A Task-Space Form-Finding Algorithm for Tensegrity Robots

A modified dynamic relaxation algorithm for the form-finding of tensegrity robots in task space is proposed in this paper. There are some form-finding problems of tensegrity structures that are hard to be handled by the node-based dynamic relaxation algorithm. For tensegrity structures with multiple interconnected rods or rigid rods, the node-based dynamic relaxation algorithm is usually difficult to perform this type of form-finding. The node-based dynamic relaxation algorithm becomes rather cumbersome if several different ratios between rod lengths and cable lengths are desired, which restricts its applicability to less regular structural forms. The performance of the algorithm is affected by the relative difference in stiffness between members(cables and rods). To solve these problems, we extend the general dynamic relaxation algorithm from node space to task space. The proposed algorithm considers multiple interconnected rigid rods as an entire rigid body to derive its motion in six degrees of freedom. We simulated the motion process of the rigid body approaching its self-equilibrium position under the force exerted by all surrounding cables. In the form-finding process, the relative location relationship of all interconnected rods on a complex rigid body is maintained. The algorithm is valid for the form-finding of tensegrity structures which are with several different ratios between rod lengths and cable lengths. Besides, the modified algorithm is not affected by the stiffness of interconnected rods on rigid bodies. To demonstrate the capability of the method, four examples, including a two-segment spine robot, a bio-inspired tensegrity arm, a multi-segment spine robot, a tensegrity robot with disconnected and interconnected rigid rods, are presented in this paper.