Trajectory Planning and Optimization for a Par4 Parallel Robot Based on Energy Consumption

A study on trajectory planning and optimization for a Par4 parallel robot was carried out, based on energy consumption in high-speed picking and placing. In the end-effector operating space of the Par4 parallel robot, the rectangular transition of the pick-and-place trajectory was rounded by a Lamé curve. A piecewise design method was adopted to accomplish trajectory shape planning for displacement, velocity and acceleration. To make the Par4 robot’s end run more smoothly and to reduce residual vibration, asymmetric fifth-order and sixth-order polynomial motion laws were employed. With the aim of reaching the minimum mechanical energy consumption for the Par4 parallel robot, the recently proposed Grey Wolf Optimizer (GWO) algorithm was adopted to optimize the planning trajectory. The validity of the design method was verified by experiments, and it was found that the minimum mechanical energy consumption of the optimal trajectory planned under the law of fifth-order polynomial motion is lower than that of sixth-order polynomial motion. In addition, the experiments also revealed the optimal values of Parameters e and f, which were the parameters of the Lamé curve function. Parameter e can be calculated as half the pick-up span for the minimum mechanical energy consumption, unlike parameter f, whose optimal value depends on specific circumstances such as the pick-and-place coordinates and the pick-up height.