# Design and Control of an Omnidirectional Mobile Wall-Climbing Robot
## 1 Introduction  
The wall-climbing robot mainly consists of two modules: the locomotion module and the adhesion module. For the locomotion types, arms and legs [1] are good at overcoming obstacles but have drawbacks in velocity, wheels and chains [2] have advantages in continuous and fast movement but cannot handle large obstacles, sliding frames [3] are simple in both structure and control but move slowly compared with wheels and chains, and wires and rails [4] are safe and carry a considerable payload weight but demand external guidance and equipment. For the adhesion types, magnetic adhesion [5] has a strong adhesion force but demands a ferromagnetic wall, passive suction cups [6] have lower energy consumption, while active suction chambers [7; 8; 9] have stable adhesion, mechanical adhesion [10; 11; 12] has low energy consumption and is stable but usually requires unique construction or materials on the wall surface, and chemical adhesion [13] has low energy consumption when the robot is not moving but is highly influenced by wall material. According to the literature [14; 15], there are few wall-climbing robotic systems attached to non-ferromagnetic walls with omnidirectional locomotion. However, compared against differential wall-climbing robotic systems, omnidirectional locomotion has better motion flexibility, including omnidirectional moving with any orientation, changing orientation arbitrarily during motion, and adapting to small spaces. A robot sometimes needs to move along a specific trajectory when carrying out a task in real applications. Therefore, trajectory tracking for ground mobile robots has been widely researched in past years. However, the dynamic characteristics of wall-climbing robots are different from that of ground robots because of the overturning moment caused by gravity. The difference makes the trajectory tracking of wall-climbing robots more challenging. In this paper, we focuson the design and control of a novel three-wheeled omnidirectional mobile wall-climbing robot with non-contact negative pressure air chamber adhesion. The same as ground robots, omnidirectional wheels [16; 17; 18] are essential for omnidirectional mobile wall-climbing robots. However, almost all these robots use magnetic adhesion, which cannot attach to non-ferromagnetic walls. Besides the omnidirectional wheeled design, steerable wheels are also available for approximate omnidirectional locomotion [19]. Although this robot can attach to non-ferromagnetic wall surfaces, its motion control is more complicated. Moreover, its flexibility is not as good as robots using omnidirectional wheels. However, there is no design of a three-wheeled omnidirectional mobile wall-climbing robot with the non-contact negative pressure air chamber adhesion at present. As a traditional hot research topic, different algorithms have been proposed to address trajectory tracking for mobile robots, e.g., traditional PID control algorithm [20], model predictive control(MPC) algorithm [21; 22], sliding-mode control algorithm [23], adaptive control algorithm [24], algorithms based on artificial neural networks [25], moving horizon \(H_{\infty}\) control algorithm [26], and fuzzy control algorithm [27]. [PERSON] et al. designed a fuzzy adaptation scheme for PD control with gravity compensation of robot manipulators [28]. [PERSON] et al. designed a digital twin-based optimization procedure for a system which is subject to both backlash and friction [29]. Specific to the trajectory tracking for omnidirectional mobile robots, a novel minimum-energy cornering trajectory tracking algorithm has been proposed for three-wheeled omnidirectional mobile robots [30]. [PERSON] et al. designed energy-optimal motion trajectory tracking algorithms for Mecanum-wheeled omnidirectional mobile robots [31]. [PERSON] et al. designed complementary route-based ICR control for steerable wheeled mobile robots [32]. However, the research on the trajectory tracking problems of wall-climbing mobile robots is still insufficient [33].