A system for providing the reliable and numerically efficient generation of time-optimum trajectories with easy-to-track or continuous acceleration profiles for simple and blended moves of single- and multi-arm robotic manipulators, such as an extension and retraction move along a straight line or a rotary move following a circular arc, with velocity, acceleration, jerk, and jerk rate constraints. A time-optimum trajectory is the set of the position, velocity, and acceleration profiles which describe the move of a selected end effector along a given path in the shortest time possible without violating given constraints, with a special case being an optimum abort trajectory, which brings the moving arm into complete rest in the shortest time. The invention involves firstly identifying the set of fundamental trajectory shapes which cover all possible combinations of constraints for a given category of moves, e.g., a move along a straight line or along a circular arc; next, decomposing the fundamental shapes into segments where a single constraint is active; and, then, determining the time optimum paths in the segments. As a result, a unique design of time-optimum trajectories is produced based on a set of pre-defined trajectory shapes. The invention also involves the blending of simple moves into a single trajectory by decomposing trajectories of the individual moves into their orthogonal components and overlapping them for a given time interval, which results in a non-stop move along a smooth transfer path.
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