Dynamics And Motion Control Of Two-stage Tensegrity Prism

The tensegrity structure is composed of the compressed rod unit and the tensioned rope unit,and there is no moment between the rod elements,and the internal force of the unit is maintained self-balanced.Tensegrity first appeared in the field of art,theoretical research to static-based.Later,the research focus gradually shifted to the dynamic characteristics of the structure,the analysis of the structure of the movement process and control.Tensegrity can change the characteristics or achieve the movement by deformation,the current tensegrity of the most research is still the structure of the motion control,that is,tensegrity robot.In addition,recent studies have shown that there are many systems in the organism that conform to the tensegrity principle,large to the biological bones and tendons,small to cytoskeletal structures,and bionic microscopic analysis of tensegrity bionic robots more in line with the natural In this paper,the whole structure of two-stage three-pole prismatic tension is taken as the main research object,in order to realize the trajectory tracking of the structure,the static characteristics of the structure are analyzed.In addition,recent studies have shown that there are many systems in the organism that conform to the tensegrity principle,large to the biological bones and tendons,to the cytoskeleton structure,and the tensegrity is more in line with the laws of nature from the perspective of bionics.In this paper,the two-stage three-bar tensegrity prism is the main research object,in order to realize the trajectory tracking of the structure,the static characteristics of the structure are analyzed.The structure dynamic response process is established,and the trajectory tracking is realized,which paves the way for the future research and application of the whole structure of tensioning.The main contents of this paper are as follows:In this paper,the dynamic relaxation method is used to form-finding analysis of the structure.The dynamic relaxation method is a pseudo-dynamic method,which simulates the motion process of the structure,and finally moves in the equilibrium position under the action of virtual damping.According to the principle of dynamic relaxation method,the iterative algorithm is completed,and the static equilibrium equation is used as the termination criterion of the algorithm.The form-finding analysis of different structures is carried out and the accuracy of the results is verified.In this paper,the method of dynamic relaxation is combined with the solution of nonlinear equations to realize the new shape finding and static response analysis,and the speed of finding and solving is improved.The dynamic model of the tensegrity is the key to the structural motion analysis,because the quality of the rod in the structure is much greater than the quality of the rope,so only the dynamic characteristics of the rod are considered.Because each rod has an independent movement,the dynamic model is abstracted for the analysis of the multi-rigid body dynamics model.The Newton-Euler equation of single rod under the force,external force and restraint of the single rod is established.The power equation of the unit is superimposed on the node by the connectivity matrix,and the dynamic equation of all nodes is obtained.Because there is a constraint,some nodes of the movement will be limited.The dynamic model is finally represented by the free nodal coordinates,that is,the minimum dynamic model,by means of the free nodal coordinates and the constraint equations of the structure.Because the structure has a large number of elastic elements,the dynamic equilibrium equation has a strong nonlinearity,the structural constraint equation and the dynamic equation form are algebraic equations and differential equations,which belong to the algebraic differential equations.In this paper,the dynamic response of the system is solved by the equation deformation.Finally,the tracking of the desired trajectory of the two-stage tensegrity is realized.The motion of the structure is changed by controlling the length of the rope,and the above six degrees of freedom of the platform describes the trajectory of the structure.The motion process is decomposed into two parts: kinematics inverse solution and motion simulation.The kinematic inverse solution uses the static equilibrium equation to solve the rope length change in a given trajectory.The motion simulation analyzes the motion of the structure under the given length of the rope.By tracking different trajectories,analyze the performance and error of structural tracking.