Cornel Sultan

Deployment of tensegrity structures

In this paper we present a strategy for tensegrity structures deployment. The main idea is to use a certain set of equilibria to which the undeployed and deployed configurations belong. In the state space this set is represented by an equilibrium manifold. The deployment is conducted such that the deployment trajectory is close to this equilibrium manifold.

A Computational Tensegrity Model Predicts Dynamic Rheological Behaviors in Living Cells

Rheological properties of living cells play a key role in the control of cell shape, growth, movement, and contractility, yet little is known about how these properties are governed. Past approaches to understanding cell mechanics focused on the contributions of membranes, the viscous cytoplasm, and the individual filamentous biopolymers that are found within the cytoskeleton. In contrast, recent work has revealed that the dynamic mechanical behavior of cells depends on generic system properties, rather than on a single molecular property of the cell. In this paper, we show that a mathematical model of cell mechanics that depicts the intracellular cytoskeleton as a tensegrity structure composed of a prestressed network of interconnected microfilaments, microtubules, and intermediate filaments, and that has previously explained static cellular properties, also can predict fundamental dynamic behaviors of living cells.

The prestressability problem of tensegrity structures: some analytical solutions

In this paper we formulate the general prestressability conditions for tensegrity structures. These conditions are expressed as a set of nonlinear equations and inequalities on the tendon tensions. Several examples of tensegrity structures for which the prestressability conditions can be analytically solved are then presented.

Linear dynamics of tensegrity structures

The linearized equations of motion for tensegrity structures around arbitrary equilibrium configurations are derived. For certain tensegrity structures which yield particular equilibrium configurations of practical interest, the linearized models of their dynamics around these configurations are presented. Evidence which indicates that these equilibria are stable is given and some stiffness and dynamic properties of these structures are investigated.  2002 Elsevier Science Ltd. All rights reserved.

Tensegrity Flight Simulator

Inthispaperweproposeanewmotionsimulatorbasedonatendon-controlledtensegritystructure.Thesimulator isequipped with anonlinearcontrollerthatachievesrobusttrackingofdesired motions.Thecontrollerparameters can be tuned to guarantee tracking to within a prespecie ed tolerance and with a prescribed rate of exponential convergence. The design is verie ed through numerical simulations forspecie clongitudinal motions of a symmetric aircraft.

Controllable tensegrity: a new class of smart structures

Tensegrity structures represent a special class of tendon space structures, whose members may simultaneously perform the functions of strength, sensing, actuating and feedback control. Thus, these structures ideally match the definition of smart structures. This paper introduces the concept of controllable tensegrity as a new class of smart structures capable of large displacement. The kinematics and nonlinear dynamics of one element of this class is derived and analyzed. Pre-stressability conditions are given and a particular equilibrium identified. The equations of motion are then linearized about this equilibrium and linear parametric models generated. These are next used for controller design. For control system design some of the tendons are chosen as actuators and some as sensors and a family of dynamic controllers designed such that the control energy is minimized while requiring output variance constraints to be satisfied. Another family of controllers is designed such that the output variance is minimized while requiring input variance constraints to be satisfied. The performances of these controllers are evaluated.

Peak-to-peak control of an adaptive tensegrity space telescope

This paper proposes a new space telescope design in which the classical truss structure of the telescope is replaced by a tensegrity structure. A tensegrity structure is a prestressed structure whose structural shape is guaranteed by the interaction between elastic members in tension (tendons) and a set of rigid members (bars). A nonlinear dynamical model of a two stage tensegrity telescope is derived. Static analysis is performed for tensegrity telescopes composed of two stages. The performance specifications for the control system are formulated in terms of the peak value (L(infinity ) norm) of the pointing and alignment errors. The control system is designed to minimize a certain upper bound on this peak value subject to a peak value constraint on the external disturbances. Evaluations of the design are performed through numerical simulations of the closed loop system.

Symmetrical reconfiguration of tensegrity structures

In this article we first present a mathematical model which describes the nonlinear dynamics of tensegrity structures. For certain tensegrity structures a particular class of motions, coined symmetrical motions, is defined. The corresponding equations of motion are derived and the conditions under which symmetrical motions occur are established. Reconfiguration procedures through symmetrical motions are proposed and examples are given.

Tendon control deployment of tensegrity structures

In this paper we consider the problem of deployment of tensegrity structures. Our idea is to make use of a certain set of equilibria to which the undeployed and deployed configurations belong. In the state space this set is represented by a connected equilibrium manifold and can be completely characterized analytically. The deployment is conducted such that the deployment trajectory is close to the equilibrium manifold and the deployment time is minimized.

Deep Space Formation Flying Spacecraft Path Planning

Efficient algorithms for collision-free energy sub-optimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of way-points through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are energy-optimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasi-quadratic parameter optimization problem in terms of the way-points parameters. The mathematical structure of the problem is further exploited to develop gradient-based algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20).