Missions targeting extreme and rugged environments such as caves, canyons, cliffs and crater rims of the Moon, Mars and icy moons are the next frontiers in solar system exploration. Exploring these sites will help ascertain the range of conditions that can support life and identify planetary processes that are responsible for generating and sustaining habitable worlds. Current landers and rovers are unable to access these areas of high interest due to limitations in precision landing techniques, need for large and sophisticated science instruments and a mission assurance and operations culture where risks are minimized at all costs. This research proposes using multiple spherical robots called SphereX for exploring these extreme environments. The design of SphereX is a complex task that involves a large number of design variables and multiple engineering disciplines. The methodology developed in this work uses Automated Multidisciplinary Design and Control Optimization (AMDCO) techniques to find near optimal design solutions in terms of mass, volume, power and control for SphereX for different mission scenarios. The implementation of AMDCO for SphereX design is a complex process because of complexity of modelling and implementation, discontinuities in the design space, and wide range of time scales and exploration objectives. We address these issues by using machine learning in the form of Evolutionary Algorithms integrated with gradient-based optimization techniques to search through the design space and find pareto optimal solutions for a given mission task. The design space is searched using a GA multi-objective optimizer at the system (global) level to find the Pareto-optimal results while gradient-based techniques are used to search at the discipline (local) level. The modeled disciplines are mobility system, power system, thermal system, shielding, communication system, avionics and shell. Using this technology, it is now possible to perform end to end automated preliminary design of planetary robots for surface exploration.