Research On Dynamic Control Methods And Experiments Of Tensegrity Structures

A tensegrity structure is a self-equilibrium system composed of compressed components and tensioned cables,which is a special structural form between fixed structure and movable mechanism in terms of its mechanical properties.In recent years,due to the merits including lightweight,deployable,the components can be used not only as load-bearing supports,but also as sensors and actuators,tensegrities have attracted the researchers’ interest from many fields,such as architecture and art,aerospace smart structures,biomechanics,flexible robotics and so on.Up to now,most of the literatures on the tensegrity structures focus on its model design,form finding,static equilibrium stability,static optimization,dynamic responses analysis and so on.However,the research work on control problem of tensegrity structures is still very few,especially the control algorithms that are suitable for some complex tensegrity structures.To some extent,it may limit the development of tensegrity structures.Therefore,more studies on the control problems are required to improve the theoretical system of tensegrities and further promote the cross applications of this kind of structures with other disciplines.This thesis follows a main line of research on the dynamic control of the tensegrity structures,which including the trajectory planning,trajectory tracking control and vibration control.By refining the common difficulties and mathematical connotation behind these problems,some cooresponding control strategies and algorithms are proposed.In addition,the effectiveness and feasibility of the proposed methods are verified by experiments.The primary findings of this dissertation are summarized as follows.(1)For the dynamic modeling problems,a general dynamic model of tensegrity structures governed by the differential-algebraic equations(DAEs)is established.Firstly,based on the positional FEM,taking the node coordinates as the basic variables,the element formulas of the compressed bars,classical cables,sliding cables and rings of the tensegrity structures can be derived.Then,the motion differential equation for whole structure can be constructed using the finite element assembly technology.Subsequently,the actuation of sliding cables is treated as the kinematic constraints of the system inspired by the concept of multibody dynamics,so that a general dynamic model of the sliding cable-driven tensegrity structures can be constructed in DAEs.In addition,according to the discrete variational principle,a symplectic approach for the DAEs systems is proposed to study the dynamic responses of tensegirty systems.(2)For the trajectory planning problems,a symplectic instantaneous optimal control(IOC)approach for the deployment and obstacle-avoidance trajectory planning of the tensegrity structures is presented.Firstly,a tensegrity deployment control system with a DAEs model is established.Then,using a symplectic discrete scheme,the original optimal control problem in the whole continuous time domain can be transformed into a local suboptimal control problem at each time grid,and a symplectic instantaneous optimal control approach for the deployment of tensegrity structures is proposed.Furthermore,allied with the penalty technology,a symplectic instantaneous optimal control approach for obstacle-avoidance trajectory planning of the tensegrity structures is further developed.The numerical results illustrate that the proposed approach can quickly compress or unfold a deployable tensegrity structure to the expected point with minimal residual vibration;also,the proposed approach can implement an obstacle-avoidance trajectory planning with long distance and multi-obstacles.(3)For the trajectory tracking control problems,a symplectic instantaneous optimal control approach for the trajectory tracking of tensegrity structures is proposed.Firstly,the DAEs-model-based trajectory tracking control problem for tensegrities with cable actuators is established.Then,based on the Lagrange-d’Alembert and the discrete variational principles,the equality constraints of the controlled DAEs are discretized symplectically,and the original problem can be transformed into an IOC problem in each iterative step by Newton iteration.Considering the safety threshold limits of the actuation length or rate,i.e.,the control input saturation,the problem is further transformed into a linear complementarity problem(LCP).So the control law,which satisfies the constraint conditions can be obtained by solving the LCP.In addition,the author has proven that the proposed controller is symplectic-structure preserving.The close-loop stability is also analyzed by the fixed point theory.Finally,a numerical experiment on trajectory tracking control of a tensegrity continuous manipulator is conducted,the results demostrate that the proposed approach can not only track some nonsmooth trajectories covering straight lines,broken lines and arcs,but also can realize the synchronous control of tracking both the end position and attitude of the manipulator.(4)For the vibration control problems,a physics-guided multilevel distributed model predictive control approach for vibration reduction of tensegrity structures is proposed.Firstly,the dynamic model for smart tensegrity structures equipped with active piezoelectric actuators is generated by the FEM.Then,guided by the actual physical characteristics,the entire structure system is divided into a series of multilevel subsystems.Considering the states of the boundary nodes for all the adjacent subsystems as the interactive information,multilevel local model predictive controllers are designed for each subsystem independently.The proposed method provides a simple,unified and flexible multilevel distributed control framework for solving tensegrity structural vibration control problems with high fault tolerance.The numerical results demonstrate that the proposed approach is valid,flexible and has good fault tolerance.(5)For the experimental verification of the proposed approaches,a closed-loop control experimental platform is established,and related control experiments are designed to further demonstrate the effectiveness and physical feasibility of the proposed approaches in this thesis.For the proposed symplectic instantaneous optimal control method of the DAEs systems,an experiment on the trajectory tracking control of a tensegrity continuous manipulator was conducted with the help of a visual motion capture system,servo motors,a 3D advanced printer and some other hardware equipments.The experiment has successfully completed the trajectory tracking control task,i.e.,the motion of the endpoint for the tensegrity continuous manipulator should track the curves formed by the letters "I Love DUT".For the proposed physics-guided multilevel distributed model predictive control method,an experiment on the shape control of a space-borne antenna reflector was taken as an example with the help of a binocular measuring instrument,an antenna reflector,some piezoelectric actuators and other hardware equipments.The effectiveness and advantages of the proposed multilevel distributed model predictive control approach were demonstrated by this experiment.