Abstract
Trajectory planning is a fundamental issue for robotic applications and automation in general. The ability to generate trajectories with given features is a key point to ensure significant results in terms of quality and ease of performing the required motion, especially at the high operating speeds necessary in many applications. The general problem of trajectory planning in Robotics is addressed in the paper, with an overview of the most significant methods, that have been proposed in the robotic literature to generate collision-free paths. The problem of finding an optimal trajectory for a given path is then discussed and some significant solutions are described.