Gathering of Opaque Robots in 3D Space

Gathering is a fundamental coordination problem for multi-robot systems. This paper presents a study of the gathering problem for a set of oblivious, autonomous mobile robots in the three dimensional Euclidean space, under obstructed visibility model. In this model, robots are considered to be opaque. Robots may not have the complete view of the configuration. This paper assumes only an agreement on the direction and orientation of one coordinate axis. A distributed algorithm is proposed to solve the gathering problem for a set of asynchronous robots, when the system does not contain any faulty robot. Another distributed algorithm is presented to solve the problem for a set of semi-synchronous robots under crash fault model. The proposed algorithm can tolerate an arbitrary number of crash faults. Both algorithms work for an arbitrary initial robot configuration.