Convex Optimization-based Stiffness Control for Tensegrity Robotic Structures

In this paper, the problem of controlling compliance of a robotic tensegrity structure (finding the state of the structure which produces desired stiffness) is discussed. Tensegrity structures have a number of unique properties: they are well suited for uncertain environments, are easily deployed, impact resistant, foldable and light-weight and thus provide a desirable component for a number of robotics applications. They are currently being studied as a structural element of robotic extraterrestrial probes, crawling robots, swimming robots and others. The compliance control problem here is solved by a convex relaxation of the original nonconvex program, which in turn is done by introducing two linear models: one for the stiffness matrix and one for the elastic forces. Solution accuracy is controlled by introducing an iterative scheme, solving the convex problem on each iteration. Proposed algorithm converges providing accuracy better than 10−2 N/m in terms of stiffness using only 10 iterations of the algorithm, and the accuracy of force equilibrium is better than 1 N.