Spherical Tensegrity Research Articles

Form-Finding and Evaluation of Spherical Tensegrity Toward Applying in Locomotive Robots

Abstract A tensegrity-based robot is a locomotive robot that operates on the principle of tensegrity, allowing it to change its shape by adjusting its internal prestress. Tensegrity-based robots can be categorized into different types based on their shape, with the spherical tensegrity-based robot garnering the most attention. However, existing designs for spherical tensegrity-based robots tend to be relatively simple and lack standardized criteria for evaluating their performance. This paper proposes an optimization approach using the force density method to design new spherical regular tensegrity configurations. This is achieved by parameterizing the topology and configuration of the structure, taking into account structural symmetry and the even distribution of internal forces. The proposed approach generates not only classical tensegrities but also novel configurations suitable for locomotive robots. To preliminarily evaluate the suitability of classical tensegrities and novel tensegrities to be used as a rolling robot, a set of performance indexes, including inner space, compactability, prestress evenness, gait repeatability, tilt stability ratio, stride length, and path efficiency, are proposed. The proposed indexes can be quickly determined based on the geometry of the tensegrity and thus are useful in the conceptual selection of the spherical tensegrities for rolling robots. They are used to evaluate a set of six spherical tensegrities. Numerical simulations are carried out to verify the feasibility of geometry-based approximating the gait-dependent indexes. Through the evaluation, a novel spherical tensegrity consisting of 15 struts and 60 tendons is identified as a promising candidate for rolling robots.

Dynamic modeling and crawling gait control of six-strut spherical tensegrity robot

In this paper, the crawling gait control of a six-strut spherical tensegrity robot is studied. The dynamic model of the robot is established by Newton-Euler equations, and the numerical simulations are constructed in MATLAB. The correctness of numerical simulation is verified by using ADAMS simulation software. Next, the motion mechanism of the crawling gait is considered, and parameters such as gravity cone and gravity moment are introduced, the initial configuration, active cables and driving parameters range suitable for robot crawling gait are obtained. Taking the maximum distance moved by the robot in a certain direction as the optimization objective, the problem of controlling the crawling gait is transformed into an optimization problem, and the particle swarm optimization algorithm is used to optimize the driving parameters of the crawling gait. The motion performance of the robot is evaluated by three indicators: motion velocity, driving energy consumption, and moving direction deviation. Two methods for optimizing the motion performance are proposed. Finally, an experimental platform is set up to carry out the crawling gait experiment and verify the above methods. The research results can provide technical support for further engineering applications of the six-strut spherical tensegrity robot.

Establishment of iterative modeling method for spherical tensegrity structure using rotational symmetry and regular polyhedron configuration

Tensegrity structures are attractive light-weight structures. In particular, spherical tensegrity structures are expected to be applied in various fields. This article proposes a simple method for modeling spherical tensegrities. Firstly, the nodal coordinates of the spherical tensegrity are systematically determined based on rotational symmetry and regular polyhedral configuration. This approach enables the systematic acquisition of the nodal coordinates of spherical tensegrities of all sizes by introducing a three-dimensional rotation matrix and the dihedral angle of the regular polyhedron. Secondly, the prestress ratio is determined iteratively. For the stability analysis of the spherical tensegrity, nonlinear analysis with prestress is required. For the analysis considering the prestress, a tangent stiffness matrix is applied in this study. The simple determination method enables the modeling of spherical tensegrities. The natural frequencies and mode shapes of the spherical tensegrity are identified by frequency analysis. A vibration experiment is conducted as a verification experiment. The natural frequencies from the analysis are compared to the resonance frequencies from the experiment. This comparison confirms the validity of the frequency analysis results, based on the two proposed methods.

Rolling gaits of a strut-actuated six-strut spherical tensegrity

A tensegrity is a self-stressed pin-jointed system consisting of tensile members and compressive members. As its shape can be actively controlled by changing the prestress of its members, it has great potential to be used as a shape-controllable locomotive system. Particularly, the six-strut spherical tensegrity has been studied intensively as a rolling locomotive system. In this study, the rolling gaits of a strut-actuated six-strut spherical tensegrity are investigated. Specifically, a mathematical model for generating the rolling gaits of locomotive spherical tensegrities is presented, and a numerical method combining dynamic relaxation method and genetic algorithm is used to solve the model. Various rolling gaits for the strut-actuated six-strut locomotive spherical tensegrity are identified using this approach. Two basic types of touching-ground triangles, two basic distributions of payload, and six cases for the numbers of used active struts are considered. Several rolling gait primitives are noted, their motion features analyzed, and a simple path-generating strategy is proposed based on idealized rolling gait primitives. A physical prototype of the strut-actuated six-strut locomotive tensegrity is manufactured, and experiments are conducted to verify the rolling gaits and locomotion paths generated by the proposed methods.

Rolling Locomotion of Cable-Driven Soft Spherical Tensegrity Robots.

Soft spherical tensegrity robots are novel steerable mobile robotic platforms that are compliant, lightweight, and robust. The geometry of these robots is suitable for rolling locomotion, and they achieve this motion by properly deforming their structures using carefully chosen actuation strategies. The objective of this work is to consolidate and add to our research to date on methods for realizing rolling locomotion of spherical tensegrity robots. To predict the deformation of tensegrity structures when their member forces are varied, we introduce a modified version of the dynamic relaxation technique and apply it to our tensegrity robots. In addition, we present two techniques to find desirable deformations and actuation strategies that would result in robust rolling locomotion of the robots. The first one relies on the greedy search that can quickly find solutions, and the second one uses a multigeneration Monte Carlo method that can find suboptimal solutions with a higher quality. The methods are illustrated and validated both in simulation and with our hardware robots, which show that our methods are viable means of realizing robust and steerable rolling locomotion of spherical tensegrity robots.

Establishment of Modeling Method for Spherical Tensegrity Using Rotational Symmetry

Establishment of Modeling Method for Spherical Tensegrity Using Rotational Symmetry

Kinodynamic planning for spherical tensegrity locomotion with effective gait primitives

Tensegrity-based robots can achieve locomotion through shape deformation and compliance. They are highly adaptable to their surroundings, and are lightweight, low cost, and physically robust. Their high dimensionality and strongly dynamic nature, however, can complicate motion planning. Efforts to date have primarily considered quasi-static reconfiguration and short-term dynamic motion of tensegrity robots, which do not fully exploit the underlying system dynamics in the long term. Longer-horizon planning has previously required costly search over the full space of valid control inputs. This work synthesizes new and existing approaches to produce dynamic long-term motion while balancing the computational demand. A numerical process based upon quasi-static assumptions is first applied to deform the system into an unstable configuration, causing forward motion. The dynamical characteristics of the result are then altered via a few simple parameters to produce a small but diverse set of useful behaviors. The proposed approach takes advantage of identified symmetries on the prototypical spherical tensegrity robot, which reduce the number of needed gaits but allow motion along different directions. These gaits are first combined with a standard search method to achieve long-term planning in environments where the developed gaits are effective. For more complex environments, the various motion primitives are paired with the fall-back option of random valid actions and are used by an informed sampling-based kinodynamic motion planner with anytime properties. Evaluations using a physics-based model for the prototypical robot demonstrate that modest but efficiently applied search effort can unlock the utility of dynamic tensegrity motion to produce high-quality solutions.

Soft Spherical Tensegrity Robot Design Using Rod-Centered Actuation and Control

This paper presents the design, analysis, and testing of a fully actuated modular spherical tensegrity robot for co-robotic and space exploration applications. Robots built from tensegrity structures (composed of pure tensile and compression elements) have many potential benefits including high robustness through redundancy, many degrees-of-freedom in movement and flexible design. However, to take full advantage of these properties, a significant fraction of the tensile elements should be active, leading to a potential increase in complexity, messy cable, and power routing systems and increased design difficulty. Here, we describe an elegant solution to a fully actuated tensegrity robot: The TT-3 (version 3) tensegrity robot, developed at UC Berkeley, in collaboration with NASA Ames, is a lightweight, low cost, modular, and rapidly prototyped spherical tensegrity robot. This robot is based on a ball-shaped six-bar tensegrity structure and features a unique modular rod-centered distributed actuation and control architecture. This paper presents the novel mechanism design, architecture, and simulations of TT-3, an untethered, fully actuated cable-driven six-bar spherical tensegrity robot. Furthermore, this paper discusses the controls and preliminary testing performed to observe the system's behavior and performance and is evaluated against previous models of tensegrity robots developed at UC Berkeley and elsewhere.

Design and control of compliant tensegrity robots through simulation and hardware validation.

To better understand the role of tensegrity structures in biological systems and their application to robotics, the Dynamic Tensegrity Robotics Lab at NASA Ames Research Center, Moffett Field, CA, USA, has developed and validated two software environments for the analysis, simulation and design of tensegrity robots. These tools, along with new control methodologies and the modular hardware components developed to validate them, are presented as a system for the design of actuated tensegrity structures. As evidenced from their appearance in many biological systems, tensegrity ('tensile-integrity') structures have unique physical properties that make them ideal for interaction with uncertain environments. Yet, these characteristics make design and control of bioinspired tensegrity robots extremely challenging. This work presents the progress our tools have made in tackling the design and control challenges of spherical tensegrity structures. We focus on this shape since it lends itself to rolling locomotion. The results of our analyses include multiple novel control approaches for mobility and terrain interaction of spherical tensegrity structures that have been tested in simulation. A hardware prototype of a spherical six-bar tensegrity, the Reservoir Compliant Tensegrity Robot, is used to empirically validate the accuracy of simulation.

Dynamic Stability and Ultimate Capacity of Suspended Dome under Earthquakes

Suspended dome is a reasonable and novel type of long-span hybrid spatial structures based upon single-layer spherical lattice shell and tensegrity system. Based upon the structural force-bearing characteristics, the combined finite element model of beam elements, truss elements and cable elements is set up. A method taking the maximum displacement on nodes under earthquake acceleration of each level as dynamic response representative parameter is proposed to study the dynamic stable ultimate capacity of suspended dome by application of the incremental dynamic analysis in combination with B-R kinetic criterion. Furthermore, considering suspended dome has the clear advantage over Single-Layer Spherical Lattice Shell for a structure with a long span and a small ratio of rise to span, the influences of factors such as structural parameters, geometric parameters, and different earthquake input are investigated on dynamic stability for a kiewitt-type suspended dome with a long span and a small ratio of rise to span. Finally of suspended dome some conclusions are obtained such as the initial defects can clearly reduce dynamic stable ultimate capacity, and since the rise-span ratio, pre-stressing level and cross section area are not monotonous as variety to the structural dynamic stability, they should be optimized to enhance or improve the structural dynamic stability, which can be rules for engineering design.

A New Tensegrity Module — “Torus”

Research on cylindrical and spherical tensegrity modules are extensively carried out. However research on other tensegrity modules is little reported. This paper presents an exploratory study on a new kind of tensegrity module – “torus”. The topology of the torus tensegrity is firstly introduced. Then the initial form-finding of the torus tensegrity is discussed. The static and dynamic analysis of the torus tensegrity shows that prestressing has a stiffening effect on infinitesimal mechanism modes if the geometry is properly arranged. A new cable dome with a torus tensegrity employed as its ring beam is finally proposed. The behavior of the new dome is also examined. The work here will provide a reference for further research and application of the torus tensegrity.

Toward a Generalised Tensegrity Model Describing the Mechanical Behaviour of the Cytoskeleton Structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.

Static and dynamic characterization of regular truncated icosahedral and dodecahedral tensegrity modules

Static and dynamic properties of a pair of dual spherical tensegrity modules invented by Buckminster Fuller are investigated. They are regular truncated icosahedral and dodecahedral tensegrity modules. The computation of the Maxwell number and the use of Calladine's relation reveal that regular truncated icosahedral and dodecahedral tensegrity modules possess 55 infinitesimal mechanism modes. A reduced equilibrium matrix is presented for the initial shape finding to economically impose the existence of a pre-stress mode. Both the initial shape and the corresponding pre-stress mode are analytically obtained by using graphs of the icosahedral group and the reduced equilibrium matrix. For both icosahedral and dodecahedral modules the maximum values of the cable tension is always less than the absolute value of bar compression. In order to classify a large number of infinitesimal mechanism modes, modal analyses are conducted. Infinitesimal mechanism modes have the stiffness due to pre-stress and are associated with lowest natural frequencies. Their natural frequencies increase proportionally to the square root of the amplitude of pre-stress. It is found that there are only 15 distinct natural frequencies associated with the infinitesimal mechanism modes.