Analytical equations for the connectivity matrices and node positions of minimal and extended tensegrity plates

Jiang, Shuhui; Skelton, Robert E.; Hernandez, Edwin A. Peraza

doi:10.1177/0956059920902375

Cited by 4 publications

(2 citation statements)

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“…Tensegrity structures are most suitable to serve as morphing structures to achieve different shapes like tensegrity plates, domes, self-tunable antennas and wings [ [18], [19], [20]]. However, much of the research in the past was done using static or kinematic analysis.…”

Section: Introductionmentioning

confidence: 99%

Robust Shape Control of Gyroscopic Tensegrity Robotic Arm

Goyal¹,

Majji²,

Skelton³

2020

Preprint

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This paper proposes a model-based approach to control the shape of a tensegrity system by driving its node position locations. The nonlinear dynamics of the tensegrity system is used to regulate position, velocity, and acceleration to the specified reference trajectory. State feedback control design is used to obtain the solution for the control variable as a linear programming problem. Shape control for the gyroscopic tensegrity systems is discussed, and it is observed that these systems increase the reachable space for the structure by providing independent control over certain rotational degrees of freedom. Disturbance rejection of the tensegrity system is further studied in the paper. A methodology to calculate the control gains to bound the errors for five different types of problems is provided. The formulation uses a Linear Matrix Inequality (LMI) approach to stipulate the desired performance bounds on the error for H∞, generalized H2, LQR, covariance control and stabilizing control problem. A high degree of freedom tensegrity T2D1 robotic arm is used as an example to show the efficacy of the formulation.

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Section: Introductionmentioning

confidence: 99%

Robust Shape Control of Gyroscopic Tensegrity Robotic Arm

Goyal¹,

Majji²,

Skelton³

2020

Preprint

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“…Tensegrity provides a unique method in which shape change can be achieved without a change in stiffness of the structure, and stiffness can also be changed without changing the shape of the structure. This is achievable as structure morphs from one equilibrium configuration to another on the control surface [6,17] as shown in figure 1.1. This morphing from one equilibrium position to another equilibrium position also results in minimal control energy requirement for shape change [18].…”

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confidence: 99%

Integrating structure and control design using tensegrity paradigm

Skelton¹

2019

Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications

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For centuries researchers have been pushing the boundaries of their respective technical domains, but it is only a few decades ago that research started taking its dig on system design theory. A system design theory encapsulates all individual components design and their simultaneous optimization, i.e., it provides a complete framework to design the structure. The approach behind this research is to make small steps in structure design, dynamic models, information architecture, and control design with some free parameters and then finally optimize those free parameters in a wholesome design approach to meet some specified performance. The author uses tensegrity design models to integrate structure and control design due to the various advantages mentioned further. This dissertation first makes three contributions to the study of tensegrity structures and then provides a system design theory to integrate structure and control design using the tensegrity paradigm. The first part of the dissertation provides a detailed study of the minimum mass tensegrity structures designed to take compressive loads, namely, D-bar and T-bar structures. These design studies consider both local and global failures in designing the optimal configuration (optimal complexity, angle, and cross-sectional area) for both D-bar and T-bar structures. The formulation developed here provides a general methodology to avoid global buckling failures for any class-k tensegrity structures. The proposed research provides different approaches to design a structure based on optimizing mass, stiffness, or mechanical energy stored in a tensegrity structure. The second part of this research work provides accurate dynamic models of axially loaded members forming any general tensegrity structure. The formulation develops a second-order matrix differential equation to perform dynamic simulation of tensegrity structures with massive strings and rigid bars. The dynamics models for novel gyroscopic tensegrity systems are also developed, which adds an extra degree of freedom to the control of the structure. A Matlab based tensegrity dynamics simulator is another outcome of this research. ACKNOWLEDGMENTS I would like to thank my advisor Prof. Robert E. Skelton for his guidance, support, and for giving me the opportunity to work for him. He accepted me with my limited knowledge of controls and no knowledge of tensegrity structures and taught me everything. I feel honored to have them as my advisor. He taught me how to think critically and scientifically during our various research discussions throughout the years. His perspective and passion for research has inspired me and will shape my career in years to come. I am also grateful to Judy Ma'am for making me feel like a family. I would also like to thank Dr. Manoranjan Majji for all the helpful discussions and for having a positive and friendly attitude towards every research topic we discussed. This dissertation could not have been successfully completed without his guidance and help over the years. I would also ...

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