A parameter optimization approach to the time-minimization of robotic motions along specified paths is presented for the case when: (i) the velocity profile is a prescribed sequence of constant acceleration/deceleration segments with unspecified, but bounded vertex velocities at given path stations; (ii) the relative robot/path location can be varied. Such optimizations occur when technological requirements impose a certain velocity profile along the path due to velocity and acceleration constraints. Full nonlinear manipulator dynamics and path parameterization are used to determine the optimal velocity profile and robot location consistent with the actuator/configuration limitations. No numerical integration or search for switching curve are involved in the solution. Examples of time-and-location optimized robotic motions with specified velocity profile are presented.

We present a new algorithm for fine motion planning in geometrically complex situations. Geometrically complex situations have complex robot and environment geometry, crowded environments, narrow passages and tight fits. They require complex robot motions with coupled degrees of freedom. The algorithm constructs a path by incrementally building a graph of linearized convex configuration space cells and solving a series of linear optimization problems with varying objective functions. Its advantages are that it better exploits the local geometry of narrow passages in configuration space, and that its complexity does not significantly increase as the clearance of narrow passages decreases. We demonstrate the algorithm on examples which other planners could not solve.