Smooth 3-Dimensional Path Generation with Guaranteed Maximum Distance from Via-Points

Path generation in 3 dimensions is addressed in this paper. In control of autonomous underwater or aerial vehicles, as well as manipulators' end-effector, it is required that the planned path exhibits specific characteristics of continuity up to the second, or third, order time derivatives. It is known, in fact, that closed loop performance benefits from regular enough control commands. In this paper, the path is supposed to be given in terms of 3D curves, such as, e.g., segments or circle' arcs, that need to be connected and that may eventually intersect in a point; in the latter case, the maximum distance from the intersection's point (via-point) needs to be strictly respected. Then, an effective solution to the problem of generating a smooth transition curve between two generic curves satisfying a maximum distance constraint from the intersecting point has been proposed. To test the approach, several case studies show its performance.