Multi-objective Optimization Allocation of Geometric Parameter Tolerances for Serial Robots Based on NSGA-II

doi:10.12068/j.issn.1005-3026.2024.06.010

Abstract

Abstract:

In order to improve the geometric positioning accuracy of robot end?effectors and allocate geometric parameter tolerances reasonably in the initial design stage of robot precision， a multi?objective tolerance optimization allocation method based on fast non?dominated sorting genetic algorithm （NSGA-II） with elite strategy was proposed. ROKAE XB7 6-DOF serial robot was studied， and the minimum cost single?objective tolerance optimal allocation based on genetic algorithm （GA） and NSGA-II multi?objective tolerance optimal allocation method were used to optimize the tolerance allocation of DH（Denavit?Hartenberg） parameters. In the case of the same precision design objectives and genetic algorithm parameter settings， compared with the minimum cost geometric parameter tolerance optimization allocation based on the genetic algorithm， the multi?objective optimal allocation based on NSGA-II could provide a series of optimal solutions with different manufacturing costs and different precision design requirements. The relaxation rate of tolerance is relatively high， and the result of parameter tolerance optimization is better.

Key words: serial robot, positioning accuracy, tolerance optimization allocation, multi‐objective optimization

CLC Number:

TH 115

Li-jin FANG, Yue GAO, Xin-xing CAO, Yun-peng GONG. Multi-objective Optimization Allocation of Geometric Parameter Tolerances for Serial Robots Based on NSGA-II[J]. Journal of Northeastern University(Natural Science), 2024, 45(6): 829-836.

Figures/Tables 14

References 14

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i	a/mm	α/rad	d/mm	θ/（°）
1	30	-π/2	0	θ₁
2	340	0	0	θ₂
3	35	-π/2	0	θ₃
4	0	π/2	345	θ₄
5	0	-π/2	0	θ₅
6	0	0	87	θ₆

i	a/mm	α/rad	d/mm	θ/（°）
1	30	-π/2	0	θ₁
2	340	0	0	θ₂
3	35	-π/2	0	θ₃
4	0	π/2	345	θ₄
5	0	-π/2	0	θ₅
6	0	0	87	θ₆

误差项	Δ_j	δ₁	δ₂
Δa₁/mm	1.4	0.064 1	0.078 0
Δa₂/mm	1.4	0.057 8	0.073 5
Δa₃/mm	1.4	0.058 4	0.073 1
Δa₄/mm	1.4	0.055 9	0.071 3
Δa₅/mm	1.4	0.061 1	0.071 1
Δa₆/mm	1.4	0.060 1	0.068 9
Δd₁/mm	1.4	0.063 5	0.072 4
Δd₂/mm	1.4	0.055 6	0.071 7
Δd₃/mm	1.4	0.052 5	0.073 7
Δd₄/mm	1.4	0.060 5	0.077 0
Δd₅/mm	1.4	0.058 6	0.076 2
Δd₆/mm	1.4	0.061 3	0.0756
Δα₁/rad	0.001 8	0.001 1	0.001 1
Δα₂/rad	0.003 2	0.001 4	0.001 4
Δα₃/rad	0.003 2	0.001 3	0.001 1
Δα₄/rad	0.016 1	0.003 4	0.003 5
Δα₅/rad	0.016 1	0.003 4	0.003 5
Δθ₁/rad	0.001 8	0.001 0	0.001 0
Δθ₂/rad	0.001 8	0.000 8	0.000 8
Δθ₃/rad	0.003 2	0.001 2	0.001 2
Δθ₄/rad	0.016 1	0.006 6	0.006 5
Δθ₅/rad	0.016 1	0.003 3	0.003 4

误差项	Δ_j	δ₁	δ₂
Δa₁/mm	1.4	0.064 1	0.078 0
Δa₂/mm	1.4	0.057 8	0.073 5
Δa₃/mm	1.4	0.058 4	0.073 1
Δa₄/mm	1.4	0.055 9	0.071 3
Δa₅/mm	1.4	0.061 1	0.071 1
Δa₆/mm	1.4	0.060 1	0.068 9
Δd₁/mm	1.4	0.063 5	0.072 4
Δd₂/mm	1.4	0.055 6	0.071 7
Δd₃/mm	1.4	0.052 5	0.073 7
Δd₄/mm	1.4	0.060 5	0.077 0
Δd₅/mm	1.4	0.058 6	0.076 2
Δd₆/mm	1.4	0.061 3	0.0756
Δα₁/rad	0.001 8	0.001 1	0.001 1
Δα₂/rad	0.003 2	0.001 4	0.001 4
Δα₃/rad	0.003 2	0.001 3	0.001 1
Δα₄/rad	0.016 1	0.003 4	0.003 5
Δα₅/rad	0.016 1	0.003 4	0.003 5
Δθ₁/rad	0.001 8	0.001 0	0.001 0
Δθ₂/rad	0.001 8	0.000 8	0.000 8
Δθ₃/rad	0.003 2	0.001 2	0.001 2
Δθ₄/rad	0.016 1	0.006 6	0.006 5
Δθ₅/rad	0.016 1	0.003 3	0.003 4

项目	Max	Mean	RMSE	合格率	成本指数	TRR
项目	mm	mm	mm	%	成本指数	%
δ₁	1.684 3	0.872 1	0.216 6	99.85	10 066	-42.78
δ₂	1.647 2	0.866 4	0.220 5	99.80	10 074	-29.26