A unified trajectory generation algorithm for manipulators by using B-spline

The unified trajectory generation algorithm proposed is applied to three types of trajectory generation: 1) trajectories of a workpiece manipulated to avoid obstacles; 2) joint trajectories of a manipulator with end-effector path constraints; and 3) collision-free joint trajectories of a manipulator with fixed or non-fixed working time. The obtained results are satisfactory and the advantages of the proposed method are confirmed: 1) it is extended to be applied to the time optimal problem, 2) it is applicable to the problem of an arbitrary performance index to evaluate trajectories, 3) it is applicable to the problem which has very complex constraints such as collision-free, kinematic, and full dynamic constraints, 4) it can generate trajectories with continuous time derivative curves, and 5) it needs less memory to store the trajectories generated.