Generation and optimality of trajectory described by B-spline

This paper discusses about the generation and optimality of the trajectory described by B-spline. In the trajectory generation values of B-spline control points are optimized by the complex method. The algorithm has following advantages: 1) it only needs computation of a performance index for the optimization but requires no computation of the gradient; 2) it is applicable to the problem of an arbitrary performance index to evaluate trajectories; 3) it can generate trajectories with continuous time derivative curves; and 4) it needs less memory to store the generated trajectories. For checking the optimality of the trajectories, it is applied to four types of trajectory generation: a manipulator trajectory generation, a solution of ordinary differential equation, a minimal time control problem, and a movement curve generation such as a cam curve one