Kinematic analysis and control of a mobile robot performing manufacturing tasks on non-planar surfaces using differential geometry

As mobile robotic systems advance, they become viable technologies for automating manufacturing and industrial processes which have lacked automation in the past. These fields include shipbuilding, windmill construction, tank or pipe inspection, and even construction on non-planar surfaces such as pipes. These mobile platforms must operate in specific climbing configurations and are usually operated on non-planar surfaces when completing the desired task. The operations are commonly considered in a planar context however in practice the tasks are performed on generally non-planar surfaces. The typical non-planar surfaces consist of common geometric shapes such as cylinders or spheres and as such allow for an accurate representation of the surface to be developed. A common example of a non-planar task is the welding performed on ship hulls. These hulls are created by welding large segments together but due to the curvature of the surface the welding usually performed by a laborer. By advancing mobile robots the ability to weld on these non-planar surfaces would increase efficiency, reduce cost, and reduce any harmful impacts to laborers. This thesis will present a kinematic model and analysis of a differential steer robot performing specified tasks on cylindrical surfaces. The analysis will define a method to determine the robot path on a work-piece surface as well as the configuration joint parameters along when the motion is prescribed in local tool space coordinates. This thesis will also present a kinematic controller which allows a variety of common manufacturing paths to be followed while completing tasks encountered when working on non-planar surfaces. The method employed assumes operation following the no-slip, pure roll conditions. The effort is motivated by a practical application of welding on steel hulls or other non-planar surfaces.