Adjustable Tensegrity Robot Based on Assur Graph Principle

The paper introduces a tensegrity robot consisting of cables and actuators. Although this robot has zero degrees of freedom, it is both mobile, and capable of sustaining massive external loads. This outcome is achieved by constantly maintaining the configuration of the robot at a singular position. The underlying theoretical foundation of this work is originated from the concept of Assur Trusses (also known as Assur Groups), which are long known in the field of kinematics. During the last three years, the latter concept has been reformulated by mathematicians from rigidity theory community, and new theorems and algorithms have been developed. Since the topology of the robot is an Assur Truss, the work reported in the paper relies on Assur Trusses theorems that have been developed this year resulting in an efficient algorithm to constantly keep the robot at the singular position. In order to get an efficient characterization of the desired configurations, known techniques from projective geometry were employed. 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. The topology of the device is an Assur Truss — a 3D triad, but the principles introduced in the paper are applicable to any robot whose topology is an Assur Truss, such as: tetrad, pentad, double triad and so forth. The paper includes several photos of the device and the output data of the control system indicating its promising application.