High-resolution orbital imagery from the LROC reveals evidence of subsurface voids and mare-pits on the lunar surface. Similar discoveries have been made with the HiRISE camera onboard the MRO observing the Martian surface. These accessible voids could be used for a future human base because they offer a natural radiation and micrometeorite shield and offer constant habitable temperatures. Exploration of these extreme and rugged environments remains out of reach from current planetary rovers and landers. A credible solution is to develop an architecture that permits taking high exploratory risks that translates into high reward science. Rapid advancement in electronics, sensors, actuators, and power have resulted in ever-shrinking devices and instruments that can be housed in small platforms. We propose to use a small, low-cost, modular spherical robot called SphereX that is designed to hop and roll short distances. Each robot is of several kilograms in mass and several liters in volume. Each SphereX will consist of space-qualified electronics like command data handling board, power board for power management and s-band radio transceiver for communication. Power is provided using lithium-ion primary batteries or a PEM fuel cell power supply. Communication is established through multi-hop communication link to relay data from inside the caves to a lander outside on the planetary surface. Since the temperature inside underground lunar pits is expected at -25°C, thermal management for the space-grade electronics is minimal as they can operate up to -40°C, however thermal management for the battery pack and the propellants will be done through active and passive elements. Moreover, SphereX requires use of a propulsion system and Attitude Determination and Control System (ADCS) to perform controlled ballistic hops. Hopping on very-low gravity environments is more time-efficient than rolling due to the reduced traction. In this paper, we present detailed analysis of each subsystem of SphereX and also detailed dynamics and control simulations of SphereX for ballistic hopping and rolling mobility. For ballistic hopping control, the robot has two modes: soft landing mode for traversing long distances and entering the pit through its collapsed entrance, and a fuel-efficient hard landing mode for traversing short distances. We will then present experimental results for mapping unknown cave-like environments which is done using a quadcopter for simulating low-gravity (e.g. Moon, Mars) environments and testing the control algorithms. The quadcopter mimics the dynamics of SphereX and also carries a 3D LiDAR for mapping and navigation. 3D point cloud data collected by the LiDAR is used for performing SLAM and path planning in unknown and GPS-denied environments much like the pits, caves and lava tubes on the Moon and Mars.