Accurate Numerical Methods for Computing 2D and 3D Robot Workspace

Exact computation of the shape and size of robot manipulator workspace is very important for its analysis and optimum design. First, the drawbacks of the previous methods based on Monte Carlo are pointed out in the paper, and then improved strategies are presented systematically. In order to obtain more accurate boundary points of two-dimensional (2D) robot workspace, the Beta distribution is adopted to generate random variables of robot joints. And then, the area of workspace is acquired by computing the area of the polygon what is a closed path by connecting the boundary points together. For comparing the errors of workspaces which are generated by the previous and the improved method from shape and size, one planar robot manipulator is taken as example. A spatial robot manipulator is used to illustrate that the methods can be used not only on planar robot manipulator, but also on the spatial. The optimal parameters are proposed in the paper to computer the shape and size of 2D and 3D workspace. Finally, we provided the computation time and discussed the generation of 3D workspace which is based on 3D reconstruction from the boundary points.