## 1 Introduction  
Independently rotating wheels (IRW) are increasingly utilized in rail transit systems. Compared with solid-axle wheelsets, the unique structure of IRWs allows individual wheels on the same axle to rotate independently, eliminating the longitudinal creep forces generated from the wheel-rail contact interface and suppressing hunting motion [1, 2, 3, 4]. However, IRWs no longer exhibit restoring torque in the yaw direction due to the decoupling of the wheels, which leads to dynamical instability and significantly increased wheel-rail wear [5]. Scholars have proposed various active solutions to restore the steering ability of IRWs. The basic steering strategy mimics the dynamic behavior of solid-axle wheelsets [6]. Controllers based on the proportional-integral-derivative (PID) have been extensively studied [7, 8], but adjusting the gain parameters under varying vehicle operating conditions is difficult. The robust Hoo algorithm is applied by representing nonlinear characteristics with uncertain parameters [9]. However, a trade-off between robustness and performance leads to a conservative controller. Other model-based controllers, such as sliding mode control [10], linear parameter-varying (LPV) control [11], and gain scheduling techniques [12], often rely on simplified mathematical models that have difficulty capturing the intricate dynamics of railway vehicles, especially the nonlinear interactions at the wheel-rail interface and changing operating conditions. This results in a significant gap between the reference model and the actual dynamics, leading to a lack of robustness in real applications. Recognizing the limitations of traditional control strategies, there is a growing interest in data-driven methods. Our previous research explored the application of deep reinforcement learning (DRL)-based controllers, including the deep deterministic policy gradient (DDPG) and Ape-X DDPG [13; 14], leveraging deep neural networks' ability to fit nonlinear systems. Nevertheless, several limitations are encountered: (a) the existing DRL-based controllers require multiple dynamic parameters from all IRWs, and the high dimensionality of observation spaces leads to slow convergence during training; (b) current strategies mainly focus on the centralized control of the entire vehicle without achieving local control for an individual IRW, potentially affecting computational efficiency in practical applications. To overcome the limitations of current DRL controllers for IRWs, exploring multiagent reinforcement learning (MARL) algorithms is a promising area. MARL-based controllers can simultaneously enhance the adaptability advantages of DRL for complex systems and achieve local control of each IRW via the distributed control method [15; 16]. Based on the centralized training and decentralized execution (CTDE) framework of the MARL algorithm, the multiagent deep deterministic policy gradient (MADDPG) algorithm was introduced [17]. The MADDPG equips each agent with individual actor and critic networks, enabling the consideration of other agents' influences while independently evaluating actions. This approach facilitates coordinated learning during training and independent decision making during execution. Thus, MADDPG enhances the global performance in multiagent scenarios, as evidenced in different MAS control issues [18; 19; 20]. In this study, we utilize the MARL algorithm to develop a novel distributed active guidance controller for IRW vehicles. Our decentralized approach assigns modular controllers to each independently rotating wheelset, enabling local control within a sensor-controller-motor subsystem. We adopt the MADDPG algorithm and integrate it with the prioritized experience replay (PER) mechanism, which we refer to as the PER-MADDPG algorithm. This approach efficiently optimizes the behavior policy of each agent by interacting with the vehicle's operating environment, aiming to maximize the IRWs' performance and the overall reward of the MARL model.