Read here about the Assur truss and its applicability to tensegrity structures generated from well known principles, as opposed to tensegrity structures generated by trial and error.
Assur Trusses, also known as Assur groups, are a familiar subject in the field of kinematics. In the 2000's mathematicians adopted the concept from the rigidity theory community, and developed new theorems and algorithms.
Offer Shai adopted the Assur graph or truss as an ideal, practical basis for the development of dynamic tensegrity structures robotics. His reasoning is as follows: Assur trusses have a well defined mathematical model with a well known singularity, defined as a locus where the structural equations are solvable. This solution conforms with a physical truss that can be both deployed and expected to conform to its theoretical model. Using this approach, the engineers would inherit a huge set of accurate and discrete mathematics that has already been developed and proven to describe such structures' behavior.
Assur Graph Generated Robotic Truss
Adjustable Tensegrity Robot Based on Assur Graph Principle by Shai, Tehori, Bronfeld, Slavutin, Ben-Hanan Link: http://www.scribd.com/doc/35190328/Adjustable-Tensegrity-Robot-Based-on-Assur-Graph-Principle-by-Shai-Tehori-Bronfeld-Slavutin-Ben-Hanan
A tensegrity robot is proposed and built of cables and actuators, based on the Assur Truss. The main idea of the control system of the device, that was also mathematically proved, is that changing the length of only one element, causes the robot to be at the singular position. Therefore, the system measures the force in only one cable, and its length is modified accordingly by the control system.