Abstract
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.
Highlights
Tensegrity structures are composed of compressive members and tensile members [1]
The modified dynamic relaxation algorithm can be applied to the form-finding of tensegrity structures which are with several different ratios between rod lengths and cable lengths
The relative location relationship of all interconnected rods on a complex rigid body is maintained in the form-finding process and the algorithm is valid for the form-finding of tensegrity structures which with several different ratios between rod lengths and cable lengths
Summary
Tensegrity structures are composed of compressive members and tensile members [1]. In 1948, Snelson invented a tensegrity structure named X-Piece, while the term ‘‘tensegrity’’ was coined by Fuller [2], [3]. The dynamic relaxation method mentioned above focuses mainly on the form-finding of tensegrity structures in node space. It is difficult to perform form-finding of tensegrity robots with multiple interconnected rods by the node-based dynamic relaxation algorithm. The modified dynamic relaxation algorithm can be applied to the form-finding of tensegrity structures which are with several different ratios between rod lengths and cable lengths. The performance of the traditional node-based dynamic relaxation method is affected by relative difference in stiffness between members [26]. It is difficult for the method to find the self-equilibrium positions of tensegrity structures with interconnected rigid rods in node space. We extended traditional node-based dynamic relaxation methods to handle form-finding problems of tensegrity structures with interconnected rigid rods in task space. For a certain rigid part of the structure fixed on the ground, the proposed algorithm is still valid
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