Dynamic Workspace and Control of Planar Active Tensegrity-Like Structures

This paper addresses the issues of control and workspace determination of planar active tensegrity or tensegrity-like structures. The motion of such structures is generally produced by actuated cables, which cannot tolerate compressive forces. Hence, a controller which not only satisfies the system dynamic equations, but also maintains positive tension in cables is necessary. A null-space controller based on feedback linearization theory is developed for this purpose. This controller utilizes redundant active cables to overactuate the system. The concept of a ‘dynamic workspace’ for these structures is then introduced. This workspace consists of all configurations that are achievable from a given initial configuration while maintaining positive tensions throughout the entire system motion and is a powerful tool in analyzing the performance of a variety of tensegrity structures. This idea extends the concept of the static workspace, which consists of statically maintainable configurations, by incorporating system motion and dynamics to guarantee positive tensions during transition between the states. A critical benefit of this procedure is that it may be used to find the dynamic workspace of a system regardless of whether actuator redundancy is utilized, and thus can be used to objectively illustrate the degree to which overactuation improves mobility of a tensegrity structure. The effectiveness of the developed concepts is demonstrated through computer simulation and actual physical experimentation.