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.
Highlights
In the past three decades, the use of parallel manipulators [1,2,3] has been increased in industrial and academic fields [4,5,6], especially in the fields of product transportation and classification, motion simulators, multi-dimensional force sensors, micro-operation consoles, precision positioning devices, etc., for their relative features like superior rigidity, higher accuracy, lighter mechanical construction, resulting in a homogenous and symmetric force/torque distribution, easier inverse kinematic calculations [7,8,9]
This paper proposes a trajectory planning method for Delta parallel robot
A trajectory planning approach on the basis of quintic Pythagorean–Hodograph curve for Delta robot with a prescribed geometrical constraint is proposed in this paper
Summary
In the past three decades, the use of parallel manipulators [1,2,3] has been increased in industrial and academic fields [4,5,6], especially in the fields of product transportation and classification, motion simulators, multi-dimensional force sensors, micro-operation consoles, precision positioning devices, etc., for their relative features like superior rigidity, higher accuracy, lighter mechanical construction, resulting in a homogenous and symmetric force/torque distribution, easier inverse kinematic calculations [7,8,9]. The study of trajectory planning for a parallel Delta robot with prescribed geometrical constraint is more challenging problem. The PPO path should be transitioned through the smooth curve which deviates from the apex of the right angle by no more than a prescribed geometrical constraint. The relationship between the PH curve and constraint is used to improve the efficiency of the method, and the trajectory symmetry is used to generate part of the trajectory directly through a symmetric operation In this way, the real-time performance is improved.
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