Modeling, design, and control of tensegrity structures with applications

Cornel Sultan, Purdue University

Abstract

Classical flexible structures dynamics and control suffer from several major deficiencies. First, reliable mathematical models involve partial differential equations which are difficult to deal with analytically as well as numerically. A partial differential equations mathematical model of a system's dynamics is not practical for control system design, since most of the modern control systems design methodologies assume a state space representation. Second, from a practical perspective, the control of classical truss structures involves the use of expensive and short life mechanisms like telescopic struts. Third, the control of classical truss structures involves high energy, massive, hydraulic actuators. Fourth, classical controllable structures have many, complicated, bar to bar joints, which make the control task difficult. This thesis proposes a class of lightweight, space structures, called tensegrity structures, which can be reliably modeled using ordinary differential equations. Tensegrity structures offer excellent opportunities for physically integrated structure and control system design since their members can serve simultaneously as sensors, actuators, and load carrying elements. The actuating functions can be carried by tendons, controlled by electric motors. Thus, telescopic struts and hydraulic actuators can be eliminated. Additionally, tensegrity structures can be built without any bar to bar connections. The general prestressability conditions for tensegrity structures are derived from the principle of virtual work. In several cases these conditions are analytically solved, allowing for the parameterization of certain classes of prestressable configurations. A general methodology for the investigation of the prestressability conditions is also developed. The methodology uses symbolic and numeric computation, and it is meant to significantly reduce the complexity of the prestressability conditions for certain prestressable configurations. Mathematical models for tensegrity structures dynamics are developed using the Lagrangian approach. For certain classes of structures, particular motions are investigated and simpler dynamic equations are derived. These equations are next used for a simple, efficient, tendon control reconfiguration procedure. For certain classes of tensegrity structures linear parametric dynamical models are also developed. A tendon control deployment procedure for tensegrity structures is developed. The procedure is time optimal and uses continuous time control laws. It is based on the discovery of a connected equilibrium manifold to which the deployed and undeployed configurations belong. The deployment is conducted such that, in the state space, the deployment path is close enough to the equilibrium manifold. A force and torque sensor based on a tensegrity structure is proposed, enabling the simultaneous measurement of six quantities, three orthogonal forces and three orthogonal moments. An optimal estimator is designed, based on the linearized model of the structure. Finally, a motion simulator which exploits the intrinsic advantages of a tensegrity structure, is proposed. The actuating functions are carried out by the tendons, eliminating the telescopic actuators. A nonlinear robust tracking controller is designed to assure exponential convergence of the tracking error to a ball of prespecified radius, with a prespecified rate of convergence.

Degree

Ph.D.

Advisors

Corless, Purdue University.

Subject Area

Aerospace materials|Mechanical engineering|Civil engineering

COinS