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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (5): 1030-1037    DOI: 10.3785/j.issn.1008-973X.2023.05.019
    
Multi-orientation trajectory smoothing planning of robot for dental implant
Chong-liang ZHONG1(),Yun-feng LIU2,Wei-dong ZHU1,Fu-dong ZHU3,*()
1. School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
2. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, China
3. Stomatological Hospital, School of Medicine, Zhejiang University, Hangzhou 310006, China
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Abstract  

A highly automated dental implant surgery robot system was developed based on the optical positioning technology according to the requirements of dental implant surgery. The transformation of system space coordinate system was studied. The smooth orientation trajectory planning has an important impact on the accuracy and efficiency of the dental implant robot. Then a multi-orientation C2 continuous smooth interpolation algorithm was proposed based on the quaternion and rotation vector. The rotation vector was interpolated by smooth splicing of linear interpolation and the B-spline curve in three-dimensional space, and the corresponding quaternion would maintain the continuity in three-dimensional space. The multi-orientation C2 continuous interpolation calculation of unit quaternion was realized. The proposed B-spline multi-orientation smooth interpolation algorithm has C2 continuity through the experimental analysis and comparative verification is superior to the SQUAD algorithm in real-time performance and motion efficiency, and is suitable for multi-orientation trajectory planning of robot end effector.

Key words： dental implant      dental implant surgery robot system      orientation trajectory planning      quaternion      multi-orientation smooth interpolation     
Received: 28 May 2022      Published: 09 May 2023
CLC:  TP 242  
Fund:  中国牙病防治基金会资助项目(A2021-008); 国家自然科学基金资助项目(52175280)
Corresponding Authors: Fu-dong ZHU     E-mail: zhongcl@zju.edu.cn;zfd@zju.edu.cn
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Chong-liang ZHONG
Yun-feng LIU
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Cite this article:

Chong-liang ZHONG,Yun-feng LIU,Wei-dong ZHU,Fu-dong ZHU. Multi-orientation trajectory smoothing planning of robot for dental implant. Journal of ZheJiang University (Engineering Science), 2023, 57(5): 1030-1037.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.05.019     OR     https://www.zjujournals.com/eng/Y2023/V57/I5/1030


面向口腔种植的机器人多姿态轨迹平滑规划

根据口腔种植手术的要求，基于光学定位技术开发了一套自动化程度较高的种植牙手术机器人系统，并且对系统空间坐标系转换进行研究. 平滑的姿态轨迹规划对口腔种植机器人工作时的精度和效率有着重要的影响，提出一种基于四元数和旋转向量的多姿态C2连续的平滑插值算法. 在三维空间中采用线性插值与B样条曲线平滑拼接的方式对旋转向量进行插值计算，所对应的四元数将保持在三维空间中的连续性，实现对单位四元数C2连续的多姿态平滑插值. 通过实验分析和对比验证，所提B样条多姿态平滑插值算法具有C2连续性，在实时性能和运动效率方面优于SQUAD算法，适用于机器人末端执行器的多姿态轨迹规划.


关键词： 口腔种植,  种植牙手术机器人系统,  姿态轨迹规划,  四元数,  多姿态平滑插值 
性能指标 参数
最大负载/kg 7.0
轴数 7
定位精度/mm ±0.1
转速精度/% ±2.0
重量/kg 25.5
防护等级 IP54
Tab.1 Performance parameters of LBR Med 7 R800 robot
技术指标 参数
定位误差/mm 0.12
最大帧频/Hz 250
平均延迟/ms <4.00
视场范围/mm 950~2 400
工具类型 被动式
工具最大数量/件 25
Tab.2 Technical parameters of Polaris Vega XT system
Fig.1 Dental implant surgery robot system
Fig.2 Coordinate system transformation relationship of surgical robot system
Fig.3 Construction of smooth transition curve
序号 $\theta /{\text{rad}}$ ${\boldsymbol{n}}$ ${\boldsymbol{q}}$ ${\boldsymbol{P}}$
$A$ ${\text{π/4} }$ $ \left[ {0.2,0.3,0.9327} \right] $ $ [0.9239,0.0765,0.1148,0.3569] $ $ \left[ {0.1571,0.2356,0.7325} \right] $
$B$ ${\text{π/3} }$ $ \left[ {1,0,0} \right] $ $ [0.8660,0.5000,0,0] $ $ \left[ {1.0472,0,0} \right] $
$C$ ${\text{π/6} }$ $ \left[ {0,1,0} \right] $ $ [0.9659,0,0.2588,0] $ $ \left[ {0,0.5236,0} \right] $
Tab.3 Information of key orientations
Fig.4 Quaternion multi-orientation interpolation curves for different algorithms
Fig.5 Augular, angular velocity and angular acceleration changing curves during multi-orientation interpolation
Fig.6 Rotation axis trajectory curves for different algorithms
关键姿态数量 ${t }{\text{/s} }$
SLERP SQUAD 所提算法
3 0.618 18.200 5.690
50 10.200 451.0 169.0
100 21.1 917.0 346.0
Tab.4 Calculation time of different algorithms
关键姿态数量 ${\theta _{\text{d}}}{\text{/rad}}$
SLERP SQUAD 所提算法
3 4.541 4.587 4.561
100 197.5 212.9 203.9
1000 2188 2468 2282
Tab.5 Total angular displacement of different algorithms
Fig.7 Change of euler angles in robot Cartesian space for different algorithms
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