Planning the trajectory of an autonomous wheel loader and tracking its trajectory via adaptive model predictive control
Introduction
Wheel loaders are a type of flexible and mobile transportation equipment often used to transport materials on uneven terrain such as that found in mines and on construction sites. They consist of a front and rear body, which are connected by a hinge joint point and a swing ring. The front and rear body are connected by hydraulic actuators to steer the wheel loader. There is no relative connection between the wheel and the frame in the steering process; therefore, the steering drive axle and other components were omitted. This structure reduced the turn radius of the wheel loader, improved the maneuverability of the vehicle, and gave it a good adaptability in its operating environment [1], [2]. However, owing to this steering structure, the trajectory planning and tracking methods typically used in conventional autonomous passenger vehicles cannot be applied to wheel loaders.
The adverse working environment and frequent acceleration, deceleration, and steering actions of wheel loaders present considerable challenges to the physical and mental state of drivers, making it nearly impossible to guarantee high working efficiency and quality over long periods of operation. In order to improve the potential efficiency of wheel loader operation, automation has been a focus of attention in the field of earthmoving machinery for many years [3], [4], [5]. Roberts et al. [6] proposed five stages from manual driving to fully automatic driving for the underground mining vehicles. Frank et al. [7] proposed five similar stages for wheel loaders, consisting of manual operation, auxiliary operation, semi-automatic operation, highly automatic operation, and fully automatic operation. In general, wheel loader automation can be divided into two types: automatic driving and automatic bucket filling. Trajectory planning and trajectory tracking are considered automatic driving activities. The process of trajectory planning and trajectory tracking for automatic driving of a wheel loader involves a variety of sensors, including cameras to detect operational areas, vehicles, and other materials, laser radar and ultrasonic sensors to detect obstacles and take precise distance measurements, and an inertial measurement unit and wheel encoder for dead reckoning. During the automatic driving process, the wheel loader determines its surrounding environment using these various sensors and calculates a feasible trajectory using a planning algorithm. Then, under the action of its control system, it realizes longitudinal and lateral control through steering, acceleration, and deceleration actions to drive in accordance with the established trajectory.
There are many challenges in the process of wheel loader automation, among which accurate trajectory planning and tracking are quite urgent [8]. The V-shaped work path of the wheel loader planned in previous studies [9], [10], [11] consists of a symmetrical “clothoid” path (i.e., a curvature that changes linearly with its length) and a straight line segment. However, during actual operation, the driving path of the loader will change owing to ongoing operational requirements; thus, symmetry cannot always be guaranteed. Therefore, the current path planning algorithm cannot easily meet the actual requirements of on-site operation. Alshaer et al. [12] studied path planning and tracking problems related to an autonomous wheel loader using these V-shaped working conditions. The shortest path algorithm proposed by Reeds and Shepp was improved and extended, and a proportional–integral–derivative (PID) controller was used to track the planning path. Nayl et al. [13] built an online motion planning controller for articulated vehicles based on a model predictive control (MPC) system and analyzed the influence of parameters such as the velocity of the vehicle, maximum allowable change in the articulated steering angle, safe distance from obstacles, and total number of obstacles in the operating arena on the online motion planning algorithm. Another study considered the effect of side angles on the nonlinear kinematic model of a non-holonomic articulated vehicle and developed a switching control scheme based on multi-model predictive controller [14]. A sliding mode controller based on an articulated vehicle nonlinear kinematics model has been constructed and was found to improve the tracking control of the planned trajectory [15]. However, these studies did not consider the tracking control of the vehicle in a non-uniform driving state and did not deeply analyze the influence of path curvature on the time-varying state of the tracking process. Choi and Huhtala [16] used the search-based A* algorithm to optimize the global path of an articulated vehicle under a high-constraint environment to realize obstacle avoidance behavior, but did not analyze the trajectory tracking of the vehicle under variable speed. In another study [17], a driver model for a wheel loader operating under V-shaped working conditions was constructed based on input from the throttle, brake, and steering using model predictive control (MPC). The results indicated that the simulation data and measured speed trends were basically the same. However, the displacement and heading errors, which represent the tracking effect in the simulation process, were not elaborated upon in detail, and the influence of the path curvature on the tracking of the loader trajectory was not considered.
Given these issues, the following factors remain to be fully considered when planning the trajectory and tracking of an autonomous wheel loader in a V-shaped operation mode. First, because a running wheel loader frequently accelerates and decelerates, the vehicle is often in a non-uniform driving state. Second, as the path curvature of a wheel loader is not constant, in a time-varying state this will have a certain impact on the tracking effect.
Therefore, a non-uniform motion trajectory under forward and reverse driving conditions is proposed in this study by combining the actual operating characteristics and the minimum stable turning radius of a wheel loader based on the optimal rapidly exploring random tree (RRT*) and continuous curvature steer (CC Steer) algorithms. In this manner, a new adaptive model predictive control (AMPC) system is constructed based on the kinematics of the loader and the dynamic deviation model. The AMPC system uses the path curvature in the time-varying state as the disturbance input, the acceleration and articulated angle velocity as control inputs, and the vehicle speed and articulation angle as control outputs. The trajectory tracking of an autonomous wheel loader is then conducted to implement the planned non-uniform trajectory using the constructed AMPC trajectory tracking system. Based on the outcomes of this implementation, the influences of path curvature on the trajectory tracking performance and robustness of the proposed AMPC system are verified for different curvature amplitudes.
Though acceleration and deceleration processes as well as path curvature disturbances are unavoidable during actual vehicle travel, this problem has often been overlooked in previous trajectory planning and tracking control studies. In this study, the entire vehicle trajectory of an autonomous wheel loader under V-mode operation was planned according to its acceleration and deceleration processes to accommodate path curvature disturbances, and the desired trajectory was effectively tracked, addressing such deficiencies in existing research and improving the accuracy of trajectory tracking. This method not only forms a basis for realizing autonomous wheel loader driving functions, but also provides a key technology for improving the active safety of the vehicle. Notably, the method proposed in this paper is not only applicable to wheel loaders, but can also be used as a basis for trajectory planning and tracking research using other types of autonomous vehicles.
The overall structure of this article is as follows. In Section 2, the dynamic and driving dynamic deviation models for the wheel loader are established. Section 3 details the planning of the non-uniform velocity trajectory of the wheel loader, and the AMPC trajectory tracking system is constructed under conditions in which the path curvature is disturbed. Section 4 presents an analysis of the simulation used to verify the influence of the path curvature on the performance and robustness of the AMPC trajectory tracking system when accounting for different curvature amplitudes. Finally, the conclusions are presented in Section 5.
Section snippets
Dynamic model
The dynamic model presented in this paper was primarily used as a predictive model in the model controller. This model must therefore describe the dynamic process as accurately and simply as possible in order to reduce the computational burden of the control algorithm. Accordingly, the following assumptions were made in the dynamic analysis:
(1) Considering the large mass of the wheel loader, changes in longitudinal speed due to the longitudinal components of the tire lateral forces were ignored;
Trajectory planning and tracking control
When a wheel loader performs short-distance shovel loading, its operation is mainly divided into I, V, L, and T-shaped modes according to its loading and running route. Among these modes, the V-shaped operation mode is highly efficient and provides a short working cycle time. Thus, it is the most common mode used in shovel loading operations [1], [21]. The V-shaped wheel loader operation mode is shown in Fig. 3. The work process is usually divided into four stages: driving forward and loading
Simulation analysis
The V-shaped operation of the wheel loader was evaluated using a simulation in which the control target traveled along a desired path at a planned velocity. The control target tracked its trajectory by continuously reducing any deviations in the path and velocity from the reference trajectory. Two different simulation conditions were designed to comprehensively analyze the feasibility of the proposed control method. The upper driving speed limit for the desired trajectory was set to 3 m/s [42],
Conclusion
A non-uniform driving trajectory satisfying the conditions of driving forwards and in reverse using a path-velocity decomposition method was planned and combined with the characteristics of a wheel loader with a minimum stable turning radius and functioning in a typical operation mode.
An adaptive model predictive control (AMPC) system operating under conditions in which the path curvature was perturbed was constructed based on a kinematic model of the loader and a dynamic driving deviation
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was sponsored by the National Natural Science Foundation of China (Grant No. 51875055); Scientific and Technological Research Program of Chongqing Municipal Education Commission, China (Grant No. KJQN201800718); Scientific and Technological Research Program of Chongqing Municipal Education Commission, China (Grant No. KJQN201803106).
Junren Shi received the M.S. degree in mechanical and electronic engineering from Chongqing University of Technology, China, in 2016. He is currently a Ph.D. student in vehicle engineering at the Chongqing University, China. His current research activities focusing in the areas of: Model Predictive Control, Trajectory planning and tracking, Data mining.
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Junren Shi received the M.S. degree in mechanical and electronic engineering from Chongqing University of Technology, China, in 2016. He is currently a Ph.D. student in vehicle engineering at the Chongqing University, China. His current research activities focusing in the areas of: Model Predictive Control, Trajectory planning and tracking, Data mining.
Dongye Sun received Ph.D. degree in mechanical engineering from Jilin University, China, in 1996. Now he is a Professor at State Key Laboratory of Mechanical Transmission, Chongqing University, China. His research areas of interest include power transmission and integrated control, hybrid powertrain design theory and control methods.
Datong Qin received Ph.D. degree in Mechanical Engineering Department from Chongqing University, China, in 1993. Now he is a Professor at State Key Laboratory of Mechanical Transmission, Chongqing University, China. His research areas of interest include structural design and optimization, mechanical transmissions and control, especially in gear dynamics.
Minghu Hu received Ph.D. degree in Mechanical Engineering Department from Chongqing University, China, in 2008. Now he is a Professor at State Key Laboratory of Mechanical Transmission, Chongqing University, China. His research areas of interest include structural design and optimization, mechanical transmissions and control.
Yingzhe Kan received the M.S. degree in vehicle engineering from Chongqing University of Technology, China, in 2018. He is currently working toward the Ph.D. degree in the School of Vehicle Engineering at Chongqing University, Chongqing, China. His research interests include hydro-mechanical transmission system and battery management system.
Ke Ma received the B.S. degree from Southwest Jiaotong University and M.S. degree from Chongqing University of Technology, China, in 2015 and 2018 respectively. He is currently working toward the Ph.D. degree in the School of Vehicle Engineering at Chongqing University, China. His research interests include electro-hydraulic intelligent control technology and new power transmission technology.
Ruibo Chen received the B.S. and M.S. degrees in mechanical engineering from Xinjiang University, China, in 2015 and 2018 respectively. Now he is a Ph.D. student studying in the College of Mechanical Engineering of Chongqing University. His research area is mechanical system dynamics, transmission system electromechanical integration technology.