The formation control of mobile underwater wireless sensor networks (MUWSNs) is difficult due to the severe errors in distance and motion measurements. To address this problem, we propose a new scheme, TRiForm, for the distributed formation control of an MUWSN. TRiForm constructs a rigid graph virtual structure from triangles to improve the reliability and efficiency. TRiForm effectively utilizes anchor information to detect and compensate for measurement errors. We have proven the correctness of the rigidity construction by TRiForm. We have also performed extensive simulations to evaluate TRiForm in various application scenarios using the measured parameters from real underwater nodes. The results show that TRiForm can successfully maintain the formations of an MUWSN and control it to arrive at the destination under distance and motion measurement errors.

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