## 8 Experiment  
In this paper, a fixed-base, single-segment continuum robot is used to verify the effectiveness of the explicit time algorithm. Figure 22 presents the physical prototype of the continuum robot and its experimental platform. The experimental prototype consists of three main components: the continuum body, the motor control system, and the driving mechanism. The body of the continuum robot is made of a polyurethane (PU) rod synthesized from urethane material. During experiments, the length of the central rod remains fixed, and ten support discs are evenly distributed along the main body to better conform to the constant curvature assumption.The host computer runs MATLAB R2023B, responsible for processing robot motion calculations, trajectory planning, sensor data acquisition, and sending motor control commands. The entire control system operates at a sampling rate of 100 Hz (i.e., executing once every 0.01 s). The core of the motor control system is an Arduino development board, which handles the main control tasks and sends control signals to the AQMD6008 NS-TBE driver board (Akelc, Chengdu, Sichuan province, China). This driver board regulates the rotational speed of each motor. The motors used are DC motors from the Maxon Motor brand, equipped with an 84:1 gearbox and a 512-pulse ABZ three-phase encoder. The driving mechanism is designed such that the motors drive the movement of sliders via ball screws, which in turn pull the driving cables to achieve the motion of the continuum robot.  
Figure 21: Attitude tracking error of end effector.  
Figure 22: Experimental platform.  
During the experiment, an Intel RealSense D435I depth camera (Intel, Santa Clara, CA, USA) was used to acquire data for obtaining the position information of the continuum robot's end-effector. The camera has a calibration accuracy of 1 mm. Its position relative to the continuum robot follows an \"eye-to-hand\" configuration. A cubic marker was attached to the end of the continuum robot. By detecting the April Tag on the marker, the position of the robot arm's end-effector was obtained. The velocity and acceleration of the end-effector were estimated using a low-pass filter. The acquired data were transmitted to the host computer via a USB interface for processing. During the experiment, the host computer continuously transmitted the processed data to the motor control system in real time. Upon receiving the commands, the control system drove the motors, causing the driving cables on the sliders to move linearly. This adjustment of cable length enabled precise control of the continuum robot's motion.  
In the experiment, a point-to-point task in 3D space was used for validation. The same planned trajectory as in the simulation was applied, with a duration set to 10 s, as shown in Figure 23. During the experiment, the parameters were set to \(T_{c}=1.5\), \(m=0.3\), and \(e_{c}=0.05\). Figure 23 shows the tracking error curve of the actual end-effector position of the continuum robot. It can be seen that the proposed method enables the end-effector position tracking error to converge to near zero within \(2T_{c}\), meeting the predefined convergence time. Figure 24 is a schematic diagram of the continuum robot motion.  
Figure 23: End position tracking error.  
Figure 24: Schematic diagram of the motion process.