改进灰狼算法在搬运机器人轨迹规划中的应用

张攀; 刘雨晗; 张威

doi:10.13433/j.cnki.1003-8728.20220286

改进灰狼算法在搬运机器人轨迹规划中的应用

doi: 10.13433/j.cnki.1003-8728.20220286

张攀^{1, 2,},
刘雨晗³,
张威^{1, 2, 4, ,}

1.
中国民航大学航空工程学院，天津　300300
2.
民航航空公司人工智能重点实验室，广州　510470
3.
中国民航大学安全科学与工程学院，天津　300300
4.
中国民航航空地面特种设备研究基地，天津　300300

基金项目: 国家自然科学基金民航联合基金重点项目（U2033208）、中央高校基本科研业务费项目（3122023018）及天津市研究生科研创新项目（2021YJSS122）

详细信息

作者简介:
张攀，讲师，博士，p-zhang@cauc.edu.cn

通讯作者:
张威，教授，博士生导师，博士，weizhang@cauc.edu.cn

中图分类号: TP242；V354
计量
- 文章访问数: 76
- HTML全文浏览量: 33
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2022-03-29
- 刊出日期: 2024-03-25

Application of Improved Gray Wolf Algorithm in Trajectory Planning of Pallet Handling Robot

ZHANG Pan^{1, 2
,},
LIU Yuhan³,
ZHANG Wei^{1, 2, 4
, ,}

1.
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China
2.
Civil Aviation Key Laboratory of Artificial Intelligence for Airlines, Guangzhou 510470, China
3.
College of Safety Science and Engineering, Civil Aviation University of China, Tianjin 300300, China
4.
CAAC Aviation Ground Special Equipment Research Base, Tianjin 300300, China

摘要

摘要: 为提高托盘式搬运机器人的运行稳定性，提出一种基于改进灰狼算法的机器人加速度最优轨迹规划方法。针对灰狼算法局部收敛、寻优性能不足等问题，引入Logistic-Tent混沌映射，优化初始种群；引入差分优化算法，提高全局搜索能力；引入淘汰进化机制，优化种群结构，从而全面提升优化性能。仿真结果表明，对比标准灰狼算法和粒子群算法，改进灰狼算法在不同类型的测试函数中具有更好的收敛速度和算法精度；在搬运机器人轨迹规划的应用中，经过该算法优化后的机器人最大关节角加速度下降了44.11%，大幅提高了运行稳定性。
- 搬运机器人 /
- 轨迹规划 /
- 加速度 /
- 灰狼算法
Abstract: In order to improve the running stability of the pallet handling robot, an optimal trajectory planning method for robot acceleration based on the improved gray wolf algorithm is proposed. Aiming at the problems of local convergence and insufficient optimization performance of gray wolf algorithm, the Logistic-Tent chaotic map is introduced to optimize the initial population; the differential optimization algorithm is introduced to improve the global search ability; the elimination evolution mechanism is introduced to optimize the population structure and improve the optimization performance in all-round way. Compared with the standard gray wolf algorithm and the particle swarm algorithm, simulation results show that improved gray wolf algorithm has better convergence speed and algorithm accuracy in different types of test functions. In the application of the trajectory planning of the handling robot, after the optimization of the algorithm, the maximum joint angular acceleration of the robot is reduced by 44.11%, which greatly improves the running stability.
- handling robot /
- trajectory planning /
- acceleration /
- gray wolf algorithm

HTML全文

图 1 PSO、GWO和IGWO算法求解8种基准函数的收敛曲线图

Figure 1. Convergence curves of PSO, GWO, and IGWO algorithms for solving 8 benchmark functions

下载: 全尺寸图片幻灯片

图 2 机器人接放行李运动轨迹

Figure 2. Robot's movement trajectory for handling luggage

下载: 全尺寸图片幻灯片

图 3 机器人各关节角度

Figure 3. Angles of robot joints

下载: 全尺寸图片幻灯片

图 4 机器人各关节角速度

Figure 4. Angular velocity of robot joints

下载: 全尺寸图片幻灯片

图 5 机器人各关节角加速度

Figure 5. Angular acceleration of robot joints

下载: 全尺寸图片幻灯片

图 6 优化后的关节角加速度曲线

Figure 6. Optimized joint angular acceleration curve

下载: 全尺寸图片幻灯片

表 1 各算法参数设置

Table 1. Parameter settings for each algorithm

算法	参数
IGWO	交叉概率0.8；缩放因子0.6；种群淘汰比例因子6
PSO	惯性权重分别为0.9和0.6，学习因子c₁=c₂=2；个体速度范围为[−0.5,0.5]

下载: 导出CSV

表 2 各基准函数

Table 2. Each benchmark function

函数	表达式	维数	定义域
F₁	${F_1}(x) = {\max _i}\left\{ {\|{x_i}\|,1 \leqslant i \leqslant 30} \right\}$	30	[−100, 100]
F₂	${F_2}(x) = \displaystyle\sum\limits_{i = 1}^{30} {{\left(\displaystyle\sum\limits_{i = 1}^{30} {{x_j}} \right)^2}} $	30	[−100, 100]
F₃	${F_3}(x) = - 20\exp \left( - 0.2\sqrt {\dfrac{1}{ {30} }\displaystyle\sum\limits_{i = 1}^{30} {x_i^2} } \right) - {\rm exp}\left(\dfrac{1}{ {30} }\displaystyle\sum\limits_{i = 1}^{30} {\cos 2{\text{π} } x_i^2} \right) + 20 + e$	30	[−32, 32]
F₄	${F_4}(x) = \displaystyle\sum\limits_{i = 1}^{30} {\|{x_i}\|} + \displaystyle\prod\limits_{i = 1}^{30} {\|{x_i}\|} $	30	[−10, 10]
F₅	${F_5}(x) = \displaystyle\sum\limits_{i = 1}^{30} {i{x_i}^4} + {\rm rand}[0,1)$	30	[−1.28, 1.28]
F₆	${F_6}(x) = \displaystyle\sum\limits_{i = 1}^{30} { - {x_i}\sin (\sqrt {\|{x_i}\|} )} $	30	[−10, 10]
F₇	${F_7}(x) = {\left[\begin{array}{c}\dfrac{1}{{500}} + \displaystyle\sum\limits_{j = 1}^{25} {\dfrac{1}{{j + \displaystyle\sum\limits_{i = 1}^2 {{{({x_i} - {a_{ij}})}^6}} }}} \end{array}\right]^{ - 1}}$	2	[−65, 65]
F₈	${F_8}(x) = \displaystyle\sum\limits_{i = 1}^{30} {[{x_i}^2} - 10\cos (2{\text{π}} {x_i}) + 10]$	30	[−5.12, 5.12]

下载: 导出CSV

表 3 基准测试函数寻优结果

Table 3. Benchmarking function optimization results

函数	方法	平均值	最差值	最优值	标准差
F₁	PSO	1.135816	1.514037	0.907737	0.183233
	GWO	7.29 × 10⁻⁷	1.58 × 10⁻⁶	6.31 × 10⁻⁸	5.01 × 10⁻⁷
	IGWO	7.18 × 10⁻¹⁰	3.09 × 10⁻⁹	5.12 × 10⁻¹¹	8.28 × 10⁻¹⁰
F₂	PSO	81.48382	114.4711	39.78484	21.821
	GWO	3.20 × 10⁻⁵	2.95 × 10⁻⁴	2.29 × 10⁻⁹	8.76 × 10⁻⁵
	IGWO	2.46 × 10⁻¹¹	1.62 × 10⁻¹⁰	2.79 × 10⁻¹⁵	4.71 × 10⁻¹¹
F₃	PSO	0.129362	1.159753	0.003876	0.343681
	GWO	1.01 × 10⁻¹³	1.29 × 10⁻¹³	7.90 × 10⁻¹⁴	1.58 × 10⁻¹⁴
	IGWO	2.86 × 10⁻¹⁴	3.29 × 10⁻¹⁴	2.22 × 10⁻¹⁴	3.10 × 10⁻¹⁵
F₄	PSO	4.25 × 10⁻²	1.55 × 10⁻¹	5.81 × 10⁻³	0.041668
	GWO	9.24 × 10⁻¹⁷	2.84 × 10⁻¹⁶	1.46 × 10⁻¹⁷	8.49 × 10⁻¹⁷
	IGWO	1.23 × 10⁻²⁵	4.04 × 10⁻²⁵	1.32 × 10⁻²⁶	1.18 × 10⁻²⁵
F₅	PSO	0.173628	0.279294	0.102187	0.059145
	GWO	0.002243	0.006324	0.000439	0.001718
	IGWO	0.000745	0.001364	0.000493	0.000237
F₆	PSO	−5089.57	−2701.84	−6686.21	1129.513
	GWO	−5844.04	−4751.61	−7069.2	726.476
	IGWO	−8.80 × 10⁵⁷	−1.70 × 10⁵²	−4.50 × 10⁵⁸	1.33 × 10⁵⁸
F₇	PSO	2.679246	5.928845	0.998004	1.766345
	GWO	3.844082	10.76318	0.998004	3.555987
	IGWO	1.295817	2.982105	0.998004	0.635439
F₈	PSO	56.04584	96.30331	31.89847	17.4922
	GWO	4.181775	22.25851	5.68 × 10⁻¹⁴	6.871585
	IGWO	5.24 × 10⁻¹⁴	4.7 × 10⁻¹³	0	1.415671

下载: 导出CSV

表 4 路径点序列

Table 4. Path point sequence

位置	d₁/m	θ₂/(°)	θ₃/(°)	θ₄/(°)	θ₅/(°)	θ₆/(°)	θ₇/(°)
A	1.1874	47.2280	−65.2963	−20.1557	85.8047	−47.3947	83.8156
B	2.6150	0.8813	−49.8247	−45.1954	−9.97077	5.09677	0.06786
C	2.4393	6.6172	−83.8267	−0.533756	49.7327	−8.6861	59.4064
D	1.8821	47.2274	−65.2832	−20.1933	85.8270	−47.3923	83.8487
E	1.0969	25.7134	−99.5115	17.6056	73.7020	−26.8743	71.8517
F	0.8791	25.3446	−49.9048	19.7835	28.7049	−63.0295	13.9472
G	0.9968	33.0464	−68.6310	53.4117	33.9881	−77.2882	8.4386
H	1.0602	30.6196	−113.7357	41.3231	62.9544	−34.8809	58.1045

下载: 导出CSV

参考文献(20)

[1]	NAGY Á, VAJK I. Nonconvex time-optimal trajectory planning for robot manipulators[J]. Journal of Dynamic Systems, Measurement, and Control, 2019, 141(11): 111007. doi: 10.1115/1.4044216
[2]	KIM J J, LEE J J. Trajectory optimization with particle swarm optimization for manipulator motion planning[J]. IEEE Transactions on Industrial Informatics, 2015, 11(3): 620-631. doi: 10.1109/TII.2015.2416435
[3]	XIDIAS E K. Time-optimal trajectory planning for hyper-redundant manipulators in 3D workspaces[J]. Robotics and Computer-integrated Manufacturing, 2018, 50: 286-298. doi: 10.1016/j.rcim.2017.10.005
[4]	LIU C, CAO G H, QU Y Y, et al. An improved PSO algorithm for time-optimal trajectory planning of Delta robot in intelligent packaging[J]. The International Journal of Advanced Manufacturing Technology, 2020, 107(3): 1091-1099.
[5]	MA J W, GAO S, YAN H T, et al. A new approach to time-optimal trajectory planning with torque and jerk limits for robot[J]. Robotics and Autonomous Systems, 2021, 140: 103744. doi: 10.1016/j.robot.2021.103744
[6]	米根锁, 李明. 布谷鸟搜索算法在空间机械臂轨迹规划中的应用研究[J]. 机械科学与技术, 2018, 37(12): 1805-1810. MI G S, LI M. Applying cuckoo search algorithm to path planning of space manipulator[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(12): 1805-1810. (in Chinese)
[7]	WU L, CHEN M S, XU J T, et al. Minimum-acceleration local modification method for planning tool orientations in 5-axis ball-end machining[J]. The International Journal of Advanced Manufacturing Technology, 2021, 114(7): 2271-2287.
[8]	梁常春, 张晓东, 唐自新, 等. 空间机械臂关节故障引起速度突变的抑制[J]. 宇航学报, 2016, 37(1): 48-54. LIANG C C, ZHANG X D, TANG Z X, et al. Suppression of velocity mutation caused by space manipulator joint failure[J]. Journal of Astronautics, 2016, 37(1): 48-54. (in Chinese)
[9]	MIRJALILI S, MIRJALILI S M, LEWIS A. Grey wolf optimizer[J]. Advances in Engineering Software, 2014, 69: 46-61. doi: 10.1016/j.advengsoft.2013.12.007
[10]	LI Y, LIN X X, LIU J S. An improved gray wolf optimization algorithm to solve engineering problems[J]. Sustainability, 2021, 13(6): 3208. doi: 10.3390/su13063208
[11]	NADIMI-SHAHRAKI M H, TAGHIAN S, MIRJALILI S. An improved grey wolf optimizer for solving engineering problems[J]. Expert Systems with Applications, 2021, 166: 113917. doi: 10.1016/j.eswa.2020.113917
[12]	RODRÍGUEZ L, CASTILLO O, SORIA J. Grey wolf optimizer with dynamic adaptation of parameters using fuzzy logic[C]//2016 IEEE Congress on Evolutionary Computation (CEC). Vancouver: IEEE, 2016: 3116-3123.
[13]	左剑, 张程稳, 肖逸, 等. 基于灰狼优化算法的多机电力系统稳定器参数最优设计[J]. 电网技术, 2017, 41(9): 2987-2995. ZUO J, ZHANG C W, XIAO Y, et al. Multi-machine PSS parameter optimal tuning based on grey wolf optimizer algorithm[J]. Power System Technology, 2017, 41(9): 2987-2995. (in Chinese)
[14]	MIRJALILI S, GANDOMI A H. Chaotic gravitational constants for the gravitational search algorithm[J]. Applied Soft Computing, 2017, 53: 407-419. doi: 10.1016/j.asoc.2017.01.008
[15]	吕鑫, 慕晓冬, 张钧, 等. 混沌麻雀搜索优化算法[J]. 北京航空航天大学学报, 2021, 47(8): 1712-1720. doi: 10.13700/j.bh.1001-5965.2020.0298 LYU X, MU X D, ZHANG J, et al. Chaos sparrow search optimization algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1712-1720. (in Chinese) doi: 10.13700/j.bh.1001-5965.2020.0298
[16]	XU H L, QIAN X, ZHANG L. Study of ACO algorithm optimization based on improved tent chaotic mapping[J]. Journal of Information & Computational Science, 2012, 9(6): 1653-1660.
[17]	ZHANG J Q, SANDERSON A C. JADE: adaptive differential evolution with optional external archive[J]. IEEE Transactions on Evolutionary Computation, 2009, 13(5): 945-958. doi: 10.1109/TEVC.2009.2014613
[18]	曾念寅, 宋丹丹, 李寒, 等. 改进鲸鱼优化算法及涡轮盘结构优化[J]. 机械工程学报, 2021, 57(20): 254-265. doi: 10.3901/JME.2021.20.254 ZENG N Y, SONG D D, LI H, et al. Improved whale optimization algorithm and turbine disk structure optimization[J]. Journal of Mechanical Engineering, 2021, 57(20): 254-265. (in Chinese) doi: 10.3901/JME.2021.20.254
[19]	吴虎胜, 张凤鸣, 吴庐山. 一种新的群体智能算法-狼群算法[J]. 系统工程与电子技术, 2013, 35(11): 2430-2438. WU H S, ZHANG F M, WU L S. New swarm intelligence algorithm-wolf pack algorithm[J]. Systems Engineering and Electronics, 2013, 35(11): 2430-2438. (in Chinese)
[20]	TENG Z J, LV J L, GUO L W. An improved hybrid grey wolf optimization algorithm[J]. Soft Computing, 2019, 23(15): 6617-6631. doi: 10.1007/s00500-018-3310-y