Stochastic optimal control of cable vibration in plane by using axial support motion

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.

Research on End-force Output of 8-cable Driven Parallel Manipulator

The return capsule needs to be launched to the moon and return back to earth in the third stage of the Chinese lunar exploration project.Therefore,it is necessary to perform simulations on the ground.This paper presents an 8-cable-driven parallel manipulator to achieve end-force output in a low-gravity environment.End-force output refers to the vector sum of the external force on the end-effector.A model of end-force output is established based on a kinematics model,a dynamic model,and a force analysis of an 8-cable driven parallel manipulator.To obtain end-force output in a low-gravity environment,the cable force has to be controlled to counteract gravity.In addition,a force-position mix control strategy is proposed to proactively control the cable force according to the force optimal distribution given by the closed-form force distribution method.Furthermore,a suitable choice for an end-force output is obtained by modeling the effect of cable force on end-force output.Experimental results show that the actual cable force agrees well with the calculated force distribution,indicating that it is feasible to realize end-force output in a low gravity environment.