Spatial uncertainty as covariance between frames
In the Winter 1986 issue of The International Journal of Robotics Research (volume 5, issue 4, pages 56-68) Randall Smith of SRI and Peter Cheeseman of NASA Ames gave a way to estimate the nominal relationship and expected error (covariance) between coordinate frames known only through a chain of uncertain relations. Two operations: compounding collapses a chain of uncertain transformations into one, merging combines parallel estimates into one with less uncertainty. The example is a mobile robot in three degrees of freedom (x, y, theta); the method generalises to six, and the estimates agree with an independent Monte Carlo simulation.
Why it matters
The uncertainty of a robot’s position and of the objects around it became a quantity one can compute in advance: whether a relation is known accurately enough for a task, and how much a proposed sensor would improve it. This is the formulation of a network of relations with covariances from which simultaneous localisation and mapping grew; MonoSLAM in 2003 holds the same thing in one state vector.
The paper starts from the position that a mobile robot needs no global reference frame (citing Brooks 1985): local frames linked by uncertain transformations suffice, and the reduction of uncertainty from a sensor can be mapped into any of them. The theory assumes small errors (a first-order model) and sensor errors independent of the locational error; for explicit probabilities a Gaussian distribution is assumed, and an appendix explains how to read ellipse parameters off a covariance. The authors say the work was first motivated by off-line programming of industrial manipulators; the text contains the term relational map. Smith had moved to General Motors Research Laboratories by publication. Read from the full-text copy on Rodney Brooks's MIT CSAIL page, because the publisher's page sits behind a Cloudflare challenge. What the record does not claim: that the paper introduced the term SLAM (the word does not occur) or any figure beyond the volume and pages.