Mobile robotic systems are advancing manufacturing operations in fields that generally exhibit less automation such as shipbuilding, pipe inspection, and construction applications on non-planar surfaces. Mobile robots operating in such environments are typically required to assume climbing configurations to complete desired tasks. These tasks are usually considered planar in nature, however, in practice are generally non-planar. A common task seen on non-planar surfaces is the welding of ship hulls. This process consists of welding segments together and is normally completed by a skilled laborer due to the complexity of the surface. Through the advancement of kinematic modeling of mobile robots there exists the ability to develop future platforms with the potential to perform efficient operations on non-planar surfaces. While the majority of kinematic models presented for mobile robots assume operations on planar surfaces, a number of studies consider kinematic behavior on non-planar surfaces. These past works generally take one of two approaches: 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 shown to be applicable for both general and specific terrains. However, the previous works main focus is on differential-steer platforms with a passive castor. Conversely, Skid-Steer mobile robots, (SSMR), 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 spherical surface with a method readily generalized to other surface geometries.

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