# Fault-Tolerant Tripod Gait Planning and Verification of a Hexopod Robot
## 1 Introduction  
With the rapid development of robot technology, autonomous mobile robots have been widely studied. Multi-legged robots have high stability and environment adaptability compared with wheeled or crawler robots since they do not require consecutive contacts between the foot and ground [1]. Although most of the inspiration for robot design and motion planning comes from insects [2], robots are not yet as flexible as insects. Legged robots are almost always applied in a structured environment while insects are faced with a more complex variable environment. Currently, significant achievements have been made in the research of robots in a normal state in terms of structure, gait, stability, and energy consumption [3]. Through phase coordination, tripod gait, tetrapod gait, wave gait, etc., have been realized. An adaptive gait that can be applied on irregular terrain also has come into reality through a central pattern generator (CPG) network [4, 5]. Moreover, the Walknet Controller is a robust, decentralized controller that incorporates findings from the behavior of stick insects for gait coordination of multi-legged robots [6]. In recent years, it has been developed into different versions through expansions [7]. However, greater robustness and reliability are expected for robots to enhance environmental adaptability, such as fault-tolerance ability after failure. In the unstructured environment, it is highly likely for robots to suffer from component failure. Nevertheless, little attention has been devoted to machine malfunction, such as the failure or damage affecting actuators, sensors, or leg structures. Hexapod robots have excellent joint redundancy compared to a quadrupedal robot, so has superior fault tolerance potentiality. Some exceptional conditions, such as broken legs and overturned bodies, have captured scholars' attention. The Walknet Controller mentioned above was expanded to tolerate amputation, for the loss of one or two legs, by implementing additional inter-leg connections [8]. In addition, finite state automata (FSA) were used by [PERSON] to analyze the attitude transformation of the robot during normal operation and fault operation [9]. An organic computing method, specifically self-organization, was demonstrated to provide the hexapod with fault tolerance in unforeseen situations [10]. However, these studies relate to control. Regarding fault-tolerance gait analysis, [PERSON] conducted a detailed motion analysis of the hexapod when joint locked failure occurred. First, he derived fault-tolerant quadruped periodic gaits with a fault stability margin over the perfectly even terrain of the hexapod [11], then extended it to a Follow-The-Leader (FTL) gait on uneven roads [12]. Furthermore, the FTL gait was applied in post-failure walking, having the advantages of both fault-tolerance and terrain adaptability [13]. [PERSON] discussed the stability, fault tolerance, turning ability, and terrain adaptability of rectangular hexapod and symmetric hexapod robots; the static stability of different fault-tolerant gaits were also analyzed [14]. Based on behavior research of insects, he proposed the self- recovery method, Sidewise-Self-Recovery (SSR), of a hexagonal robot [15]. However, only overturning of the robot was taken into consideration. Further, [PERSON] and his team undertook a significant amount of research in this field. They deduced a fault tolerant criterion of a single broken leg and all leg fault combination types were analyzed using this criterion [16]. Residual mobility was analyzed using the screw theory in the case of a partial actuator fault, and a motion planning method based on a fault tolerance Jacobian matrix was proposed [17; 18]. Currently, with the development of artificial intelligence, some scholars have begun to use the method of machine learning or reinforcement learning to generate the walking gait of the six legged-robot with a leg injury.