Space Vector Planning For A Multi-robot Collaborative Towing System

By combining the structural features and advantages of a multi-robot system with a flexible cable parallel towing system,a new type of tightly coupled system is born called the multi-robot collaborative towing system.This system performs specific towing tasks with great flexibility by changing the end positions of multiple robots and adjusting the cable length.The characteristics of the multi-robot collaborative towing system are remarkable,as it belongs to the category of multi-robot systems and can also be classified as parallel robotic systems,so it has strong reconfigurable characteristics,and also has the advantages of large working space,large load capacity and fast operation speed.These outstanding features determine a wider range of practical applications for multi-robot collaborative towing systems,and at the same time contribute to the high research value and broad application prospects of such flexible cable-type parallel towing systems.As the flexible cable in the towing system is very flexible and can only provide unidirectional tension to the lifted object,the structural characteristics of this type of system are different from those of traditional rigid parallel robots,which determines that the research methods are not entirely consistent with those of rigid parallel robots.Thus,the system needs to combine its own structural characteristics and motion characteristics to conduct in-depth research on the trajectory tracking and cable planning of the lifted object.The planning scheme of this kind of unconstrained system is proposed.Firstly,according to the spatial geometric configuration of the multi-robot collaborative towing system,the position of the robot end relative to the robot base is described by the vector closure principle,and the whole system is divided into two parts: the robot part and the towing system,and the generalized kinematic models of these two parts are established respectively by the D-H method.The Newton-Euler equation and Lagrange equation are used to establish the kinetic model of the system respectively,and after classifying and discussing the kinematic solution of the towing system,which lay the foundation for the next trajectory planning research and cable obstacle avoidance planning research.Secondly,on the basis of the above analysis of the forward and inverse kinematics solutions,and the inverse kinematics solution strategy based on point-to-point trajectory planning is proposed.Then three improved algebraic programming methods are analyzed:S-ladder method,cycloid method and quintic polynomial method.Then,the expected trajectory of the point-to-point closed curve of the lifted object is given,and the trajectory is planned by the three methods mentioned above.The results show that a more universal and feasible inverse solution can be obtained,which effectively solves the problem that cannot be directly applied to the inverse solution of kinematics due to the discontinuity of velocity and acceleration,and verifies the validity of the three algebraic programming methods: only the tension obtained by the quintic polynomial programming method meets the condition of the flexo-soles force.The research lays a foundation for the subsequent planning of cable obstacle avoidance.Then,in order to solve the problem of misjudgment and missing judgment of the existing collision detection algorithm between cables and environmental obstacles in the process of collaborative towing of the same object by multiple robots through flexible cables,a cable optimization model and an environmental obstacle model are established according to the OBB theory considering the characteristics of cables themselves,and a new basic geometric collision detection model is proposed.Aiming at the optimized collision detection model,considering the relationship between the vertical position of the common vertical line and the relationship between the center distance and geometric distance of the collision model,a fast detection algorithm of cable vector collision is proposed: The reasonableness of the cable collision detection model and the effectiveness of the proposed algorithm are verified by simulation.The simulation results show that the proposed method can meet the fast detection principle and the accuracy requirements in complex virtual environment.Finally,a planning research method suitable for such under-constrained cable-driven system is proposed.By constructing the cable sweeping equation and the obstacle implicit equation,the cable’s univariate polynomial equations are obtained simultaneously.A point to point decomposition trajectory planning is carried out for the initial trajectory of the lifted object in the variable cable length workspace.The differential manifold and the tangent space theory of manifolds are introduced to plan the predicted trajectory of the decomposition trajectory of the lifted object.Based on the dynamic characteristics of the system,the tangent vector selection of the predicted trajectory is determined.Finally,a three-layer planning strategy of unconstrained multi-robot collaborative towing system is realized,which took the lifted object as the planning object,the robot end as the planning intermediate link,and the cable obstacle avoidance as the planning purpose.