| This dissertation presents a new method for the planning of minimum-time robot trajectories under actuator constraints when the workspace of the robot contains obstacles and smooth motion of the robot is desired. The trajectory functions adopted are a set of localized polynomials defined in joint space. The end-effector positions defined by the trajectory polynomials are constrained to be inside of a collision-free space represented by a "tube". The configuration of the tube is specified by a set of tube parameters; reference points and path tolerances. In this dissertation, the tube parameters are assumed to be given by a path planner.; A two-phase optimization algorithm, consisting of a branch-and-bound search followed by a gradient search, is developed for three polynomial construction schemes. The three schemes are different in the way they handle the final boundary conditions for the robot motion. The resulting order of polynomials for scheme 1 is all cubic except for the last segment which is quintic. Scheme 2 consists of all cubic polynomials except the last two segments which are both quartics, while scheme 3 consists of all quartics. To test the two-phase algorithm for the three schemes, six FORTRAN codes are developed, and implemented for a two-link manipulator simulated on an IBM 3081 computer.; The results of the experiments showed that scheme 3 is dominant over scheme 1 and scheme 2. Scheme 1, in general, resulted in the largest minimum-times. Although scheme 3 needs longer computing time than others, scheme 3 turns out to be the most appropriate for off-line trajectory planning. Compared to the conventional and other existing methods, the new method provides considerably superior solutions as the path tolerance increases. Fundamental issues regarding the behavior of the minimum-time trajectory are discussed including algorithmic issues, such as convergence and optimality. |
