In 2366, the Ansata were lead by Kyril Finn, a devoted terrorist. At this time, it was thought that the group numbered only 200 actual members, but there were over a thousand sympathizers. During this year, Finn and his cell abducted Captain Jean-Luc Picard and Doctor Beverly Crusher from the USS Enterprise-D in an attempt to draw the Federation into the conflict on this planet.
By 2366, the Ansata had become more and more of a threat to Rutian society. They had developed folded-space transport technology (using a device known as the inverter) to instantly transport themselves anywhere without leaving a trace. This device was later discovered to be the cause for an illness from which the Ansata were suffering.
Their attempt to capture the Enterprise officers was initially very successful; the Enterprise had no defenses against the various folded-space transport incursions. However, further analysis of the data collected on board and on the surface of the planet revealed the location of the inverter, and Finn's cell. (TNG: "The High Ground")