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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (11): 2229-2236    DOI: 10.3785/j.issn.1008-973X.2025.11.001
    
Desensitization design for parallel robots under multi-source hybrid uncertainty
Mingzhe TAO1,2(),Jinghua XU1,*(),Shuyou ZHANG1,Jianrong TAN1
1. Design Engineering Institute, Zhejiang University, Hangzhou 310058, China
2. State Key Laboratory of Transvascular Implantation Devices and TRIDI, Hangzhou 310009, China
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Abstract  

A desensitization design method for parallel robots considering multi-source uncertain hybrid perturbation was proposed aiming at the problem of optimal design of high-performance parallel robots. A probabilistic error model was established by using the first-order perturbation method for error modeling. The optimal dimension design parameters were obtained by using multi-target subregion meta-heuristic iterations after analyzing the high-value targets corresponding to the working subregion. A performance sensitivity index was constructed to optimally allocate the design tolerances. The sensitivity of maintenance to parameters was calculated by establishing an in-service accuracy performance sensitivity model, and a low-sensitivity preventive maintenance strategy was obtained. An additive manufacturing parallel robot was used as an example for validation. Results show that the static performance and dynamic in-service accuracy maintenance can be effectively improved via desensitization design.

Key words： parallel robots      multi-source hybrid uncertainty      desensitization design      multi-target subregion iteration      optimal tolerance allocation      preventive maintenance     
Received: 25 October 2024      Published: 30 October 2025
CLC:  TP 391  
Fund:  国家重点研发计划资助项目（2022YFB3303303）；国家科技重大专项资助项目（2024ZD0714401）
Corresponding Authors: Jinghua XU     E-mail: 12225017@zju.edu.cn;xujh@zju.edu.cn
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Mingzhe TAO
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Cite this article:

Mingzhe TAO,Jinghua XU,Shuyou ZHANG,Jianrong TAN. Desensitization design for parallel robots under multi-source hybrid uncertainty. Journal of ZheJiang University (Engineering Science), 2025, 59(11): 2229-2236.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.11.001     OR     https://www.zjujournals.com/eng/Y2025/V59/I11/2229


考虑多源混合不确定性的并联机器人降敏设计

针对高性能并联机器人优化设计的难题，提出考虑多源不确定混合扰动的并联机器人降敏设计方法. 利用一阶摄动方法进行误差建模，建立概率误差模型. 在分析工作子区域所对应的高价值靶目标后，采用多靶分域元启发式迭代获取最优的尺寸设计参数. 构建性能敏感度指标，对机器人设计公差进行优化分配. 通过建立在役精度性能敏感性模型，计算获取维保效果对于预防性维保策略参数的敏感性，制定得到低敏预防性维保策略. 以增材制造并联机器人为例进行分析，结果表明，利用降敏设计方法，能够有效地提高静态设计性能及动态在役精度保持能力.


关键词： 并联机器人,  多源混合不确定性,  降敏设计,  多靶分域迭代,  公差优化分配,  预防性维保 
Fig.1 Kinematical diagram of parallel robot for additive manufacturing
候选解设计变量/cm适应度
$ {r}_{{\mathrm{c}}} $$ {r}_{{\mathrm{a}}} $$ {l}_{{\mathrm{c}}} $$ {l}_{{\mathrm{a}}} $$\left| {{\mathrm{\Delta }{{\boldsymbol Z}}}} \right|/{\mathrm{mm}}$$ k $$ {F}_{\max} $$ {D}_{\max} $
110555115158.710.16281.321.09×10?41.60×104
296.1759.91115.02159.900.16581.101.01×10?41.20×104
3104.9955115148.130.16271.401.07×10?41.84×104
4104.9755115158.710.16281.321.09×10?41.60×104
5(选用解)86.8356.85115.43156.990.16681.07519.63×10?51.20×104
Tab.1 Candidate dimension for parallel robot after multi-objective sub-regional optimization
方法设计变量$ /\mathrm{c}\mathrm{m} $适应度
$ {r}_{{\mathrm{c}}} $$ {r}_{{\mathrm{a}}} $$ {l}_{{\mathrm{c}}} $$ {l}_{{\mathrm{a}}} $$ \left\| \Delta{\boldsymbol{Z}} \right\| /{\mathrm{mm}}$$ k $$ {F}_{\max} $$ {D}_{\max} $
原始设计变量90651251500.16911.188.88×10?51.58×104
PSO105551151400.16271.461.06×10?42.02×104
NSGA-II87.8564.31115.02159.680.16961.141.05×10?41.24×104
多靶分域优化86.8356.85115.43156.990.16681.079.63×10?51.20×104
Tab.2 Comparison of multi-objective sub-regional optimization with typical optimization algorithm
Fig.2 Error sensitivity of each independent error source
Fig.3 Comparison of effect before and after performing tolerance optimization allocation
编号基本尺寸/cm公差优化
分配值		依照国标
修整值		对应公差
等级
1120~18088.0 μm100 μmIT9
2120~18088.2 μm100 μmIT9
3120~18088.2 μm100 μmIT9
480~120134.0 μm140 μmIT10
580~120150.0 μm140 μmIT10
680~120150.0 μm140 μmIT10
7100~160622.28 μrad500 μradAT9
8100~160729.33 μrad800 μradAT10
9100~160729.33 μrad800 μradAT10
1040~631500 μrad1250 μradAT10
1140~631300 μrad1250 μradAT10
1240~631300 μrad1250 μradAT10
1363~1001200 μrad1000 μradAT10
1463~100500 μrad400 μradAT8
1563~100500 μrad400 μradAT8
1650~8050.0 μm46 μmIT8
1780~12050.0 μm54 μmIT8
Tab.3 Optimized distribution of tolerance grade after adjustment
参数数值参数数值
$ \mu $0.000 3$ {t}_{{\mathrm{m}}}/{\mathrm{d}} $0.5 d
$ \sigma $0.000 1$ {N}_{{\mathrm{m}}} $10
$ {C}_{{\mathrm{m}}} $/元1 200$ {e}_{\varepsilon }/{\mathrm{mm}} $[0.1, 0.3]
$ {C}_{{\mathrm{b}}} $/元5 000——
Tab.4 Parameter table of error source precision degradation model and in-service performance sensitivity model
Fig.4 Yields of preventive maintenance for additive manufacturing parallel robot
维保策略LR/d
未实施维保281
实施普通维保方法（Nm=0）1124
实施高敏维保策略参数的预防性维保方法（Nm=2）2036
实施高敏维保策略参数的预防性维保方法（Nm=8）1456
预防性维保降敏设计方法（Nm=4）2297
Tab.5 Effect comparison of different maintenance strategies on additive manufacturing parallel robot
Fig.5 Error distribution along contour of check valve and schematic of additive manufacturing
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