  There are thousands of asteroids in near-Earth space and millions in the Main
Belt. They are diverse in physical properties and composition and are time
capsules of the early solar system. This makes them strategic locations for
planetary science, resource mining, planetary defense/security and as
inter-planetary depots and communication relays. However, asteroids are a
chal-lenging target for surface exploration due it its low but highly nonlinear
gravity field. In such conditions, mobility through ballistic hopping possess
multiple advantages over conventional mobility solutions and as such hop-ping
robots have emerged as a promising platform for future exploration of asteroids
and comets. They can traverse large distances over rough terrain with the
expenditure of minimum energy. In this paper we present ballistic hopping
dynamics and its motion planning on an asteroid surface with highly nonlinear
gravity fields. We do it by solving Lambert's orbital boundary val-ue problem
in irregular gravity fields by a shooting method to find the initial velocity
required to intercept a target. We then present methods to localize the hopping
robot using pose estimation by successive scan matching with a 3D laser
scanner. Using the above results, we provide methods for motion planning on the
asteroid surface over long distances. The robot will require to perform
multiple hops to reach a desired goal from its initial position while avoiding
obstacles. The study is then be extended to find optimal tra-jectories to reach
a desired goal by visiting multiple waypoints.

Robotics;Earth and Planetary Astrophysics;Instrumentation and Methods for Astrophysics