Tractor-trailer System Research Articles

Designing a time path tracking stabilizing controller for a tractor-trailer robot in the presence of uncertainties

In this article, the discussion of track tracking in tractor-trailer systems with the condition of non-slip and non-holonomic multi-controllers is presented. One of the significant issues in the control of this system is the limitation and saturation of operators, which in real conditions causes serious challenges in the discussion of control and instability of the system. Therefore, the control of these systems, taking into account the considerations of the operator, is of great importance. The aim of this research is to design a stabilizing controller for the tractor-trailer robot in the presence of uncertainties and considering the limitations of operator saturation. In order to track the time path, the controller is presented in two kinematic and dynamic stages. The focus of this research is on the application of operator restrictions in dynamic controllers, and two control approaches are presented for that. Dynamic modeling of the robot is done using Lagrange’s equations. At first, in order to use the anti-jackknife control of the nonlinear tractor-trailer system, it is estimated by identifying the system with a linear and uncertain system. This article investigates the use of neural networks to solve kinematic problems in an omnidirectional mobile robot. The neural network is trained to learn the speed of desired angles of the robot tires, corresponding to different routes. The results show that the neural network can control the robot’s movement without dynamic and kinematic knowledge. In the next section, a neural network is used as compensation for the malfunction of the operators in a feedback linear controller in order to prevent the saturation of the operators. The weights of the neural network are updated in such a way that the stability of the system is guaranteed using the Lyapunov candidate. This article investigates the use of neural networks to solve kinematic problems in an omnidirectional mobile robot. The neural network is trained to learn the speed of desired angles of the robot tires, corresponding to different routes. The results show that the neural network can control the robot’s movement without dynamic and kinematic knowledge. Also, a comparison has been made to validate the method used in Adams and MATLAB software and the simulation conditions of the proposed method with a reference article. The simulation results show the efficiency of the designed controllers. According to the investigations carried out, it can be seen from the angular and planar error of the robot that the neural network method has a better performance than the comparative methods with an approximation between 10% and 15% and the anti-jackknife method also because of the reference method and also The anti-jack knife shows between 13% and 16% due to the complexity of the angular movement of the steering wheel and the rotation and connections of the trailer to the tractor.

A Study on Sway Stability Control Methods for Tractor-Trailer System Using Rear Wheel Steering

A Study on Sway Stability Control Methods for Tractor-Trailer System Using Rear Wheel Steering

Robust Trajectory Tracking Control of an Autonomous Tractor-Trailer Considering Model Parameter Uncertainties and Disturbances

This paper discusses the robust trajectory tracking control of an autonomous tractor-trailer in agricultural applications. Firstly, considering the model parameter uncertainties and various disturbances, the kinematic and dynamic models of the autonomous tractor-trailer system are established. Moreover, the coordinate transformation is adopted to convert the trajectory tracking error into a new unconstrained error state space model. On this basis, the prescribed performance control (PPC) technique is designed to ensure the convergence speed and final tracking control accuracy of the tractor-trailer control system. Then, this paper designs a double closed-loop control structure. The posture control level adopts the model predictive control (MPC) method, and the dynamic level adopts the sliding mode control (SMC) method. At the same time, it is worth mentioning that the nonlinear disturbance observer (NDO) is designed to estimate all kinds of system disturbances and compensate for the tracking control system to improve the system’s robustness. Finally, the proposed control strategy is validated through comparative simulations, demonstrating its effectiveness in achieving robust trajectory tracking of the autonomous tractor-trailer system.

A symplectic method for trajectory planning of general tractor-trailer systems

Trajectory planning is a key issue in the motion control of tractor-trailer system. In this paper, a unified differential-algebraic equation approach to establish the kinematic models of general tractor-trailer systems is developed. By analyzing practical physical limitations and transportation requirements, the trajectory planning of tractor-trailer system is formulated as a nonlinear constrained optimal control problem. Aiming at efficient numerical solution, a novel symplectic method is proposed. In the proposed method, a symplectic discretization is first implemented to transform the necessary conditions for the original optimal control problem into a set of non-smooth equations. Then, a composite strategy that integrates preconditioned iteration techniques is employed for robust solution. The proposed symplectic method is validated by three examples with different system configurations. Simulation results demonstrate that our method outperforms pseudospectral methods in computational efficiency and robustness to initial guesses. Specifically, a multi-stage strategy can be adopted to achieve robust solution in the presence of obstacles, making the system successfully travel across narrow corridors. An animation of the simulation results is available at www.bilibili.com/video/BV1EN4y1P7Ar.

Improving path-tracking performance of an articulated tractor-trailer system using a non-linear kinematic model

This paper presents a novel non-linear mathematical model of an articulated tractor-trailer system that can be used, in combination with receding horizon techniques, to improve the performance of path tracking tasks of articulated systems. Due to its dual steering mechanisms, this type of vehicle can be very useful in precision agriculture, particularly for seeding, spraying and harvesting in small fields. The articulated tractor-trailer system model was embedded within a non-linear model predictive controller and the trailer position was monitored. When the kinematic of the trailer was considered, the deviation of trailer’s position was reduced substantially alongside not only straight paths but also in headland turns. Using the proposed mathematical model, we were able to control the trailer’s position itself rather than the tractor’s position. The Robot Operating System (ROS) framework and Gazebo simulator were used to perform realistic simulations examples.

The Control Reversing Algorithm for Autonomous Vehicles with PSD-Controlled Trailers

Abstract Driving a vehicle with a passive trailer has been the subject of numerous studies. Current control strategies are mostly used by differential geometry, linear algebra, fuzzy regulators, and artificial neural networks. The objective of this study is to design an algorithm for autonomous control of the tractor-trailer system reversing based on an algorithm using a PSD controller and to verify it on a simulated mathematical model. All parameters listed in the models and experiments are performed based on the existing tractor-trailer system. Dynamic models of steering and velocity control were identified and incorporated into the simulation. Result includes a stable operation of the steering without oscillating. The proposed algorithm can be implemented in microcontrollers without the need for high computing power.

Control Design and Assessment for a Reversing Tractor–Trailer System Using a Cascade Controller

In recent years, control design for unmanned systems, especially a tractor–trailer system, has gained popularity among researchers. The emergence of such interest is caused by the potential reduction in cost and shortage of number of workers and labors. Two industries will benefit from the advancements of these types of systems: agriculture and cargo. By using the unmanned tractor–trailer system, harvesting and cultivating plants will become a safe and easy task. It will also cause a reduction in cost which in turn reduces the price on the end consumers. On the other hand, by using the unmanned tractor–trailer system in the cargo industry, shipping cost and time for the item delivery will be reduced. The work presented in this paper focuses on the development of a path tracking and a cascaded controller to control a tractor–trailer in reverse motion. The path tracking controller utilizes the Frenet–Serret frame to control the kinematics of the tractor–trailer system on a desired path, while the cascade controller’s main objective is to stabilize the system and to perform commands issued by the path tracker. The controlled parameters in this proposed design are the lateral distance to a path, trailer’s heading angel, articulated angel, and articulated angle’s rate. The main goal of such controller is to follow a path while the tractor–trailer system is moving in reverse and controlling the stability of the articulated vehicle to prevent the occurrence of a jackknife incident (uncontrolled state). The proposed controller has been tested in a different scenario where a successful implementation has been shown.

Leader–follower formation with reduction of the off-tracking and velocity estimation under visibility constraints

This article addresses the time-varying leader–follower formation control problem for nonholonomic mobile robots, under communication and visibility constraints. Although the leader–follower formation control under visibility constraints has been studied, the elimination of the off-tracking effect has not been widely addressed yet. In this work, a new method to eliminate the off-tracking effect, considering the time-invariant formation as a tractor–trailer system, for unknown and circular tractor paths, taking into account the visibility constraints, is proposed. For a time-varying formation with not circular tractor’s path, the proposed method significantly reduces the off-tracking. Only the relative position and the relative orientation, provided by the on board monocular camera, are required. Thus, both the leader robot’s absolute position and the leader robot’s velocities are not needed. Furthermore, to avoid explicit communication among the robots, an extended state observer is implemented to estimate both the translational and the rotational leader’s velocity. In this way, the desired tasks are executed and achieved in a decentralized manner. For a time-varying formation, with constant leader robot’s velocities, the proposed control strategy, based on the kinematic model, guarantees that the formation errors asymptotically converge to the origin. Based on the Lyapunov theory, the stability proof of the formation errors dynamics is shown. Simulation results, considering time-varying leader robot’s velocities, show the efficiency of the proposed scheme.

Hitch Angle Estimation of a Towing Vehicle With Arbitrary Configuration

In this paper, ultra-sonic sensors along with kinematics and dynamics equations of a towing vehicle are used to develop three approaches for hitch angle estimation. The first approach is based on direct calculation of hitch angle using certain a priori geometric information and distance measurements of four ultra-sonic sensors. An angle estimate is generated for each of the six possible sensor-pair combinations, and these six estimates are passed through a voting algorithm to produce a single estimate. As the second and third approaches, kinematic and dynamic models of the tractor-trailer system are used to develop least-squares and Kalman filtering based recursive hitch angle estimations. A more reliable hitch angle estimation scheme is then proposed as the integration of the algorithms developed following each of the three approaches via a switching data fusion logic. It is shown that the proposed integrated hitch angle estimation scheme can be used for any ball type box trailer with a flat or symmetric V-nose frontal face without any priori information on the trailer parameters. Based on the validity of the assumptions, the proposed scheme can estimate the hitch angle in both low-speed using the kinematic model, and high-speed using the dynamic model of the tractor-trailer system. Experimental results corroborate the algorithms in estimating the hitch angle estimates in various cases conducted in this study.

A Novel EPT Autonomous Motion Control Framework for an Off-Axle Hitching Tractor-Trailer System With Drawbar

A tractor-trailer system is an underactuated system that is subject to nonholonomic constraints and exhibits extremely nonlinear behaviors. Its trajectory planning and control issues remain widely researched. In this paper, on the basis of establishing a precise kinematic model, a novel method is proposed to realize autonomous motion control of an off-axle hitching tractor-trailer system with a drawbar. The proposed method is roughly divided into three steps: EXTRACTING (E) a virtual subsystem, trajectory PLANNING (P) for the original full system, and trajectory TRACKING (T) by feedback control techniques, thus the “EPT method”. In the E step, two alternative strategies are considered to construct a virtual subsystem by extracting a part of an original towed aircraft system. Then, in the P step, a two-layer optimal control-based method is developed to generate a reference trajectory. A trajectory for the virtual subsystem is generated in the first layer, where the Reeds-Shepp curve with artificial expertise in selecting intermediate nodes is introduced to provide initial guesses. The results obtained in the first layer are utilized to initialize partial state and control variables in the trajectory planning for the original full system in the second layer. Finally, in the T step, a receding horizon controller is designed to drive the carrier aircraft to track the reference trajectory under various external disturbances. Numerical simulations demonstrate that the EPT method is applicable and highly efficient. The proposed method is also applicable for generalized tractor-trailer systems and other chain-link systems.

Adaptive Backstepping Sliding Mode Control of Tractor-trailer System with Input Delay Based on RBF Neural Network

In this paper, an adaptive sliding mode neural network(NN) control method is investigated for input delay tractor-trailer system with two degrees of freedom. An uncertain camera-object kinematic tracking error model of a tractor car with n trailers with input delay is proposed. Radial basis function neural networks(RBFNNs) are applied to approximate the unknown functions in the error model. A sliding mode surface with variable structure control is designed by using backstepping method. Then, an adaptive NN sliding mode control method is thus obtained by combining Lyapunov-Krasovskii functionals. The controller realizes the global asymptotic trajectories tracking of the kinematics system. The stability of the closed-loop system is strictly proved by the Lyapunov theory. Matlab simulation results demonstrate the feasibility of the proposed method.

Model predictive driving for tractor-trailer system with omni-directional tractor

Model predictive driving for tractor-trailer system with omni-directional tractor

Quintic Polynomial-based Obstacle Avoidance Trajectory Planning and Tracking Control Framework for Tractor-trailer System

In this paper, a dynamic automatic obstacle avoidance trajectory planning and tracking control framework is proposed for tractor-trailer system. Tractor-trailer is a special class of multibody and nonholonomic system, whose backward and forward operations have difference kinetic mechanisms. Because the obstacle avoidance behaviors are concerned with the two motion modes, the kinematic models including backward and forward movements are firstly derived. Secondly, a time-based quintic polynomial function is developed to plan two kinds of dynamic obstacle avoidance trajectories based on dynamics constraints and the information from on board sensors, so as to minimize the collision risk. Thirdly, a model predictive control (MPC)-based posture controller is designed, by which better tracking performance can be achieved for both forward and backward obstacle avoidance maneuvers. Lastly, the simulation results validate the effectiveness of the proposed dynamic obstacle avoidance framework and the designed methods.

Trajectory planning and tracking control for towed carrier aircraft system

As an efficient and safe dispatching scheme is of great importance to ensure the effectiveness and safety of personnel on the Aircraft Carrier, and the towed aircraft system without bar is a common means of dispatching, the dispatching of the system is a significance and interesting question. In this paper, the towed carrier aircraft system without bar is transformed into a tractor–trailer system, and the nonlinear motion constraint is proposed. In order to improve the efficiency and safety of dispatching, the trajectory-planning and tracking of the system are studied, respectively. Obstacles in the environment and the nonlinear motion constraints are taken into consideration, the trajectory-planning is transformed into the optimal control problem, and combined with the symplecticity and pseudospectral method, an offline optimal control algorithm with high efficiency is proposed firstly. In order to accurately track the obtained trajectory, an online tracking method is proposed based on the receding horizon control (RHC) theory and the offline optimal control algorithm. Finally, the offline trajectory-planning algorithm has been proved by simulation experiment, it shows that the algorithm has high computational efficiency and good applicability. And the system can track the standard trajectory, even though there are disturbances in the environment, with high precision using the online tracking method, the calculation efficiency is also verified, and real-time tracking can be achieved.

Use of Liquefied Biomethane (LBM) as a Vehicle Fuel for Road Freight Transportation: A Case Study Evaluating Environmental Performance of Using LBM for Operation of Tractor Trailers

The environmental performance of Liquefied Biomethane (LBM) and Diesel operated Tractor Trailer (TT) is compared using the Life Cycle Assessment (LCA) study. In this study we consider, raw biogas produced from an anaerobic digestion process of a Wastewater Treatment Plant (WWTP) in Umea, Sweden, which is then upgraded and liquefied to LBM and used as a fuel for TTs. Currently, the WWTP in Umea is utilizing biogas, produced onsite for cogeneration of heat and electricity, thereby meeting its energy needs. A system expansion approach is applied where electricity and heat equivalent to amount of biogas displaced for LBM production is supplied from Swedish grid (SE) mix and incineration of wood chips respectively. Correspondingly, the biogas avoided for cogeneration of electricity and heat is accounted in the study. The equivalent functional unit chosen for the LCA study is “16,000,000 ton-km of a TT transporting products and goods”. The study is modelled using SimaPro LCA Software. The ReCiPe Midpoint (H) impact assessment methodology is used to quantify ten selected and relevant midpoint environmental impacts. When compared with Diesel TT system, LBM TT exhibits superior environmental performance in seven out of ten impact categories measured than the Diesel TT system. The highest reduction is seen in Global Warming Potential (GWP) and Fossil Depletion Potential (FDP) impacts thereby suggesting that LBM derived from raw biogas of WWTP an environmentally preferred alternative to diesel for operation of TTs. However, this value proposition can have other trade-offs such as increase in eutrophication and ecotoxicity impacts. Further, replacing diesel with LBM for TT operation may not have any significant environmental benefits when electricity is drawn from carbon intensive grid mixes (e.g. coal).

Soil mechanical stresses in high wheel load agricultural field traffic: a case study

Subsoil compaction is a serious long-term threat to soil functions. Only a few studies have quantified the mechanical stresses reaching deep subsoil layers for modern high wheel load machinery. In the present study we measured the vertical stresses in the tyre–soil contact area and at 0.3, 0.6 and 0.9 m depths of a sandy loam soil at field capacity water content. The soil was ploughed annually to a depth of 0.25 m and was tested in the spring following autumn ploughing but before secondary tillage. The machinery tested was a tractor–trailer system for slurry application with a total weight of 52 Mg. Wheel loads ranged from approximately 20 to 70 kN. The tyres were all radial ply with volumes ranging from 0.63 to 1.23 m3. The tyre inflation pressures were generally above those recommended by the manufacturer and ranged from 170 to 280 kPa. The stress distributions in the contact area were highly skewed. Across tyres, the maximum stress in the contact area correlated linearly with, but was much higher than, the mean ground pressure. For each of the three soil depths, the maximum stresses under the tyres were significantly correlated with the wheel load, but not with other loading characteristics. The data predict a 6.6-kPa increase in vertical stress at 0.9 m depth for each 1-Mg addition to the wheel load. The soil stress observations support a simple rule of thumb combining wheel load and inflation pressure in calculation of subsoil vertical stress. We measured vertical stresses up to 300, 100 and 45 kPa at soil depths of 0.3, 0.6 and 0.9 m respectively. Comparing these with the data in the literature regarding soil strength and measured compaction effects on the soil studied, we conclude that the traffic event investigated is likely to induce serious effects on soil properties and functions to a depth of at least 0.7 m.

Navigation of autonomous tractor for orchards and plantations using a laser range finder: Automatic control of trailer position with tractor

The autonomous control of a tractor-trailer system in orchards and plantations has frequently been observed for the transportation, loading and unloading of products between plants and trees. The objective of this research was to develop a control algorithm for a single-sensor tractor-trailer navigation system for navigating within a row plantation and travelling between plots. A control scheme for stopping the tractor-trailer for various in-field tasks, such as product loading/unloading using a laser range finder (LRF), is presented. The LRF was used to navigate a full-size autonomous agricultural tractor equipped with a two-wheeled trailer. For ease of operation in narrow rows, a sliding hitch bar (SHB) was developed to control the trailer by adjusting the position of the hitch-point between the tractor and trailer. Compared to the tractor-trailer system driven by human, the control system could navigate the tractor-trailer with the RMS differences of 0.275 m (SD: 0.009 m), 0.373 m (SD: 0.030 m) and 0.518 m (SD: 0.022 m) for wide curve , tight curve and U-turn experimental paths, respectively. The SHB unit also supported the navigation system with wider turn for the trailer than conventional single hitch point about 0.383 m (7.66% of the 5 m path width, SD: 0.028 m), 0.762 m (15.23% of 5 m path width, SD: 0.010 m) and 1.094 m (21.88% of 5 m path width, SD: 0.037 m) for wide curve , tight curve and U-turn experimental paths, respectively. The control system also stopped the tractor-trailer at the specified landmarks. The results show that the navigation of the tractor-trailer was demonstrated with satisfactory accuracy and that the trailer position was controlled by the SHB with a wider turn in the experimental paths. Therefore, this laser-based landmark navigation system, and the SHB unit, can be adopted for different applications of autonomous tractor-trailer systems with controlled trailer positioning.

Robust Trajectory Tracking Error Model-Based Predictive Control for Unmanned Ground Vehicles

This paper proposes a new robust trajectory tracking error-based control approach for unmanned ground vehicles. A trajectory tracking error-based model is used to design a linear model predictive controller and its control action is combined with feedforward and robust control actions. The experimental results show that the proposed control structure is capable to let a tractor-trailer system track both linear and curvilinear target trajectories with low tracking error.

Effect of Lateral Slope and Loading Pattern on Static Stability of Single Axle Trailer

Single axle trailers are most common means of transportation in rural areas. For maintaining stability of tractortrailer system, it is necessary to ascertain different factors and forces which disturb equilibrium during transportation. The effect of operating conditions and design parameters of single axle trailers on its stability were analysed using scaled physical model under static conditions. Static load tests on varying slopes were carried out using scaled physical model to determine the variation in load pattern on the trailer tyre and its hitch point. The angle of inclination along with the normal load influenced the load shift from outer wheel to inner wheel, causing instability of the tractor-trailer system. The axle position had a paramount effect on vertical hitch load. Hitch length and axle position were two major design considerations that ensured proper distribution of normal load. A normal load less than 4273 N, and the centre axle position of trailer was safe operating conditions for tractor-trailer system at lateral slope (angle of inclination) of less than 15 degrees.

Robust Tube-Based Decentralized Nonlinear Model Predictive Control of an Autonomous Tractor-Trailer System

This paper addresses the trajectory tracking problem of an autonomous tractor-trailer system by using a decentralized control approach. A fully decentralized model predictive controller is designed in which interactions between subsystems are neglected and assumed to be perturbations to each other. In order to have a robust design, a tube-based approach is proposed to handle the differences between the nominal model and real system. Nonlinear moving horizon estimation is used for the state and parameter estimation after each new measurement, and the estimated values are fed to robust tube-based decentralized nonlinear model predictive controller. The proposed control scheme is capable of driving the tractor-trailer system to any desired trajectory ensuring high control accuracy and robustness against neglected subsystem interactions and environmental disturbances. The experimental results show an accurate trajectory tracking performance on a bumpy grass field.