Trajectory Planning of Robot End-Effector Position and Orientation Based on Cubic Spline

Trajectory planning for the end effector of industrial robots has been a hot topic in the field of robotics. A continuous and smooth trajectory of the end effector’s pose is beneficial for avoiding unnecessary impacts and vibrations, thereby improving the performance and lifespan of industrial robots. In recent years, researchers have predominantly focused on the trajectory planning of multi-directional variations in orientation using quaternions, while giving less attention to the coordinated planning of position and orientation. To address this issue, this paper proposes an efficient trajectory planning method based on improved spline curve interpolation. The orientation of key pose points, characterized by multi-directional variations, is represented using quaternions. By employing a quaternion dimension reduction algorithm, these quaternions are transformed into vector forms in three-dimensional space, allowing for unified representation of position and orientation within the same dimension. Taking the chord length between key pose points as a parameter, the position and orientation components are subjected to cubic spline curve interpolation with chord length as the independent variable. The proposed method is applicable for coordinated planning of position and orientation trajectories, ensuring high-order continuity of the pose trajectory. The effectiveness and rationality of the proposed method are validated through a set of key pose points featuring multi-directional variations. Finally, a comparative analysis is conducted between this set of key pose points and existing trajectory planning algorithms. Experimental results demonstrate that the proposed method not only guarantees high-order continuity of the trajectory but also exhibits higher smoothness.

I. Introduction

With the continuous advancement of intelligence and unmanned trends, industrial robots have become important equipment widely used in the manufacturing industry. The smoothness requirement for the pose trajectory of the robot’s end effector has become increasingly stringent. A smooth end effector pose trajectory not only improves the efficiency of the robot’s operations but also reduces unnecessary vibrations and impacts, thereby enhancing the robot’s lifespan. Pose trajectory planning is a crucial research area in the field of robot motion control, encompassing both position planning and orientation planning.