A Parallel Algorithm for Computing 3-D Reachable Workspaces

The problem of computing the 3-D workspace for redundant articulated chains has applications in a variety of fields such as robotics, computer aided design, and computer graphics. The computational complexity of the workspace problem is at least NP-hard. The recent advent of parallel computers has made practical solutions for the workspace problem possible. Parallel algorithms for computing the 3-D workspace for redundant articulated chains with joint limits are presented. The first phase of these algorithms computes workspace points in parallel. The second phase uses workspace points that are computed in the first phase and fits a 3-D surface around the volume that encompasses the workspace points. The second phase also maps the 3-D points into slices, uses region filling to detect the holes and voids in the workspace, extracts the workspace boundary points by testing the neighboring cells, and tiles the consecutive contours with triangles. The proposed algorithms are efficient for computing the 3-D reachable workspace for articulated linkages, not only those with redundant degrees of freedom but also those with joint limits.