Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Abstract

A new trajectory planning approach on the basis of the quintic Pythagorean–Hodograph (PH) curve is presented and applied to Delta robot for implementing pick-and-place operation (PPO). To satisfy a prescribed geometrical constraint, which indicates the distance between the transition segment curve and right angle of PPO trajectory is no greater than a prescribed value, the quintic PH curve is used to produce a connection segment path for collision avoidance. The relationship between the PH curve and constraint is analyzed, based on which PH curve is calculated simply. Afterwards, the trajectory is planned in different phases with different motion laws, i.e. polynomial motion laws and PH curve parameter-dependent motion laws, to obtain a smooth performance both in Cartesian and joint space. The relationship between the PH curve and constraint is also used to improve the efficiency of calculation, and the trajectory symmetry is used to reduce calculation time by direct symmetric transformation. Thus, real-time performance is improved. The results of simulations and experiments indicate that the approach in this paper can provide smooth motion and meet the real-time requirement under the prescribed geometrical constraint.