Three-dimensional workspace visualization for redundant articulated chains

This thesis deals with the problem of the 3D workspace visualization for anthropomorphic linkages, not only those with redundant degrees of freedom but also those with joint limits. Although the workspace problem has important applications in a variety of fields such as computer-aided design, ergonomic studies, and robotics, the problem's computational complexity has never been analyzed. In addition, previous techniques suffer from one or more of the following drawbacks: high computational cost, computing 2D workspace cross sections, dealing with manipulators that have specialized geometry, or sensitivity to geometrical and numerical errors or approximations. We analyze the computational complexity of the problem and prove that it is NP-hard. Then, we decompose it into three major subproblems: workspace point generation, visualization, and criteria selection. We describe and compare different techniques for computing workspace points: direct kinematics based algorithms, nonlinear programming based algorithms, and force application based algorithms. Each class of these algorithms has advantages and disadvantages, and none of them supersedes the others in all applications. Instead of debating the merits of these algorithms, we integrate them into "Hybrid algorithms" that are capable of generating workspace points efficiently. The visualization module can be built by either surface-based or volume-based algorithms. Each class of these algorithms is more suitable than the others for certain applications. The criteria selection module interacts with the user and tailors the most appropriate techniques, from the workspace point generation and the visualization modules, based on the application requirements.