arXiv subjects

Robert E. Skelton

Publications and source records attributed to Robert E. Skelton.

14 recordsLinked to original sources

arXiv2022

An extended ordinary state-based peridynamics for non-spherical horizons

This work presents an extended ordinary state-based peridynamics (XOSBPD) model for the non-spherical horizons. Based on the OSBPD, we derive the XOSBPD by introducing the Lagrange multipliers to guarantee the non-local dilatation and non-local strain energy density (SED) are equal to local dilatation and local SED, respectively. In this formulation, the XOSBPD removes the limitation of spherical horizons and is suitable for arbitrary horizon shapes. In addition, the presented XOSBPD does not need volume and surface correction and allows non-uniform discretization implementation with various horizon sizes. Three classic examples demonstrate the accuracy and capability for complex dynamical fracture analysis. The proposed method provides an efficient tool and in-depth insight into the failure mechanism of structure components and solid materials.

cs.CE↗

arXiv2022

Design and control analysis of a deployable clustered hyperbolic paraboloid cable net

This paper presents an analytical and experimental design and deployment control analysis of a hyperbolic paraboloid cable net based on clustering actuation strategies. First, the dynamics and statics for clustered tensegrity structures (CTS) are given. Then, we propose the topology design of the deployable hyperbolic paraboloid cable net. The deployability of the cable net is achieved by using clustered cables. It is shown that the clustered cables significantly reduce the number of actuators required for control. The deployment trajectory and actuation prestress in the cables are designed to ensure the tensions are feasible during the deployment process. Then, we compare the deployment analysis's open-loop and closed-loop control strategies. Finally, a lab-scale model is constructed to validate the actuation laws. We test the static performance and deployment process of the experimental model. Results show that the closed-loop control approach is more stable and smoother than the open-loop one in the deployment process. The approaches developed in this paper can also be used for various deployable tensegrity structures.

eess.SY↗

arXiv2022

Equilibrium and stiffness study of clustered tensegrity structures with the consideration of pulley sizes

This paper presents the equilibrium and stiffness study of clustered tensegrity structures (CTS) considering pulley sizes. We first derive the geometric relationship between clustered strings and pulleys, where the nodal vector is chosen as the generalized coordinate. Then, the equilibrium equations of the clustered tensegrity structure with pulleys based on the Lagrangian method are given. Since the stiffness of a structure is usually weakened when using clustering strings, we formulate the tangent stiffness matrix equations for analysis. It is also shown that as pulley sizes go to zero, the governing equations of the clustered tensegrity system with pulleys yield to the classical clustered tensegrity structure without pulleys, which is consistent with the existing literature. Three examples are demonstrated to validate the given theory. The proposed method allows one to conduct equilibrium, stiffness, and robustness studies of cluster tensegrity structures with pulleys. Nevertheless, the approach developed in this paper is not limited to the tensegrity structures. It can also be applied to a wide range of applications with pulley-rope systems, such as drilling rigs, ocean platform anchors, and cargo cranes.

eess.SY↗

arXiv2021

Dynamics and control of clustered tensegrity systems

This paper presents the formulations of nonlinear and linearized statics, dynamics, and control for any clustered tensegrity system (CTS). Based on the Lagrangian method and FEM assumptions, the nonlinear clustered tensegrity dynamics with and without constraints are first derived. It is shown that the traditional tensegrity system (TTS), whose node to node strings are individual ones, yield to be a special case of the CTS. Then, equilibrium equations of the CTS in three standard forms (in terms of nodal coordinate, force density, and force vector) and the compatibility equation are given. Moreover, the linearized dynamics and modal analysis of the CTS with and without constraints are also derived. We also present a nonlinear shape control law for the control of any CTS. The control turns out to be a linear algebra problem in terms of the control variable, which is the force densities in the strings. The statics, dynamics, and control examples are carefully selected to demonstrate the developed principles. The presented approaches can boost the comprehensive studies of the statics, dynamics, and control for any CTS, as well as promoting the integration of structure and control design.

eess.SY↗

arXiv2021

Minimal mass design of a tensegrity tower for lunar electromagnetic launching

Lunar explorations have provided us with information about its abundant resources that can be utilized in orbiting-resource depots as lunar-derived commodities. To reduce the energy requirements of a launcher to send these commodities from the lunar surface to the space depots, this paper explores the application of the electromagnetic acceleration principle and provides an assessment of the actual technical characteristics of the launcher's installation to ensure the acceleration of a payload with a mass of 1,500 kg to a speed of 2,200 m/s (circumlunar orbit speed). To fulfill a lightweight (fewer materials and less energy) support structure for the electromagnetic launcher with strength requirements, the tensegrity structure minimum mass principle without global buckling has been developed and applied to support the electromagnetic acceleration device. Therefore, this paper proposes and develops a minimal mass electromagnetic tensegrity lunar launcher. We first demonstrate the mechanics of launcher and payload, how a payload can be accelerated to a specific velocity, and how a payload carrier can be recycled for another launch. Then, a detailed discussion on the lunar launch system, procedures of propulsion, the required mass, and energy of the launch barrel are given. The governing equations of tensegrity minimal mass tensegrity design algorithm with gravity and without global buckling. Finally, a case study is conducted to show a feasible structure design, the required mass, and energy. The principles developed in this paper are also applicable to the rocket launch system, space elevator, space train transportation, interstellar payload package delivery, etc.

physics.acc-ph↗

arXiv2021

Design and analysis of deployable clustered tensegrity cable domes

This study presents the design and analysis of deployable cable domes based on the clustered tensegrity structures (CTS). In this paper, the statics and dynamics equations of the CTS are first given. Using a traditional Levy cable dome as an example, we show the approach to modify the Levy dome to a deployable CTS one. The strings to be clustered are determined by the requirement of prestress mode and global stability. The deployment trajectory is proposed by changing the deployment ratio (the ratio between the radius of the inner and outer rings of the cable dome). Then, the quasi-static and dynamic deployment of clustered tensegrity dome is studied. Results show that the proposed CTS cable dome always has one prestress mode and is globally stable in its deployment trajectory. In the deployment process analysis, the dynamics show that the system's dynamic response differs from the quasi-static simulation as the actuation speed increases. That is, for a fast deployment process, quasi-static simulation is not accurate enough. The dynamics effects of the deployment must be considered. The developed approaches can also be used for the design and analysis of various kinds of CTS.

eess.SY↗

arXiv2021

Tensegrity system dynamics based on finite element method

This study presents a finite element analysis approach to non-linear and linearized tensegrity dynamics based on the Lagrangian method with nodal coordinate vectors as the generalized coordinates. In this paper, nonlinear tensegrity dynamics with and without constraints are first derived. The equilibrium equations in three standard forms (in terms of nodal coordinate, force density, and force vectors) and the compatibility equation are also given. Then, we present the linearized dynamics and modal analysis equations with and without constraints. The developed approach is capable of conducting the following comprehensive dynamics studies for any tensegrity structures accurately: 1. Performing rigid body dynamics with acceptable errors, which is achieved by setting relatively high stiffness for bars in the simulation. 2. Simulating FEM dynamics accurately, where bars and strings can have elastic or plastic deformations. 3. Dealing with various kinds of boundary conditions, for example, fixing or applying static/dynamic loads at any nodes in any direction (i.e., gravitational force, some specified forces, or arbitrary seismic vibrations). 4. Conducting accurate modal analysis, including natural frequency and corresponding modes. Three examples, a double pendulum, a cantilever truss with external force, and a double prism tensegrity tower, are carefully selected and studied. The results are compared with rigid body dynamics and FEM software ANSYS. This study provides a deep insight into structures, materials, performances, as well as an interface towards integrating control theories.

physics.app-ph↗

arXiv2020

Integrating Structure, Information Architecture and Control Design: Application to Tensegrity Systems

A novel unified approach to jointly optimize structural design parameters, actuator and sensor precision and controller parameters is presented in this paper. The joint optimization problem is posed as a covariance control problem, where feasibility is achieved by bounding the covariance of the output as well as that of the control signals. The formulation is used to design a tensegrity system, where the initial prestress parameters, sensor and actuator precisions, and the control law are jointly optimized. Tensegrity system dynamics models linearized about an equilibrium point are used for system design, where minimality is ensured by constraint projection. The feedback loop is assumed to have a full-order dynamic compensator with its characteristic matrices chosen as optimization variables. The suboptimal solution of this non-convex system design problem is found by iterating over an approximated convex problem through the use of a convexifying potential function that enables the convergence to a stationary point. It is shown that for a linear dynamical system, the approximated joint optimization problem can be formulated using Linear Matrix Inequalities (LMIs).

eess.SY↗

arXiv2020

Robust Shape Control of Gyroscopic Tensegrity Robotic Arm

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 $\mathcal{H}_\infty$, generalized $\mathcal{H}_2$, LQR, covariance control and stabilizing control problem. A high degree of freedom tensegrity $T_2D_1$ robotic arm is used as an example to show the efficacy of the formulation.

cs.RO↗

arXiv2020

Markov Data-Based Reference Tracking of Tensegrity Morphing Airfoils

This letter presents a data-based control design for reference tracking applications. This design finds the optimal control sequence, which minimizes a quadratic cost function consisting of tracking error and input increments over a finite interval [0,N]. The only information needed is the first N+1 Markov parameters of the system. This design is employed on a tensegrity morphing airfoil whose topology has been described in detail in this letter. A NACA 2412 airfoil with specified morphing targets is chosen to verify the developed design. The principle developed in this letter is also applicable to other structural control problems.

cs.RO↗

arXiv2020

Deployable Tensegrity Lunar Tower

A tensegrity tower design to support a given payload for the moon mining operation is proposed in this paper. A non-linear optimization problem for the minimal-mass structure design is posed and solved, subject to the yielding constraints for strings and yielding and buckling constraints for bars in the presence of lunar gravity. The optimization variables for this non-linear problem are structural complexity and pre-stress in the strings. Apart from local failure constraints of yielding and buckling, global buckling is also considered. The structure designed as a deployable tower is a TnD1 tensegrity structure. A case study demonstrates the feasibility and advantage of the tower design. The principles developed in this paper are also applicable for building other structures on the Earth or other planets.

physics.app-ph↗

arXiv2014

Parametric Design of Minimal Mass Tensegrity Bridges Under Yielding and Buckling Constraints

This paper investigates the use of the most fundamental elements; cables for tension and bars for compression, in the search for the most efficient bridges. Stable arrangements of these elements are called tensegrity structures. We show herein the minimal mass arrangement of these basic elements to satisfy both yielding and buckling constraints. We show that the minimal mass solution for a simply-supported bridge subject to buckling constraints matches Michell's 1904 paper which treats the case of only yield constraints, even though our boundary conditions differ. The necessary and sufficient condition is given for the minimal mass bridge to lie totally above (or below) deck. Furthermore this condition depends only on material properties. If one ignores joint mass, and considers only bridges above deck level, the optimal complexity (number of elements in the bridge) tends toward infinity (producing a material continuum). If joint mass is considered then the optimal complexity is finite. The optimal (minimal mass) bridge below deck has the smallest possible complexity (and therefore cheaper to build), and under reasonable material choices, yields the smallest mass bridge.

cond-mat.mtrl-sci↗

arXiv2014

Multiscale tunability of solitary wave dynamics in tensegrity metamaterials

A new class of strongly nonlinear metamaterials based on tensegrity concepts is proposed and the solitary wave dynamics under impact loading is investigated. Such systems can be tuned into elastic hardening or elastic softening regimes by adjusting local and global prestress. In the softening regime these metamaterials are able to transform initially compression pulse into a solitary rarefaction wave followed by oscillatory tail with progressively decreasing amplitude. Interaction of a compression solitary pulse with an interface between elastically hardening and softening materials having correspondingly low-high acoustic impedances demonstrates anomalous behavior: a train of reflected compression solitary waves in the low impedance material; and a transmitted solitary rarefaction wave with oscillatory tail in high impedance material. The interaction of a rarefaction solitary wave with an interface between elastically softening and elastically hardening materials with high-low impedances also demonstrates anomalous behavior: a reflected solitary rarefaction wave with oscillatory tail in the high impedance branch; and a delayed train of transmitted compression solitary pulses in the low impedance branch. These anomalous impact transformation properties may allow for the design of ultimate impact mitigation devices without relying on energy dissipation.

cond-mat.mtrl-sci↗

arXiv2014

Experimental investigation of the softening-stiffening response of tensegrity prisms under compressive loading

The present paper is concerned with the formulation of new assembly methods of bi-material tensegrity prisms, and the experimental characterization of the compressive response of such structures. The presented assembly techniques are easy to implement, including a string-first approach in the case of ordinary tensegrity prisms, and a base-first approach in the case of systems equipped with rigid bases. The experimental section shows that the compressive response of tensegrity prisms switches from stiffening to softening under large displacements, in dependence on the current values of suitable geometric and prestress variables. Future research lines regarding the mechanical modeling of tensegrity prisms and their use as building blocks of nonlinear periodic lattices and acoustic metamaterials are discussed.

cond-mat.mtrl-sci↗