Abstract—This paper embraces the problem of controlling backward movements of multi-trailer systems (in present case trucks with three and four trailers) by the means of fuzzy logic. It is shown that decomposition of the problem is a great help when finding the solution, however, as the number of trailers increases, it becomes increasingly complex to find a satisfying solution as the control object itself becomes less and less controllable. I. INTRODUCTION NYONE who has ever tried backing up a car with a trailer knows how complicated it is and how easily it can go wrong. In fact, even experienced drivers have difficulties and will need to go forward and backward numerous times in order to position the truck at the dock properly. If the driver is not allowed to make forward movements, successful backing becomes unlikely. One particularly nasty property of the truck backer-upper is so called jackknifing that means a condition where the cab and trailer are jammed together at 90. Once it occurs the control over the system is lost so understandably it is very important to avoid jackknifing that actually can happen very easily when backing the truck. Due to its interesting properties, truck backer-upper has appeared as a test object in a large number of scientific contributions [1-14] since its introduction in the paper of Nquyen and Widrow [15]. Very few researchers, however, have ventured outside the scope of the original problem, i.e. tried their luck on backing up the trucks with more trailers than just one. Although backing of multi-trailer systems has perhaps little practical significance (the trailers can be detached and backed individually if the need arises), it is nonetheless a very challenging control problem (and increasingly complex one as the number of attached trailers grows) that can be investigated just for the fun of that. The most outstanding attempts of handling multi-trailer systems that can be found in scientific literature are probably presented in the works of Tanaka et al. [16-18], where they have managed to maintain control over the systems with no less than 10 trailers by representing the vehicle model by a Takagi-Sugeno fuzzy model and then solving the controller Andri Riid is with the Department of Computer Control of Tallinn University of Technology, Ehitajate tee 5, Tallinn 19086, Estonia (phone: +372-6202-109; fax: +372-6202-101; e-mail: andri@dcc.ttu.ee). Jaakko Ketola is with Lappeenranta University of Technology Laboratory of Applied Mathematics, P.O. Box 20, FIN-53851 Lappeenranta, Finland (e-mail: jaakko.ketola@lut.fi). Ennu Rüstern is with the the Department of Computer Control of Tallinn University of Technology, Ehitajate tee 5, Tallinn 19086, Estonia (e-mail: ennu.rystern@dcc.ttu.ee). design problem in terms of linear matrix inequalities. However, the control goal in these contributions has been restricted to stabilizing the system along the x-axis. In our previous works [19-22], on the other hand, we have worked on a knowledge-based fuzzy control approach to obtain a controller capable of backing the truck from virtually arbitrary initial position to a freely chosen destination. The key idea is to decompose the control task in a manner what would facilitate efficient control knowledge acquisition and would result in improved control quality. Initially this principle was applied to the simplest case of backing control – a trailerless truck [19]. In subsequent papers we have managed to show that the approach similarly works with more complex cases of truck backing – one trailer truck in [20] and two-trailer system in [21]. Although the approach stems from the paradigm of knowledge-based control – its efficiency is dependent on the designer abilities and stability conditions cannot be shown explicitly - it highly benefits from the hierarchical structure of the control system that helps us to focus our knowledge and common sense- based reasoning and has so far produced successful results. The logical next step is to extend the approach to even more complex cases of multi-trailer systems. While we are able to find the solutions for three- and four-trailer systems in current paper, it turns out that it becomes more and more difficult to find a satisfying solution both in terms of maneuverability and stability as the number of trailers grows (each additional trailer increases the potential for jackknifing), which implies that apparently, the potential of given approach has been thoroughly exhausted. II. SYSTEM DEFINITION The driving system (or the car as we shortly address it throughout the paper) consists of the cab part and N attached trailers (Fig. 1) and is described by N + 3 state variables – the coordinates (x, y) of the reference point placed at the end of the last (N-th) trailer and 0, 2, 4, …, 2N that are the angles between the x-axis and car components - the cab part, first trailer, second trailer, third trailer etc., up to the N-th trailer. These angles are shortly addressed as orientations of respective components of the car in this paper. The length (l) and the width (w) of the cab part are both 2m and the dimensions of trailers are 24m. The main challenge is to design a control system that is able to provide an appropriate steering angle  throughout the backing cycle so that the car will ultimately be positioned at x = xf, y = yf , at the expected angle 2N = f (that defines the loading dock). Fuzzy Knowledge-Based Control for Backing Multi-Trailer Systems Andri Riid, Jaakko Ketola and Ennu Rüstern, Member, IEEE A