Although the kinematics and dynamics of spherical robots (SRs) on flat horizontal and inclined 2D surfaces are thoroughly investigated, their rolling behavior on generic 3D terrains has remained unexplored. This paper derives the kinematics equations of the most common SR configurations rolling over 3D surfaces. First, the kinematics equations for a geometrical sphere rolling over a 3D surface are derived along with the characterization of the modeling method. Next, a brief review of current mechanical configurations of SRs is presented as well as a novel classification for SRs based on their kinematics. Then, considering the mechanical constraints of each category, the kinematics equations for each group of SRs are derived. Afterward, a path‐tracking method is utilized for a desired 3D trajectory. Finally, simulations are carried out to validate the developed models and the effectiveness of the proposed control scheme.

Methanol is a key component in producing formaldehyde, acetic acid, and methyl tert-butyl ether (MTBE) and supports a wide array of industries, including plastics, textiles, and automotive. It also plays a growing role in renewable energy solutions. However, the conventional production of methanol involves steam reforming of methane, which is very energy-intensive and produces significant quantities of the greenhouse gas carbon dioxide. In this research, a chemical looping scheme is combined with dry reforming of natural gas in a novel microwave reactor to produce an industrial quantity of methanol. A heat exchanger network is developed to substantially reduce hot and cold utility usage. The effect of the cost of purchasing carbon dioxide from an external source for dry reforming, the capital cost of the microwave reactor, and the cost of electricity on the net present value is analyzed. Technoeconomic comparison with the conventional industrial process that produces methanol via steam reforming of methane indicates that the chemical looping generates a significant positive net present value along with a substantial reduction in carbon dioxide emissions while producing methanol significantly below the U.S. Department of Energy’s goal of $800/ton.