# Design and Research of a Flexible Foot for a Multi-Foot Bionic Robot
## 1 Introduction  
Multi-legged robots are widely used in complex working environments due to their strong terrain adaptability and high flexibility [1; 2]. However, there are many problems with these robots, such as large impact and limited operation space [3; 4]. As robot technology develops toward achieving higher speeds and greater precision, the flexible effects of components are becoming more and more obvious [5; 6]. Research on flexible materials and flexible mechanisms is of great significance in improving the service life, compliance control, stability, and terrain adaptability of legged robots [7; 8]. Flexible structures and flexible materials have become an important direction for research on multi-legged robots [9]. In order to optimize the motion performance of the robot foot and reduce the impact between the foot and the ground [10; 11], many research works have been conducted on flexible feet and flexible bionic joints. [PERSON] et al. designed and developed a hexapod robot leg structure that used the variable stiffness flexible leg \"C-leg\" to improve the robot's bounce ability [12]. [PERSON] [13] and [PERSON] [14], designed a flexible foot crawling robot that could buffer the impact between the foot and terrain and sense the ground environment. It was shown in Reference [15; 16] that a passive buffer structure composed of linear springs was attached to the foot tip of the quadruped robot, which provided good buffering when the robot struck the ground. [PERSON] et al. [17] designed a flexible leg model was designed to reduce the impact of the robot foot. Inspired by the biological system, the principle of binding force closure [18] simulates the muscle tension of animal legs and improves the stability of the robot's bouncing movement. By analyzing the motion pattern of the insect foot during its landing stage, it has been found that an insect's movement process can be divided into two stages: (1) the claw with the claw pad is incontact with the ground, the deformation of the claw pad adapts to the complex terrain, and the impact force of the claw in contact with the ground is slowed down; and (2) by the flexible membrane between the connecting claw and the tarsus, a contraction of the sacral joint is made to open all the claws, and the knuckles and the claws are completely in contact with the ground, thereby increasing the contact area. The flexible membrane serves to attenuate the impact force and protect the joints of the legs [19]. Many attempts have been made by experts at home and abroad to use flexible materials to absorb the impact force [20; 21]. It was shown in Reference [22] that a new structure was proposed to absorb the impact force with a combination of wheel, intermediate, and stabilizer. [PERSON], [PERSON] et al. [23; 24] show that by compensating the flexible structure with a control algorithm, the errors caused to the robot system by the flexible structure were reduced. The structure designed in Reference [25] can well realize mechanical information perception. It was shown in Reference [26; 27] that carried out research on the acquisition method and signal transmission mode of force signals that has great innovative significance and provided us with a good idea. Therefore, this study drew on the bionics analysis results to design and manufacture a flexible, two-degrees-of-freedom foot unit. When the foot strikes the ground, the flexible sole deforms to adapt to complex terrain while reducing the impact force, and the force is then transmitted to the compression spring through the push-pull rod to achieve secondary absorption of the impact force. The flexible sole was made by 3D printing mold-casted silicone, and the other modules of the flexible foot were 3D printed using photosensitive resin. The effects of the flexible materials, flexible parameters, and structural forms on the performance of the foot end were analyzed by simulation and experimentation. Force analysis and flexible foot-end force calibration were carried out for the foot tips.