Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(4): 1238-1251

https://doi.org/10.1007/s12555-022-1082-8

© The International Journal of Control, Automation, and Systems

Time-optimal and Smooth Trajectory Planning for Multi-axis Motion Systems Based on ISC Similarity

Tie Zhang*, Jia Cheng, and Yanbiao Zou

South China University of Technology

Abstract

Aiming at time-optimal smooth trajectory planning for multi-axis motion systems, this paper proposes a planning algorithm based on improved sqrt-cosine (ISC) similarity in the phase plane. The improved sqrt-cosine similarity algorithm and the kinematic constraint of the interpolated trajectories are used to find the time-optimal smooth trajectory. In the proposed algorithm, the trajectory of the multi-axis motion system workbench is represented by scalar path coordinates. And it is re-discretized by adjusting the spacing of the discrete points several times to obtain trajectories with different numbers of discrete points. The corresponding time-optimal trajectories in the phase plane are planned through a numerical integration-like algorithm. The similarity between the timeoptimal trajectories is then compared using an improved sqrt-cosine similarity algorithm to find the trajectories with high similarity. Finally, the time-optimal smooth trajectory is obtained by the acceleration constraint of the interpolated trajectory. Experiments on a two-axis motion system have shown that the time-optimal trajectory planned by the proposed algorithm satisfied the constraints of dynamics and kinematics, effectively reduced the planning calculation time, and obtained a smooth trajectory. In experiments, compared with numerical integration-like timeoptimal trajectory planning algorithm, the maximum accelerations in the Z-axis, X-axis, and vertical directions of the two-axis motion system have been reduced by 37.66%, 11%, and 31.42%, respectively.

Keywords Improved-sqrt-cosine similarity, multi-axis motion system, smooth trajectory, time-optimal.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(4): 1238-1251

Published online April 1, 2024 https://doi.org/10.1007/s12555-022-1082-8

Copyright © The International Journal of Control, Automation, and Systems.

Time-optimal and Smooth Trajectory Planning for Multi-axis Motion Systems Based on ISC Similarity

Tie Zhang*, Jia Cheng, and Yanbiao Zou

South China University of Technology

Abstract

Aiming at time-optimal smooth trajectory planning for multi-axis motion systems, this paper proposes a planning algorithm based on improved sqrt-cosine (ISC) similarity in the phase plane. The improved sqrt-cosine similarity algorithm and the kinematic constraint of the interpolated trajectories are used to find the time-optimal smooth trajectory. In the proposed algorithm, the trajectory of the multi-axis motion system workbench is represented by scalar path coordinates. And it is re-discretized by adjusting the spacing of the discrete points several times to obtain trajectories with different numbers of discrete points. The corresponding time-optimal trajectories in the phase plane are planned through a numerical integration-like algorithm. The similarity between the timeoptimal trajectories is then compared using an improved sqrt-cosine similarity algorithm to find the trajectories with high similarity. Finally, the time-optimal smooth trajectory is obtained by the acceleration constraint of the interpolated trajectory. Experiments on a two-axis motion system have shown that the time-optimal trajectory planned by the proposed algorithm satisfied the constraints of dynamics and kinematics, effectively reduced the planning calculation time, and obtained a smooth trajectory. In experiments, compared with numerical integration-like timeoptimal trajectory planning algorithm, the maximum accelerations in the Z-axis, X-axis, and vertical directions of the two-axis motion system have been reduced by 37.66%, 11%, and 31.42%, respectively.

Keywords: Improved-sqrt-cosine similarity, multi-axis motion system, smooth trajectory, time-optimal.

IJCAS
April 2024

Vol. 22, No. 4, pp. 1105~1460

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IJCAS

eISSN 2005-4092
pISSN 1598-6446