## 1 Introduction
Intelligent control methods such as artificial neural networks, genetic algorithms, and fuzzy logic can be implemented in engineering practice more easily and effectively than classical control methods. For example, [PERSON] et al. proposed a class of constrained Takagi-Sugeno fuzzy system with a simple control structure and a low level of numerical complexity. That study provided better results than some recent works developed in a non-quadratic Lyapunov framework [27]. In addition, the fuzzy method they developed can also be used to handle a large variation range of vehicle speed [28]. In general, these algorithms have recently been targets of rapid development [29]. They can cope with the nonlinear problems that affect almost all EVs without exact mathematical models [30]. However, most EV studies utilize separate drive and steering systems. Vehicle structures have become complex, thus complicated manufacturing engineering is required. These proposed control strategies have focused mainly on the stability and efficiency of the steering system, or the drivability and safety of the driving system. Few studies have considered a combined steering-driving system for EVs. In the case of the FC, a kind of off-center steering shaft mechanism (OSM) is utilized. The drive and steering systems are combined because the forces involved in both driving and steering come from the in-wheel motor [31]. For this reason, the FC structure is quite simple. It can achieve multiple motion modes, including cross motion (CM), in-place rotation (IR), diagonal motion (DM), and steering motion (SM), and can be used flexibly in narrow or closed environments. The FC is expected to be used for low-speed transportation work in greenhouses, warehouses, or orchards. Flexible motion mode switching (MMS) based on OSM provides the chassis with the ability to adapt to difficult environments. Namely,the posture of the chassis can be adjusted according to different work environments. The high ground clearance and suspension also allow it to adapt to uneven roads [32]. However, due to the lack of a rigid constraint mechanism, it is difficult to coordinate the motion of each FC OSM during MMS in situ. The objective of this paper is to provide a coordinated control strategy to reduce MMS angular velocity coupling errors (CEs) and guarantee smooth, steady MMS. To achieve this, a CE model is derived based on coupling control and Lyapunov stability theory. A fuzzy PID controller is then designed for CE control. To shorten the response time and reduce steady-state errors of OSM steering tracking motion, a fuzzy PI control method is employed for steering tracking control. The feasibility of the proposed control strategy is confirmed via MATLAB/Simulink simulations and then experimentally validated on hard pavement. This paper provides two main contributions to the engineering community: (i) a control algorithm that integrates coupling control, Lyapunov stability theory, fuzzy PID control, and fuzzy PI control is proposed for FC MMS in order to cope with the lack of a linkage relationship among the four OSMs, and (ii) the CE performance and MMS stability are improved under the proposed control methodology. The rest of the paper is organized as follows. In Section 2, the overall structure of the FC and system modeling are described. In Section 3, a coupling control strategy for MMS of the FC is designed. In Section 4, we discuss the MATLAB/Simulink simulation. Section 5 is dedicated to experimental validation. Finally, our conclusions and proposals for future work are provided in Section 6.