This paper proposes a novel parallel robot - Virtual Ground Robot (VGR) - that is driven by three Series Elastic Actuators (SEAs) to interact with a human. The proposed Virtual Ground Robot provides a virtual ground on which a human can stand on and interact in three directions: the pitch, the roll and the height directions. The most significant features of the proposed VGR are that 1) it is driven by RFSEAs (Reaction Force-sensing Series Elastic Actuator), and thus it can provide precise forces and torques, 2) the size of the VGR is small enough for a human to stand on with ease, and 3) it can generate torque/force large to support a weight of a human. Taking advantage of RFSEAs utilized in the proposed VGR, Spatial Force control algorithm is proposed in this paper. In order to design this controller, the motions of VGR are defined in the task space, the joint space and the RFSEA level. Based on the Kinematics, force control of VGR in the task level, which is named Spatial Force Control is designed and verified using experiments.