Original Article Control of a tractor-trailer robot subjected to wheel slip Ali Keymasi Khalaji and Mostafa Jalalnezhad Abstract Tractor-trailer wheeled robots (TTWRs) are highly nonlinear and underactuated dynamical systems. It is necessary to use nonlinear control methods, for the control of wheeled robots. Back-stepping method is a Lyapunov-based systematic technique for designing nonlinear control algorithms. In this paper, an adaptive back-stepping controller is proposed for the TTWRs. The proposed algorithm uses an adaptive layout for the compensation of the system wheel slips, which updates controller parameters based on a combination of error signals and estimated uncertainties. This paper is one of the firsts to propose a control algorithm for off-axle TTWRs in the presence of wheel slips. The control algorithm is designed to track the reference trajectories and make the robot asymptotically stable around the reference trajectories. The stability of the method is proved using Lyapunov theory. In order to compensate the sliding of wheels as the system uncertainties, appropriate adaptive rules have been investigated. Obtained results demonstrate the efficiency of the proposed method. The results for the tracking control of the TTWR in the presence of wheel slips show that the slip effects are effectively compensated using the proposed adaptive back-stepping control algorithm. Keywords Tractor-trailer wheeled robot, trajectory following, adaptive back-stepping control, sliding of wheels Date received: 31 August 2018; accepted: 26 February 2019 Introduction Modeling and control of Wheeled Mobile Robots (WMRs) is one of the important challenges in the field of robotics. Based on the characteristics of WMRs, locomotion tasks can be performed faster with higher precision which require the design of non- linear control algorithms. 1 There exist unknown uncertainties and disturbances in real engineering sys- tems, therefore, the control algorithms should be cap- able of withstanding against these phenomena. Most of the previous works for the WMRs have assumed the ideal non-holonomic constraints assuming nonslip conditions on robot wheels. These constraints are not always realistic and they may be violated due to the deformation of the wheels or undesirable environmen- tal effects, such as frozen roads which are mostly inev- itable in real systems. If the uncertainties in the mathematical models are not taken into account, tracking control of the TTWRs may lead to instability or inaccurate results. Therefore, tracking control algorithms may represent undesirable performance, taking into account anomalies such as slipping of wheels. These uncertainties affect the control of Tractor-Trailer Wheeled Robots (TTWRs) which is focused in this paper. TTWRs have a variety of appli- cations from vehicle assistance systems in human transportations to intelligent and independent vehi- cles in automatic transmission and guidance systems. Various control algorithms have been examined for the control of WMRs but the researches on TTWRs are very limited. Control of a TTWR using linearization method is accomplished in DeSantis. 2 However, control of the last passive trailer trajectory is more important in applications. 3–5 Modeling and control of an n-trailer system using feedback linearization method is pro- posed in Keymasi Khalaji and Moosavian. 6 An adap- tive sliding-mode control is also presented in Keymasi Khalaji and Moosavian. 7 A survey in the control of TTWRs is elaborated in David and Manivannan. 8 Most of the proposed algorithms are on the ideal mathematical models and the number of researches on the uncertainty compensation such as slipping of wheels is much lower. Proc IMechE Part K: J Multi-body Dynamics 0(0) 1–12 ! IMechE 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1464419319839848 journals.sagepub.com/home/pik Faculty of Engineering, Department of Mechanical Engineering, Kharazmi University, Tehran, Iran Corresponding author: Ali Keymasi Khalaji, Faculty of Engineering, Department of Mechanical Engineering, Kharazmi University, No. 43. South Mofatteh Ave., Tehran 15719-1491, Islamic Republic of Iran. Email: keymasi@khu.ac.ir