Robot Dash and its control methodWe present a novel and minimalistic design of an aerial-terrestrial robot DASH-Ducted Aerial Spring Hopper. The goal is to enable both aerial and ground locomotion capabilities on a unified mobile robot that is mechanically-minimalistic, locomotion-versatile, and energy-efficient. We propose an organic integration of ducted fan co-axial body with a springy leg at the bottom for realization. The ducted fan module provides thrust-vectoring as the main actuation for agile flying; when it is combined with the light-weight spring leg, the robot realizes highly efficient ground hopping with energy circulation. Moreover, to realize optimal locomotion with two modes, we employ a contact-implicit model predictive control to automatically choose locomotion modes and actuation. We successfully validated the design and control of DASH through a range of tasks, including periodic hopping, aerial flight, and mode-free locomotion with autonomous mode transitions during obstacle traversal.