Sideslip angles observer for vehicle guidance in sliding conditions: Application to agricultural path tracking tasks Roland Lenain ⋄ , Benoit Thuilot ⋆ , Christophe Cariou ⋄ , Philippe Martinet ⋆ ⋄ Cemagref ⋆ LASMEA BP50085 - 24, av. des Landais 24, av. des Landais 63172 Aubi` ere Cedex France 63177 Aubi` ere Cedex France roland.lenain@cemagref.fr benoit.thuilot@lasmea.univ-bpclermont.fr Abstract— Automatic devices dedicated to vehicle guidance in off-road conditions are necessarily confronted with sliding phenomenon, since it may considerably damage the accuracy of the following task. Control laws taking explicitly into account such a phenomenon have already been designed in previous work. They can actually improve the guidance accuracy. However their efficiency is highly dependent on the sliding parameters estimation (since these parameters cannot be provided by a direct measurement). In this paper, an observer-like estimator is designed, providing sideslip angles from a single exterocep- tive sensor, namely a Real Time Kinematic GPS (RTK-GPS). Improvements in guidance accuracy, with respect to previous estimation approaches, is demonstrated through full scale exper- iments, addressing agricultural applications. I. I NTRODUCTION The growing accuracy requirements in agricultural tasks, with respect to pollution concerns, have generated many de- velopments in machinery dedicated to farm work. In particular, autonomously guided vehicles have appeared to be attractive since they allow to increase both repetitiveness and work accuracy (e.g. overlapping areas when spraying pesticides can be limited). In addition, the benefits of such automatic systems are also the reduction of work hardness (since the tracking task is achieved autonomously), and an improvement in safety. These numerous advantages and interests for the farmers have motivated increasing research and developments in this topic. Indeed, numerous systems are under development or have al- ready been marketed (e.g. CLAAS [2], John Deere [8], see also [9]). Most of these devices are relying on a GPS sensor, often associated with additional exteroceptive sensors, such as INS, laser, cameras, etc. (see for instance [5] and [10]). However, these systems have been designed to perform specific tasks (harvesting [2], achieving perfectly straight runs [8], etc.) and are not able to preserve a good tracking accuracy, out of their dedicated application field. Moreover, few of them are able to take into account for sliding phenomena, despite these effects inevitably occur during agricultural tasks (especially when operating on sloping fields or when performing half turns), and considerably damage the guidance accuracy (as has been pointed out for instance in [11]). Designing a versatile guidance control law achieving accurate path tracking, whatever the conditions of adherence and what- ever the path to be followed, is our current research interest. Moreover, it is desired that the autonomous vehicle relies only on one exteroceptive sensor (in our case, an RTK-GPS). In order to describe accurately the vehicle behaviour in presence of sliding, it would be natural to rely on a dynamic model (see for instance [3]). However, such models are large and therefore not very tractable from a control point of view. Moreover, they demand the knowledge of numerous varying parameters (such as wheel/ground conditions) that could not be obtained from our sensor configuration. Therefore, extended kinematic models have appeared to be more convenient with respect to our aims. On one hand, sliding phenomena can be described by few parameters. On the other hand, the powerful path tracking control laws designed from classical kinematic models (under rolling without sliding condition) can still be used as a basis to derive more accurate control laws accounting for sliding. Last developments demonstrate the relevance of this approach. However, the on-line estimation of the sliding parameters (required in the extended control law) is still a concern. A basic estimation algorithm can lead to a satisfactory tracking accuracy, despite sliding effects, except when the vehicles meet harsh conditions. In this paper, a convenient and reliable method for sliding parameters estimation is proposed, based on observer theory. When associated with extended control law, a path tracking accurate to within 15cm (compatible with farmers’ expecta- tions) is demonstrated, even in harsh conditions. This paper is organized as follows. Vehicle modelling in presence of sliding and control design relying on this model are first recalled but not detailed, as well as the previous algorithm used to estimate sliding parameters. Then, an observer-like estimator providing more relevant sliding parameters is described. Finally, capabil- ities and benefits of this observer are discussed through full- scale experiments. II. VEHICLE MODEL AND PREVIOUS WORK A. Notations Vehicle modelling is based on a classical kinematic model derived under rolling without sliding assumption (such as described in [14]), completed by two parameters inherited from a dynamic consideration and consistent with sideslip angles. This model is called “extended kinematic model” and can describe vehicle motion in presence of sliding. More precisely, two sliding parameters (β R P and β F P ) have been introduced. They are representative of the difference between the theoretical orientation of the speed vector at tyre centre (i.e the wheel orientation) and the actual one, as depicted on