitted through the communication network. Therefore, the bilateral control system with the communication network is considered a type of feedback system with a communication network. Furthermore, because the communication network causes random delay, the signals transmitted through this network become noisy, and so accurate observation signals are not reliable obtained. The random delay that results might cause system instabilities. Many researchers have studied teleoperation systems with time delay, bilateral control systems, and flexible manipulators. Namerikawa discussed a simple proportional derivative (PD)-type control method and a control strategy for teleoperation systems with timevarying delay [1],[2]. Mori et al. and Hoshino et al. proved the passivity of a flexible master-slave manipulator that is controlled using a symmetric bilateral controller [3],[4]. Matsuno et al. designed a proportional derivative and strain (PDS) feedback controller to control the two-link flexible beams and proved the stability of the closed-loop system [5]. However, these studies did not consider random delay. For random delay more broadly, state estimation problems for a networked system with random delay have been studied by many researchers. Liu et al. investigated the model predictive control problem for closed-loop networked control systems. In this study, a random delay is defined as a Markov chain, and then the closed-loop networked control system is expressed as a Markovian jump system [6]. Wu et al. proved the mean-square exponential stability for a networked system with long random delay [7], and Guo et al. studied exponential stability (in the mean-square sense) for a type of discrete-time system with random delay [8]. These researchers proposed filters to estimate the state of networked control systems. Schenato investigated the design of optimal estimators with random delay and packet loss [9],[10]. However, because the random delay in these studies was not generated stochastically (e.g., as Gaussian noise), it is considered that these models of random delay do not well model actual random delay. In our previous studies, a bilateral control system with time-varying delay was investigated. The stability and passivity were proved by using the Lyapunov theorem, and the performance of the proposed bilateral control system was evaluated through numerical simulations [14]. Furthermore, state estimation problems for a networked system with random delay were considered. A Kalman filter was designed for a time-invariant linear system and the observation system that was affected by the random delay. The effectiveness of the proposed Kalman filter was confirmed through numerical simulation [15]. In this paper, a bilateral control system for flexible master–slave arms with random delay is discussed. The linearized mathematical models of the master and slave arms are derived by using Hamilton’s principle, and the random delay is defined as the sum of the average time delay and a Gaussian noise. To estimate the state and observation signals that are affected by the random delay, a novel Kalman filter is designed. The PD controller and PDS controller are designed for generating the reaction torque of the rigid master arm and the refProceedings of the 47th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Honolulu, Dec. 5-8, 2015