The xDai team is currently working on a working implementation of HoneyBadger BFT consensus. This may be implemented on the xDai chain (determined through the governance process) and will be implemented as the default consensus for the xDai NG chain.
The Honey Badger consensus algorithm allows nodes in a distributed, potentially asynchronous environment to achieve agreement on transactions. The agreement process does not require a leader node, tolerates corrupted nodes, and makes progress in adverse network conditions.
Honey Badger is Byzantine Fault Tolerant. The protocol can reach consensus with a number of failed nodes f (including complete takeover by an attacker), as long as the total number N of nodes is greater than 3 * f.
Honey Badger is asynchronous. It does not make timing assumptions about message delivery. An adversary can control network scheduling and delay messages without impacting consensus.
The following articles explain much more about HBBFT and how it works.