# A Worm-Inspired Robot Flexibly Steering on Horizontal and Vertical Surfaces
## 1 Introduction  
For a long time, the principle of bionic motion has been widely applied in the design of various crawling robots, and has attracted attention from many researchers all over the world. Bionic legged robots such as the climbing lizard described in [1] provide excellent motion performances and load capacity on not only horizontal surface, but also inclines and vertical surfaces [2; 3; 4]. However, as each joint of the legs needs to be actuated precisely, the mechanical structures of these robots are complex, which makes it hard to conduct miniaturization design. Among those bionic principles, the bionic worm-inspired motion is considered to be one of the most novel, lightweight, and compact structures. The worm's motion in nature is divided into several types; however, what has been most widely studied is the movement of earthworm, which is able to move flexibly in complex spatial environments on the surface or underground with a simple body structure [5]. It is also because of this feature that earthworms have become a source of inspiration for many research projects [6; 7; 8; 9; 10; 11; 12; 13; 14]. One of the greatest advantages of the earthworm motion is that it occupies small space when it moves, because its body does not need to be bent or arched during crawling. Therefore, this principle of bionic motion is also widely used in robots that work in confined space such as pipeline inspection robots and miniature robots. In previous research, multiple actuation methods have been applied into earthworm-inspired robots, among which the most widely used one is the pneumatic driving method [15; 16; 17], whose advantages are simple structure and easy control. For example, the multi-material-multi-actuatorsoft robot introduced in [15] totally uses pneumatic power to drive its motion. Its structure is divided into three air chambers, two of which are used as radial actuators, while the other one is used as a liner actuator. Through changing the input air pressure in each of the chambers periodically, the robot achieves bidirectional motion along pipelines. Some worm-inspired robots also adopt shape memory alloys (SMA) for actuation, which is particularly common in miniature robots [18; 19; 20]. The omega-shaped inchworm-inspired crawling robot described in [6] is a novel miniature robot that is actuated by two pairs of SMA-driven four-bar linkages. Under the control of input electric signals, the SMA spring actuators on both of the linkages will periodically perform telescopic motions and thus provide actuation force for the crawling motion of the robot. According to the frequency of the input signal, SMA-actuated robots may achieve relatively high-speed motion compared with their own sizes [20]. However, as it is hard to control the position and velocity of SMA precisely [19], this actuation method is usually applied on smaller robots with simple structures and only liner motion capacity. Solenoid actuation is another actuation method in worm-inspired robots [21]. The two adjacent segments of the miniaturized segmented robot are connected by a pair of independent solenoid actuators. The robot can achieve linear and turning motions with symmetrical and asymmetrical actuations of the solenoid pair. For designing crawling robots with the earthworm's motion principle, another difficulty lies in how to simulate the bristle of the earthworm and realize the fixation between the segments of the robot and the working platform, which is an essential problem for the robot to work on inclined or even vertical surfaces. The in-pipe robot introduced in [8] adopted a frictional self-locking mechanism to fix itself to the inner surface of the pipeline. The magnets on the front and rear clamps of the robot are pushed against the inner wall of the pipeline, and thus provide the robot with frictional force against its unidirectional motion trend along the pipeline. This principle allows the robot to move along vertical pipelines with heavy loads.