# Control Design and Assessment for a Reversing Tractor-Trailer System Using a Cascade Controller
## 1 Introduction  
Unmanned tractor-trailer systems are on the rise and current research focuses on increasing the safety of such systems. One of the main research problems in these systems is driving in a reverse direction. The main concern is to prevent the system from entering an uncontrollable mode known as jackknifing. Jackknifing is caused by exceeding the articulation angle i.e., the angle between the tractor and the trailer exceeds the derived limits in which it renders the system to be maneuverable. Other research interests are in improving the control system for the backward movement of the tractor-trailer and/or implementing safety features that aid in preventing the occurrence of a jackknifing. In recent years, the unmanned tractor-trailer system has gained popularity in fields like agriculture and cargo shipping [1]. In 2019, UPS has announced that they had been testing unmanned tractor-trailer system with the autonomous driving company TuSimple. The two companies have tested the system on a route in the State of Arizona in the USA. The system is a Level 4 Autonomous system in which the onboard computer is complete control of the system all the time and there is a driver within the system to interfere if needed. TuSimple claims that this technology is estimated to reduce the shipping cost by 30% when shipping through an unmanned tractor-trailer system. In Aug. 2019, UD trucks, a unit of Volvo Group, has showcased a Level 4 Autonomous truck in Hokuren Sugar Refining Mill in Nakashiri, Hokkaido Japan [2]. The unmanned truck system developed byUD uses a network-based Real-Time Kinematic GPS (RTK-GPS) fused with other sensors that give high accuracy localization. The system was showcased by operating on a delivery route from the factory entrance to the acceptance area, storage and the unloading area. The average speed of the unmanned system was 20 kph., and part of the traveled route was a public road. The main reason that caused a spike in such research is caused by labor cost and shortage. In a study developed by the California Farm Bureau Federation, it was shown that 69% of the 762 farmers that responded to the survey are experiencing a shortage of labor [3]. The survey has noted that surveyed farmers intend to mechanize cultivation and harvesting process. Two-thirds of the farmers surveyed have reported the utilization of mechanical utilities to aid in farming. Japan has also suffered from labor shortage. To increase farming efficiency in Japan, ref. [4] has proposed a two-tier linear backward path following controller to park an autonomous tractor-trailer system with off-axle hitching. The proposed controller issues curvature commands based on the path-following error. In the second layer, the curvature commands are then converted into steering commands using a servo loop. Several works on path tracking algorithms in general fields and in the field of tractor-trailer controller have been reviewed to formulate the solution proposed in this paper. Using non-linear control design and a designed virtual target, ref. [5] was able to control a nonholonomic mobile robot. The controllers in the study were applied to two-wheel driven cart. In [6], a Lyapunov approach was used to stabilize the distance to the path and the orientation for unicycle-type mobile robot and in [7], it was used on a tractor-trailer system. Using time scale transformation and exact linearization, ref. [8] developed a path following controller for an articulated vehicle. A generic control safety governor was developed in [9] and is used to prevent the occurrence of jackknife in a reversing tractor-trailer. The governor overrides the controller command when a controller command will cause a jackknife incident. The governor was tested on three different controllers (proportional integral controller, a sliding mode controller and a neural network controller) in [10].