Symplectic Instantaneous Optimal Control of Deployable Structures Driven by Sliding Cable Actuators

Abstract

A symplectic instantaneous optimal control (IOC) method is presented for compression/deployment of structures driven by sliding cable actuators. First, the motion of these active sliding cables is regarded as system kinematic constraints from the view of multibody dynamics, and a more general structural deployment control system can be established by differential-algebraic equations (DAEs). Mathematically, the system can be depicted as a constrained nonlinear optimal control problem for DAE systems. Then, based on the Lagrange–d’Alembert principle and the discrete variational principle, a symplectic discretization format can be constructed. The original continuous control problem will be approximated into a series of constrained IOC problems at every time slot, and to satisfy the inequality constraints of input saturation, the linear complementarity problem can finally be derived for solving these IOC problems. The proposed method provides a novel control strategy for addressing more general structure deployment control problems with fewer actuators. Structures can be quickly compressed/deployed to the target configuration, and the residual vibration can be minimized at the same time. The effectiveness and universality of the proposed method are further illustrated by numerical simulations of a telescopic tensegrity manipulator and a deployable tensegrity antenna.