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由于多机器人绳牵引负载的欠约束系统,不满足力封闭条件,同时方程组一般不相容,无法求出准确的工作空间。建立了系统的静平衡方程,提出利用最小二乘法原理结合蒙特·卡罗方法,对负载低速或准静态运动时,能够快速求出其近似静平衡工作空间,并分别利用法方程和QR分解给出了绳拉力的表达式。在机器人的位置和负载的位姿不发生力旋量失效的情况下,其有唯一的最小二乘解。通过仿真验证了该方法的有效性,利用该方法可快捷地求出不同空间构型的欠约束绳牵引系统的静平衡工作空间,为系统规划与控制的研究提供了基础。
Due to the underconstrained system of multi-robot rope traction load, the closed condition of force is not satisfied. At the same time, the equations are generally incompatible and the accurate working space can not be obtained. The static equilibrium equation of the system is established. The method of least square method combined with Monte Carlo method is proposed to calculate the approximate static equilibrium working space for low or quasi-static load with load, and use the normal equation and QR decomposition respectively Out of the rope tension expression. It has a unique least square solution in the case where the position of the robot and the pose of the load do not exert a force spin failure. The effectiveness of this method is verified by simulation. By using this method, the static balance working space of under-constrained rope traction system with different space configurations can be quickly calculated, which provides the basis for the study of system planning and control.