Dynamic Modeling And Analysis For Parallel Cable-Driven System With Multi-Robots

Multi-robot system and cable-driven parallel robot are two frontier topics in the field of robotics. Since there are the ability of completing complex tasks, improving work efficiency, distribution, good economy, good flexibility and other characteristics, multi-robot system are obtained the rapid development in recent years. Cable-driven parallel robot is developed by the parallel robot, so it not only has the characteristics of parallel robot such as high rigidity, high precision, good flexibility, strong carrying capacity, etc, but also has the advantages of cable driving like light weight, simple structure, fast transmission speed and large workspace, etc. It determines that its many advantages have application value in many fields. In this thesis, multi-robot system and cable-driven parallel robot are organically combined to form a new system that has both some features of them—parallel cable-driven system with multi-robots, which constitute a new research direction. Therefore, it has great theoretical significance and practical value to study it.Firstly, the general situation of connection point that has three translational degrees of freedom with free movement between each robot and the cable was considered for the parallel system of multi-robots cooperatively towing a payload by cables. The generalized kinematic equations of the system were established, and the dynamic equations of the system were established by using the Newton-Euler equation and Lagrange equation respectively in this thesis. Then, according to relation among robots, cables and payload, the system was divided into three types of issues. From the view whether equations have solutions, the situations of solution to all kinds of issues were analyzed respectively. Then from the view of practical application, the processing method was discussed in each case. When there were no solution or infinite solutions, some solving methods were proposed. When there were solutions, the method of removing the solutions that don't meet the design requirements was proposed. If there were multiple groups of solutions, a method of searching for optimal solution was proposed in this paper. Kinematic and dynamic model were verified by simulation examples, and the processing method of the solutions was illustrated.Secondly, for the under-constrainted system that multi-robots tow the payload by cables, which does not meet the condition of force closure and equations are generally not compatible, so the accurate workspace can't be found out. The workspace is divided into static equilibrium workspace and dynamic workspace to study in this thesis. For the static equilibrium workspace, the static equilibrium equation of the system is established, and then the least squares principle combined with the Monte-Carlo method is put forward. When the movement is low speed or quasi static for the payload, the approximate static equilibrium workspace can be found out quickly and the expression of the cable tension is given by using the normal equations and QR decomposition respectively. When position of robots and position and pose of the payload happen that the wrench isn't failed, there is the unique least square solution. Finally, the effectiveness of the proposed method is validated by computer simulation and the method can be used to quickly find out static equilibrium workspace of the under-constrainted cable-driven system for different space configuration. For the dynamic workspace, the workspace is transformed into the problem of the existence of the hyperplane based on the Farkas and Stiemke's lemma. Finally, simulation combined with the Monte-Carlo method verifies that the load acceleration has little effect on the dynamic workspace.Thirdly, the research on the optimization of the cable tension is carried out. Through the analysis of the kinematics and dynamics equations for the system, the optimization of the cable tension is converted into a nonlinear programming problem in the inverse problem. Through to obtain optimal solution, the minimum solution and the highest solution of cable tension that meet the requirements can be obtained. Then the optimal solution is between the minimum solution and the highest solution and can be expressed by linear interpolation. In the special case, unique least square solution can be obtained by using the least square method, which as the optimal solution to be used to determine whether to meet the requirements of the tension. Finally tension optimization figures are obtained by simulation examples respectively.Finally, on the basis of the above theory, the experimental platform that meets the experimental requirements is set up, and the trajectory planning experiments are carried out to verify the correctness of the model.