A Model Predictive Controller with Switched Tracking Error for Autonomous Vehicle Path Tracking

On Road Vehicle Breakdown Assistance Finder Project

A Model Predictive Controller with Switched Tracking Error for Autonomous Vehicle Path Tracking 
Autonomous vehicle path tracking accuracy and vehicle stability can hardly be accomplished by one fixed control frame in various conditions due to the changing vehicle dynamics. This paper presents a model predictive control (MPC) path tracking controller with switched tracking error, which reduces the lateral tracking deviation and maintains vehicle stability for both normal and high speed conditions. The design begins by comparing the performance of three MPC controllers with different tracking error. The analyzing results indicate that in the steady-state condition the controller with the velocity heading deviation as the tracking error significantly improves the tracking accuracy. Meanwhile, in the transient condition, by substituting the steady-state sideslip for real-time sideslip to compute the velocity heading deviation, the tracking overshoot can be reduced. To combine the strengths of these two methods, an MPC controller with switched tracking error is designed to improve the performance in both steady-state and transient conditions. The regime condition of a vehicle maneuver and the switching instant are determined by a fuzzy-logic based condition classifier. Both normal and aggressive driving scenarios with the vehicle lateral and longitudinal acceleration combination of 5 m/s2 and 8 m/s2 are designed to test the proposed controller through CarSim-Simulink platform. The simulation results show the improved performance of the MPC controller with switched tracking error both in tracking accuracy and vehicle stability in both scenarios. 
Autonomous vehicle technology aims to increase driving safety, reduce traffic congestion and emissions, and improve energy efficiency [1-4]. Path tracking is a basic part of the vehicle control module to execute the predefined path from the motion planning layer by determining the desired actuating input to correct tracking errors [5]. Code Shoppy To track the path accurately and steadily, the tracking error representation and control algorithms are of vital importance. Several kinds of tracking errors have been used in the design of path tracking controller. In some simple geometric tracking controllers, such as pure pursuit [6], the steering angle is directly determined from the lateral deviation through the geometrical relationship between the vehicle and the desired path. For the controllers based on kinematic and dynamic model, an explicit tracking error representation is usually needed to describe the relative position of the vehicle to the desired path. The most extensive tracking error used in the kinematic model based controllers is expressed with the error in longitudinal and lateral directions and orientation error in the global frame [7-9]. This method is suitable for robots and low speed vehicles. However, when the speed goes up, the tracking accuracy and vehicle stability of this class of controllers cannot be maintained due to the ignorance of vehicle dynamics. Several kinds of tracking error representations are used with dynamic vehicle model to realize path tracking at high speed. Yaw rate error and lateral deviation are one of the popular states to represent tracking error. Multiple approaches are proposed to steer the vehicle yaw rate to the desired reference value to achieve path tracking [10-14]. Since the yaw rate is directly related to the vehicle yaw stability, it is easy to keep the vehicle steady through this model. However, the desired reference value is the solution to a kinematic model or a steady-state bicycle model. Using this value as a reference input would ignore the natural transient dynamics of the vehicle [15, 16], which could lead to a poor tracking accuracy in some conditions. Some other states, such as sideslip, steering angle or a combination, are also used as the desired references [15-19], and they will face the same problem. Another common way to formulate the tracking error is utilizing the vehicle heading deviation instead of yaw rate error to maintain the vehicle travel orientation, and controllers based on this tracking error model are designed to force the vehicle heading deviation to zeros [20-25]. Chuan Hu etc. [26, 27] designed a robust controller that can minimize vehicle heading and lateral deviations under disturbances and uncertainties. Brown etc. [28] presented a path tracking controller based on model predictive control (MPC) to minimize the vehicle heading deviation, and the controller could achieve stabilization and obstacle avoidance simultaneously. A simple but effective feedback-feedforward steering controller using vehicle heading deviation as control output was proposed in [29], and the controller could keep a lower complexity and maintain stability even at the handling limits. However, choosing the vehicle heading deviation as a control output may not always minimize the lateral deviation effectively, especially when the sideslip is high, as shown in Figure 1. The vehicle heading deviation and lateral deviation cannot be made to zero at steady-state simultaneously [17, 30]. Path HeadingUPath FIGURE 1. Velocity heading deviation and vehicle heading deviation. Uis vehicle velocity, β is sideslip, is the vehicle heading deviation,  is the velocity heading deviation. To eliminate the steady-state tracking error, the vehicle velocity heading deviation, which is the deviation of the vehicle travelling orientation and path heading, as shown in Figure 1, is applied to model the tracking error. Werling et al. [31] presented a steering controller that can track the velocity heading and validated the controller through the experiment with a low friction coefficient. Kapania et al. [17] explained that zero steady-state lateral deviation requires the vehicle velocity vector to be tangent to the path, which means the vehicle velocity heading deviation to be zero. But the experiment results show that the designed feedback controller based on the velocity heading deviation would spin out at limits of handling. To maintain the stability margins, the steady-state sideslip instead of real-time sideslip is used in the final controller, and the performance was demonstrated through experiment. Although the vehicle stability is improved by combining steady-state sideslip in the vehicle heading deviation, the tracking accuracy in steady-state condition is not as good as that of using real-time sideslip, which is due to the transient dynamics is ignored when computing the steady-state sideslip. Variety of control algorithms have been used in path tracking design, including classical algorithms [32, 33], robust algorithms [34, 35], optimal algorithms [36, 37], etc. Recently, model predictive control (MPC) has become the most attractive method in the control of autonomous vehicles, due to the capability of systematically including system constraints and future predictions in the design procedure, which is perfect for dealing with vehicle stability constraints as well as changing vehicle and tire dynamics [4, 28, 38-40]. Besides, the inherent robustness of MPC guarantees the system robustness to some degree [38, 41]. Most of the existing path-tracking controllers are designed based on a fixed tracking error representation. However, in the presence of the changing vehicle dynamics under various conditions, these controllers may not guarantee a high performance in a certain scenario. Inspired by the research in [17], this paper designs a MPC controller that takes the velocity heading deviation as the tracking error, and the real-time sideslip and the steady-state sideslip are switched to compute the velocity heading deviation in the steady-state and transient condition, respectively. A fuzzy-logic based condition classifier is developed to indicate the regime condition and the switching instant. The main contributions of this paper include that: 1) the deficiencies and strengths of using steady-state sideslip and real-time sideslip to compute velocity heading deviation as the tracking error is analyzed, and the necessity of a switched tracking error is clarified; 2) a vehicle condition classifier is constructed based on fuzzy-logic to classify the vehicle maneuver into the steady-state or transient condition; 3) based on the condition classifier, an MPC path tracking controller with switched tracking error is proposed, which is capable of reducing tracking error and maintaining vehicle stability in steady-state and transient conditions, simultaneously. 

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