An improved PSO algorithm for time-optimal trajectory planning of Delta robot in intelligent packaging

  • Cheng LIU
  • Guo-Hua CAOEmail author
  • Yong-Yin QU
  • Yan-Ming CHENG


With the advancement of the times, robotics technology is also developing rapidly. Some large enterprises in China use robots to work in manufacturing and handling positions, and also make robots more and more widely used. This paper focuses on the trajectory planning strategy for three-degree-of-freedom high-speed parallel manipulator of Delta robot in Cartesian space under high-speed operation handling, the point-to-point “door” type handling operation trajectory under the condition of ensuring control accuracy and increasing productivity in intelligent packaging is established based on the inverse kinematics model of the manipulator. The 4–3–3-4 degree polynomial interpolation is presented to control height of obstacle avoidance and trajectory length, on this basis, the mapping relationship between the motion features in operation space and those in joint space is established. Taking into account the complexity of trajectory optimization due to multiple constraints, in order to reduce the difficulty of trajectory optimization, it is necessary to ensure smoothness and constrains of angular displacement, angular velocity and angular acceleration of each joint in space, an improved particle swarm optimization algorithm is proposed to optimize trajectory running time of the 4–3–3-4 degree polynomial interpolation. The simulation results by using Matlab indicate that the accurate and stable time-optimal trajectory planning of 4–3–3-4 degree polynomial interpolation can be achieved by means of the improved particle swarm optimization algorithm. Compared with other trajectory planning algorithms, the proposed algorithm is easier to implement, which not only improves the local convergence of particle swarm optimization algorithm, achieves the time optimal trajectory planning of Delta robot, but also realizes the controllability of obstacle avoidance height, therefore which realizes the fast, accurate and safe operation in intelligent packaging.


Intelligent manufacturing 4–3–3-4 degree polynomial Trajectory planning Time-optimal Particle swarm optimization Delta robot Intelligent packaging 



This works was supported by the Jilin provincial development and reform commission (Grant: 2018C035-1), Jilin provincial science and technology innovation talents & team project (Grant: 20190101018JH), and Jilin provincial science and Technology Department (Grant: 20160101276JC).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Cheng LIU
    • 1
    • 2
  • Guo-Hua CAO
    • 1
    Email author
  • Yong-Yin QU
    • 2
  • Yan-Ming CHENG
    • 2
  1. 1.College of Mechanical and Electric EngineeringChangchun University of Science and TechnologyChangchunChina
  2. 2.College of Electrical and Information EngineeringBeihua UniversityJilinChina

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