This paper addresses a problem of complete sensing coverage in 3D environments. We propose a distributed random algorithm to drive mobile robotic sensors on the vertices of a truncated octahedral grid for complete sensing coverage of a bounded 3D area. Furthermore, we develop a distributed algorithm for the self-deployment of mobile sensors to form a desired 3D geometric shape on the vertices of the truncated octahedral grid. These algorithms are developed based on some consensus rules that only rely on local information. The proposed algorithms utilize 3D grids for the coverage task. Several simulations are conducted to illustrate the validity of the proposed distributed sensing coverage and formation building algorithms for a mobile robotic sensor network. Also, we give mathematically rigorous proof of the convergence with probability 1 of our proposed algorithms.
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