Small-satellites are emerging as low-cost tools for performing science and exploration in deep space. These new class of space systems exploit the latest advances and miniaturization of electronics, computer hardware, sensors, power systems and communication technologies to promise reduced launch-cost and development cadence. These small-satellites offer the best option yet to explore some of the 17,000 Near-Earth Asteroids (NEA) and nearly 740,000 Main-Belt asteroids found. The exploration of these asteroids can give us insight into the formation of the solar-system, planetary defense and future prospect for space mining. Recent examples of asteroid/small-body missions target asteroids that are 100s of meters in length. Most of these discovered asteroids are 10s of meters in length and hence having the technology to explore them will open a new frontier in solar system exploration. However, these very small asteroids lack an accurate ephemeris and with current limitations in NASA's Deep Space Network (DSN) communication and tracking system, there is a 2-5 km uncertainty in distance between a spacecraft and a target. Some of these small-bodies are carbon-rich and have low-albedos that make them hard to find. However, it is these carbon-rich asteroids that are prime targets for solar-system origin studies and for asteroid mining. Overall, this presents a major navigations challenge. In this work, we develop a solution to the problem at hand. This encompasses integration of the right navigational instruments, detectors, attitude determination and control system, together with propulsion and software control system to autonomously search and 'home-in' on the target body. Our navigation approach utilizes an outward spiraling 'diamond maneuver'. The spacecraft spirals outwards if the small-body is not found in the volume enclosed. Once a small-body is found, the spacecraft performs gradient descent using its imagers to close-in on the small-body. In worst-case scenarios, visual techniques to detect occlusion or thermal imagery will be used to identify the target. Once found, the spacecraft performs a helical flyby maneuver to map the asteroid. The results point towards a promising pathway for further development and testing of our navigation technology aboard a demonstrator CubeSat.