ARTICLE IN PRESS Robotics and Autonomous Systems ( ) – www.elsevier.com/locate/robot Trajectory tracking control of farm vehicles in presence of sliding H. Fang a,∗ , Ruixia Fan a , B. Thuilot b , P. Martinet b a Beijing Institute of Technology, 100081, Beijing, China b LASMEA, 24, av. des Landais, 63177 Aubiere Cedex, France Received 8 March 2005; accepted 26 April 2006 Abstract In automatic guidance of agriculture vehicles, lateral control is not the only requirement. Much research work has been focused on trajectory tracking control which can provide high longitudinal-lateral control accuracy. Satisfactory results have been reported as soon as vehicles move without sliding. But unfortunately pure rolling constraints are not always satisfied especially in agriculture applications where working conditions are rough and not predictable. In this paper the problem of trajectory tracking control of autonomous farm vehicles in the presence of sliding is addressed. To take sliding effects into account, three variables which characterize sliding effects are introduced into the kinematic model based on geometric and velocity constraints. With a linearized approximation, a refined kinematic model is obtained in which sliding effects appear as additive unknown parameters to the ideal kinematic model. By an integrating parameter adaptation technique with a backstepping method,a stepwise procedure is proposed to design a robust adaptive controller in which time-invariant sliding is compensated for by parameter adaptation and time-varying sliding is corrected by a Variable Structure Controller (VSC). It is theoretically proven that for farm vehicles subjected to sliding, the longitudinal-lateral deviations can be stabilized near zero and the orientation errors converge into a neighborhood near the origin. To be more realistic for agriculture applications, an adaptive controller with projection mapping is also proposed. Both simulation and experimental results show that the proposed (robust) adaptive controllers can guarantee high trajectory tracking accuracy regardless of sliding. c  2006 Elsevier B.V. All rights reserved. Keywords: Trajectory tracking control; Nonholonomic systems; Backstepping; Robust control 1. Introduction Automatic guidance of farm vehicles develops with the requirement of modern agriculture. High-precision agriculture becomes a reality especially thanks to new localization technologies such as GPS, laser range scans and sonar. In agriculture fields it is quite common that several vehicles (including cropping, threshing, cleaning, seeding and spraying machines) compose a platoon for combined harvesting. In this case driving safety requiring constant longitudinal distances between the leading vehicle and following vehicles is an additional requirement along with the effort of improving lateral path-following performances. Therefore vehicle motions are specified not only by a geometric path but also by a time law with respect to the longitudinal direction. Since ∗ Corresponding address: 1-20-505 Xi’an Jiaotong University, 710049 Xi’an, China. Fax: +86 10 68913261. E-mail address: fangqx@mail.xjtu.edu.cn (H. Fang). longitudinal-lateral control becomes more and more important, many research teams have paid their attention to trajectory tracking control, satisfactory results have been reported as soon as vehicles satisfy pure rolling constraints [1–7]. However due to various factors such as slipping of tires, deformability or flexibility of wheels, pure rolling constraints are never strictly satisfied. Especially in agriculture applications when farm vehicles are required to move on all-terrain grounds including slippery slopes, sloppy grass grounds, sandy and stony grounds, sliding inevitably occurs which deteriorates automatic guidance performance and even system stability. Until now there are very few papers dealing with sliding. [8] prevents cars from skidding by robust decoupling of car steering dynamics, but acceleration measurements are necessary and the steering angle is assumed small. [10] copes with the control of WMR (Wheeled Mobile Robot) not satisfying the ideal kinematic constraints by using slow manifold methods, but the parameters characterizing the sliding effects are assumed to be exactly known. Therefore [8,10] are 0921-8890/$ - see front matter c  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.robot.2006.04.011