The defences in resilient consensus and Byzantine fault tolerance, side by side. Each one needs a witness of some kind, and they differ in what it is and what they do with a suspect.
| Defence | Witness | Needs to know F? | What happens to a suspect | Limits |
|---|---|---|---|---|
| W-MSR (LeBlanc and others, 2013) | the spread of neighbours’ values | yes | its extreme values are dropped every step | needs -robust graphs; coordinate-wise version only keeps a bounding box |
| Reputation-based consensus | discrepancies seen over time | no | its weight can fall to exactly zero | to read |
| Blocklist protocol | local observations that contradict a report | yes (at most F) | both ends of an accusation are blocked | an honest accuser is blocked too; assumes honest accusations are true |
| Token economy | a smart contract’s outlier filter | no | it runs out of tokens and loses its say | slower convergence as liars increase; 9 of 24 lying kept error below 2.2% |
| Confidence-weighted trust | trust observations from the wireless channel | no | its weight shrinks as evidence builds | fully trusts a genuine robot with a broken sensor |
| Spoof-resilient networks | Wi-Fi spatial fingerprints | no | forged identities are down-weighted | works best indoors with multipath; free space is hard |
| SABER | other agents’ evidence about each object | no | its trust is capped by its worst object | built for connected vehicles |
| FRAC-MARL | redundancy in two-hop messages | yes (a topology condition) | corrupted messages are ignored | only links are corrupted, not agents |
| RigidShift recovery | trusted anchors | no | geometry is rebuilt from ranges and aligned to the anchors | relative checks alone can never see a common shift |
Notes
- The trimming methods (W-MSR, the blocklist) need a bound on how many liars there are. The weighting methods (reputation, channel trust, tokens) don’t, and pay for it with slower or approximate agreement.
- Physical witnesses (radio fingerprints, ranges, anchors) catch forged identities and positions, and pass a real robot whose sensor is broken. The case in between, a genuine teammate with bad data, needs a witness that checks the data as well as the sender. More in failure recovery.
- Nearly all of these were tested in simulation, on graphs that don’t change much while the robots move.
Related: Multi-robot systems, robot security, and the Lying robots explainer.