Kinematic Analysis of a Skid-Steer Mobile Robot Operating on Non-Planar Surfaces

Mobile robotic systems are advancing manufacturing operations that generally exhibit less automation. Fields commonly experiencing a lesser degree of automation include shipbuilding, pipe inspection, and construction applications on non-planar surfaces. The mobile robotic systems operating in such environments are typically subjected to motion along non-planar surfaces and often assume climbing configurations when completing the desired tasks. These tasks are usually considered planar in nature, however, in practice the surface on which the tasks are completed is generally non-planar. The surfaces are commonly modeled as geometric shapes such as spheres or cylinders allowing for accurate surface representations. A common non-planar task is the welding of ship hulls. The process consists of welding segments together and is normally completed by a skilled laborer due to the curvature of the surface. Through the advancement of kinematic modeling of mobile robotic platforms there exists the ability to develop future robotic platforms with the potential to perform operations, in a task efficient manner, on non-planar surfaces. While the majority of kinematic models presented for mobile robots assume operation on planar surfaces, there have been a number of studies that consider the kinematic behavior on non-planar surfaces. This past work generally takes one of two approaches, either developing assumed modifications to the existing kinematic constraints as algebraic equations, or making use of a set of differential equations describing the instantaneous motion of the contact point between non-planar surfaces. The second approach is more general and has been shown to be applicable to both general and specific terrains. However, the previous work has focused solely on differential-steer platforms with a passive castor. Conversely, Skid-Steer mobile robots provide simple, robust platforms that have several features making them well suited to manufacturing tasks. This paper will present a kinematic model for an SSMR operating on a non-planar, nominally cylindrical surface. This method is readily generalized to other surface geometries. The method is based on a kinematic model consisting of a set of differential-algebraic equations with the differential equations derived from Montana’s contact equations and the algebraic equations arising from an instantaneous model of the SSMR as a hybrid mechanism consisting four, five-dof serial chains. The method is demonstrated over several applications and validated through comparison with a prototype system operating on a cylindrical tank. A discussion of the resulting approach and how this could be used in as a tool to guide the modeling and fabrication of future mobile manufacturing robot platforms is included. INTRODUCTION As mobile robots gain interest in various industries their incorporation into manufacturing applications is increasing in areas such as mobile inspection, welding, and painting, [1]. Research focusing on applications within these areas has typically been driven by the need to control the desired path in order to complete the required task at hand. The advanced control strategies needed to accommodate such motion has greatly improved in part due to continued research in the area of mobile kinematics and dynamics. This research has allowed for the development of robust models to accurately predict the behavior of the robotic platform as it navigates along a desired path. Typically, robotic topologies incorporate wheels enabling mobility, therefore rolling motion has been widely studied [2-3]. The primary constraints for this rolling motion is provided by the contact point between the wheels and the surface. Tracked mobile robots are also widely studied in the literature [4-7] and make use of an approach similar in nature to the rolling motion of wheels, [4]. The models for wheeled vehicles rely on the pure roll and no slip assumptions, which is valid when dynamic effects are minimal, however, in the case of tracked vehicles it is accepted that slipping occurs between the tracks and terrain, therefore the pure roll and no slip assumptions are not valid, [8-10]. The consideration of slip has been focused on by many works, [11-12], and is often incorporated into the kinematic models for the differential, skid, and omni-directional robot platforms, [12-14]. While these techniques are quite useful, their main limitation is the surface of operation. Typically mobile robot operation is assumed to occur on a planar surface