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.

中文翻译：

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基于ISC相似度的多轴运动系统时间最优平滑轨迹规划

摘要

针对多轴运动系统的时间最优平滑轨迹规划，提出一种基于相平面改进的平方余弦（ISC）相似度的规划算法。改进的平方余弦相似算法和插值轨迹的运动学约束用于找到时间最优的平滑轨迹。在该算法中，多轴运动系统工作台的运动轨迹由标量路径坐标表示。并通过多次调整离散点间距进行重新离散化，得到不同离散点个数的轨迹。通过类似数值积分的算法规划相平面中相应的时间最优轨迹。然后使用改进的平方余弦相似度算法比较时间最优轨迹之间的相似度，以找到具有高相似度的轨迹。最后通过插值轨迹的加速度约束得到时间最优的平滑轨迹。在两轴运动系统上的实验表明，该算法规划出的时间最优轨迹满足动力学和运动学约束，有效减少了规划计算时间，获得了平滑的轨迹。实验中，与类数值积分时间最优轨迹规划算法相比，两轴运动系统Z轴、X轴和垂直方向的最大加速度分别降低了37.66%、11%和31.42% ， 分别。