## 1 Introduction
To perform complex tasks in remote scenarios with dexterous kinematic skills, the teleoperation technique is introduced as the control strategy for manipulators, where the operator moves the leader robot and generates the desired trajectory signals and transmits to the follower through communication channel [24; 25; 26]. [PERSON] et al. proposed a control strategy for teleoperating the designed hyper-redundant robot in a hazardous environment with mixed reality and immersive technology, thus the operator could command the robot and observe a reconstructed environment via a head-mounted display in a remote location [27]. [PERSON] et al. designed a real-time control leader-salve teleoperation for a snake robot and the kinematics problem was handled via the Monte Carlo method and optimization algorithm [28]. In the research of [PERSON] [29], a teleoperation system for redundant snake-like surgery robots comprised of 26 joint variables was developed, and 6 different control methods were compared including Jacobian, iterative and linear programming methods. Though some teleoperation systems of CHCM have been proposed in the research mentioned above, the communication time delay between leader and follower robot, which may cause instability and poorer performance [30; 31], and the force feedback has not been taken into consideration generally. Therefore, to deal with these hostile factors, the wave variable method was developed to guarantee the stability of the teleoperation system, which could be guaranteed theoretically based on the passivity and scattering-based theories [32]. In the earlier research about wave variable methods, the system stability can be ensured [33; 34], but the transparency including trajectory tracking and force feedback performance is distorted because of the bias term in transmitted wave variable signals [30]. Afterwards, modified wave variable-based teleoperation structures have been proposed to improve the system transparency with guaranteed stability [35]. [PERSON] et al. presented a new wave transformation method to reduce the bias term caused by wave reflections, thus the velocity tracking and force feedback performance was improved in unknown working environments [36]. [PERSON] et al. proposed corresponding methods to satisfy different requirements of performance, for example an augmented forward wave was generated via the perceived force and follower control force to improve the trajectory tracking performance; a method helping reduce the bias term was partially adopted to enhance the fidelity of haptic feedback [37; 38]. However, the simultaneously good position-tracking and force feedback performance of teleoperation system is still challenging, especially for CHCM. In this paper, a design of CHCM for complicated tasks, which adopts a structure of separating driving subsystem and motion subsystem, is introduced and it has redundant DOFs due to the abundant numbers of joint modules. According to the system geometry structure of CHCM, the simplified forward and inverse kinematics model for real-time control is established based on some assumptions of the CHCM's motion characteristics, which avoids time-cost pseudoinverse computation of the Jacobian matrix. To achieve operator assistance and perception, a modified teleoperation control scheme is introduced for the upper-level control of CHCM with guaranteed stability and improved transparency, where a 2-DOF Cartesian working space mapping method and a virtual force feedback generation algorithm are presented. The performance of the proposed system is theoretically proved via scattering theory and experimentally indicated through a series of comparative experiments. The remaining part of this paper is organized as follows: the general structure and kinematics model of CHCM is introduced in Section 2. In Section 3, a modified wave variable-based teleoperation scheme with virtual force feedback generation is proposed, and the stability and transparency are analyzed.