Estimating a pose, a shape or a map when some of the measurements are wrong, and knowing when the answer can be trusted. Least squares is the robotic version of plain averaging: one bad loop closure can bend the whole map.
Methods
- Down-weight what doesn’t fit. Graduated non-convexity starts from an easy convex problem and gradually makes it robust, so bad measurements lose their weight. It handles 70% to 80% outliers and breaks down near 90%. Hydra and Hydra-Multi use it to reject wrong loop closures.
- Keep the largest consistent set. PCM finds the biggest group of inter-robot loop closures that agree with each other. This works against random errors, and fails if the wrong measurements agree with each other: repeated structure, or a coordinated liar.
- Certify the answer, or say you can’t. TEASER++ survives 99% random outliers with known scale, and gives a certificate when its answer is globally optimal. C-3PO and CRISP bring certificates to learned object pose and shape: C-3PO certified 22% of mug instances, and refused the rest. CP-Cert makes certification up to a thousand times faster when the problem is degenerate.
A certificate gives a robot a principled way to say “I can’t vouch for this”, which a recovery layer or a teammate can act on.
Observability
Hausman and others show why some faults can’t be caught by any residual: a bias in a direction the trajectory never excites produces no error to see. How the robot moves decides what a detector can observe. Bezzo and others inflate the noise of any speed sensor that disagrees with the predicted state, which works while fewer than half the sensors are attacked.
Adversarial outliers
TEASER++ proves that with adversarial outliers, exact recovery needs at least three more inliers than outliers. It is the estimation counterpart of the bound from Byzantine fault tolerance, and the same breakdown-point argument as in resilient consensus. RigidShift shows the limit of checking robots only against each other: a slow shift applied to the whole swarm keeps every pairwise distance intact, and only trusted anchors make it visible.
Questions
- Can a certificate travel with a measurement, so the receiving robot knows how much the sender trusted it?
- What does certifiable estimation look like when the outliers come from a teammate with an agenda?
- Turbid water and night produce dense, confident, wrong depth. Can a certifier catch that?
Related: collaborative SLAM, runtime monitoring, robust robotics.