## 1 Introduction  
Path tracking is critical for autonomous driving, as it moves a mobile robot to follow a desired path by longitudinal and lateral control [1]. The linear quadratic regulator (LQR) controller, proportional-integrated-derivative (PID) controller, and sliding mode controller are often used in path tracking control [2; 3; 4]. In addition, model predictive control (MPC) is often used in path tracking. Model predictive control strategies are applied to a wheeled mobile robot, and it has proved that MPC reduces energy consumption by 70% compared to the reduction in energy consumption provided by PID control [5]. The various path tracking control algorithms proposed for mobile robots usually employ constant control parameters, which yield optimal performance under a no-disturbance condition. Researchers focused on selecting suitable controller gains and designing compensators to improve control performance [6; 7; 8]. Adaptive control methods were widely utilized for systems with unknown dynamics and uncertain disturbances [9; 10]. The terrain changes, often considered disturbances for controller design, may have a variety of effects on a robot's motion, such as slipping and skidding [11; 12]. Slippage, however, is especially crucial for the motion control of mobile robots working in the field environment [13]. Such disturbances may lead to the degradation of tracking performance [14]. A number of studies in the literature took slippage into account and proposed path tracking control together with slipping and skidding compensation [15]. Therefore, the accuracy of slippage parameter estimation is vital to the design of such controllers. The generalized extended state observer (GESO) approach and Kalman filter were utilized to estimate the slipping parameter of wheels [13; 16], and the slippage effect was considered in a kinematic model to improve the performance of path tracking [17; 18; 19]. The disturbance led by slipping and skidding, however, is difficult to estimate and predict. Only few studieshave presented adaptive controllers with time-varying parameters to adapt to various terrains. An improved adaptive controller was proposed to allow a wheeled mobile robot (WMR) to track the desired trajectory under unknown longitudinal slip [14]. The accuracy and reliability of the path tracking of a four-wheel mobile robot when moving at high dynamics on a slippery surface were addressed by employing an adaptive and predictive controller [20]. A novel indirect adaptive controller was proposed to allow wheeled robots to finish path tracking on complicated terrains in the presence of unknown interferences and wheel slippage using integral sliding mode control (ISMC)-based neural networks with updated rules for adjustments the weights [21]. A self-tuning methodology based on probabilistic approaches and machine learning techniques was proposed to improve the path tracking performance of for autonomous vehicles maneuvering along changing terrain [22]. A new adaptive control scheme was used to overcome the difficulties in path tracking, and the scheme included designing a new adaptive state-feedback controller and two high-gain observers to estimate the unknown linear and angular velocities, respectively [23]. The adaptive sliding mode control (SMC) method combines the adaptive control method and a fast double power reaching law with the SMC method, and a complete control loop with active slip compensation and adaptive SMC is thus established [24]. The path tracking controller for field robots should overcome the terrain changes by employing a time-varying controller that can adapt to slippage disturbances. This paper addresses the problem of degradation on path tracking performance in WMRs due to slipping and skidding for. The major contributions of this paper are listed as follows:  
* An equivalent error integrating position and orientation errors, and taking account of the preview distance is employed for the development of path tracking control to achieve both a lower position error and a steady posture.