Research article Special Issues

A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm


  • In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.

    Citation: Chengjun Wang, Xingyu Yao, Fan Ding, Zhipeng Yu. A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 3364-3390. doi: 10.3934/mbe.2024149

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  • In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.



    There are still many issues related to children's health, such as lack of time for physical activity, increased time with screens, sedentary time and unbalanced diets [1][3]. It has been reported that a healthy lifestyle in childhood is associated with disease risk and mental risk in adulthood [4], and many studies have been conducted on how to promote and acquire healthy lifestyles from childhood [5]. Children's healthy lifestyles and health behaviors have been known to be affected by various factors [6],[7]. Family environment and parents/guardians are influential on children's lifestyles [5],[8], of which parental health literacy is likely to be a strongly relevant key factor [6],[9],[10]. Because children depend on their parents and guardians to prevent and deal with health problems, this suggests that children may be disadvantaged if their parents' and guardians' knowledge and skills, that is, their health literacy, are inadequate [6]. Although there are previous reports on parents'/guardians' health literacy and children's physical activity, nutrient status and screen time, it seems that reports on other patterns of behaviors and the amount of time children spend at home are limited. Therefore, this study examined the association between children's typical lifestyle behaviors, spending time at home and health literacy of their parent/guardian by a cross-sectional study.

    We conducted a cross-sectional questionnaire survey on the lifestyle of schoolchildren and their guardians between November 2015 and March 2016. Nine public elementary schools covering all grades of children (grades 1st to 6th, aged 6–12) in regional central cities in Northern and Southern districts in Japan participated, with a total of 3327 guardians among 4263 enrollees (cooperation rate: 78.0%).

    The question about time spent at home by the child asked for average times (in minutes) per day on a usual day and noted separately weekends and weekdays. The following 7 items were included: watching television, including DVDs and/or another video; playing video games (including handy-type); studying, including homework; reading books (including comic book reading, except for homework); help with family and housework; outside playing; and time doing hobbies.

    To estimate health literacy (HL), we used a validated questionnaire with five items, which was short and adapted to the Japanese population [11]. The questions asked about the degree to which a person (i) can gather information about one's own illness and health from various sources, such as newspapers, books, television and the internet; (ii) can pick out the information one needs from lots of information; (iii) can understand the information and communicate it to others; (iv) can judge the credibility of the information; and (v) can decide on plans and actions to improve one's own health based on the information. The structures of these questions are based on communicative HL for the first three questions (items i–iii) and critical HL for the latter two (items iv–v). Each item was rated on a 5-point Likert scale ranging from 1 (“strongly disagree / not at all”) to 5 (“strongly agree”), where high points mean high literacy. The points were summed, and the total scores ranged from a minimum of 5 to a maximum of 25 points.

    The questionnaire also contained basic characteristics of the parent/guardian (position from child's side, age, type of employment) and family environment (number of family, number of children, source of household income, feeling of financial leeway). As school policy limited detailed questions such as child's age, school grade, sex/gender and parents'/guardians' personal status, such as marital status, educational background, home economics and other social indicators, alternative minimum questions were adopted in this study.

    We excluded imperfect responses for child's time spent and items of health literacy, and 3188 individual data were used in analyses (4.2% of the participants excluded). Variables are presented as mean ± standard deviation for continuous variables or prevalence (%) for categorical variables. The total HL score was classified into two categories based on the median or average score. This classification has been adopted in similar previous studies for Japanese people [12][14]. In this study, the cut-off score was 18, with less than 18 as the low group (low HL) and 18 or more as the high group (high HL).

    We used the chi-square test for comparisons of proportions and Welch's t-test for continuous variables between two groups (low HL, high HL). The distribution of the data showed that a 30-minute interval was appropriate. We also calculated the odds ratio (OR) and the 95% confidence intervals (95% CI) using logistic regression analysis for each category of child time spent in the high HL group at 30 minutes or more with less than 30 minutes as a reference. Adjusting variables included the following: position of parent/guardian from the child's side, age group of parent/guardian, type of employment of parent/guardian, number of family members, number of children, major source of household income, feeling of financial leeway.

    All statistical analyses were performed using SPSS version 25 for Windows (IBM Corp., Chicago, IL, USA). The level of statistical significance for each analysis was set at P < 0.05.

    This survey was conducted according to the Ethical Guidelines for Epidemiological Studies established by the Ministry of Health, Labor and Welfare & Ministry of Education, Culture, Sports, Science and Technology in Japan. The Ethics Committee Tohoku University Graduate School of Medicine approved the research protocol (No. 2015–1–810, 2019–1–482). The survey was anonymous, and the submission of the questionnaire was regarded as consent to participate.

    Table 1 shows the background characteristics of parents/guardians and family environments. The overall characteristics of the parents/guardians who participated in this study were the following: Most were mothers (95.2%), and most were in their 30s–40s (47.4%). The most common type of employment was part-time (46.6%), and the next most common was housewife (23.1%).

    The most common number of family members was 3–5 (83.1%), with two children (49.9%) being the most common. The main source of household income was a full-time work-based company salary (71.1%), and almost half (49.5%) of the respondents answered that they felt they did not have enough financial leeway. Comparing the characteristics of the HL groups, significant differences were found in the dispersion trends for position from the child's side, number of family members, major source of household income and feeling of financial leeway.

    Table 2 shows the results of comparison of child time spent in minutes (min) for the seven behavioral categories by parent/guardian HL group. The child's time spent on watching television was longer in the group with low HL on both weekdays and weekends, with statistically significant differences between the two groups (weekday: low HL group 90.3 min, high HL group 83.2 min, difference 7.07 min, P < 0.001; similarly, weekend: 146.9 min, 136.3 min, difference 10.67 min, P = 0.001). The child's time spent on playing video games was also longer in the group with low HL on both weekdays and weekends, with statistically significant differences between the two groups (weekday: low HL group 34.7 min, high HL group 30.1 min, difference 4.62 min, P < 0.001; similarly, weekend: 70.5 min, 62.0 min, difference 8.51 min, P = 0.001). There were no significant differences between HL groups for time spent studying, reading books or helping with family/housework. The tendency was for time of studying and helping family/housework to be slightly longer in the higher HL group and time of reading books to be slightly longer in the lower HL group. The child's time spent on playing outside was greater in the high HL group both on weekdays and on weekends. A statistically significant difference was shown only on weekdays (low HL group 28.8 min, high HL group 32.3 min, difference 3.50 min, P < 0.001). The child's time spent on doing hobbies was greater in the high HL group on both weekdays and weekends, with statistically significant difference (weekday: low HL group 8.4 min, high HL group 10.0 min group, difference 1.64 min, P < 0.038; similarly, weekend: 17.8 min, 21.6 min, difference 3.74 min, P = 0.014).

    Table 1.  Demographic characteristics among parents/guardians according to HL groups.
    Total
    (n = 3188)
    Parent/guardian HL score
    P*
    Low group
    (n = 1689)
    High group
    (n = 1499)
    Position from child's side
    Mother 95.2 94.6 95.8 0.035
    Father 3.5 3.8 3.2
    Others 0.8 1.2 0.4
    Age group, years old
    <30 2.4 2.1 2.7 0.351
    30–39 47.4 47.0 47.8
    40–49 47.2 47.7 46.7
    >49 2.5 2.8 2.2
    Type of employment
    Full time job 22.0 23.1 22.5 0.114
    Part time job 46.6 43.4 45.1
    Self-employed 4.0 4.9 4.4
    Housewife 23.1 24.5 23.8
    On leave of absence/parental leave 0.9 1.4 1.2
    Seeking employment 0.4 0.4 0.4
    Others 2.4 1.3 1.9
    Number of family members
    <3 persons 2.4 2.8 1.8 0.003
    3–5 persons 83.1 81.1 85.5
    >5 persons 14.1 15.7 12.1
    Unknown 0.5 0.4 0.6
    Number of children
    1 child 15.0 14.8 15.3 0.896
    2 children 49.9 49.8 50.0
    >2 children 35.1 35.4 34.8
    Major source of household income
    Self-employed (including agriculture, forestry, and fisheries) 7.6 7.7 7.4 0.045
    Company employee, full-time salary 71.1 72.2 70.0
    Company employee, part-time salary 12.6 11.1 14.2
    Public servant salary 5.1 4.9 5.3
    Others 0.4 0.5 0.3
    Feeling of financial leeway
    Enough 26.6 22.9 30.9 <0.001
    Not enough 49.5 51.5 47.4
    Neither 22.8 24.3 21.1

    *Note: *Comparisons of variance between groups of HL; “Unknown” responses were removed from the table; total % is less than 100 in some places.

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    Table 2.  Contents and minutes of child's time spent at home compared by HL groups.
    Parent/guardian HL score
    Difference* P#
    Low group High group
    Contents of daily spending time
    Watching television
    Weekday 90.3±57.4 83.2±54.3 7.07 <0.001
    Weekend 146.9±94.5 136.3±90.2 10.67 0.001
    Playing video games
    Weekday 34.7±39.6 30.1±34.4 4.62 <0.001
    Weekend 70.5±72.1 62.0±68.0 8.51 0.001
    Studying
    Weekday 49.2±25.7 49.3±25.4 −0.11 0.902
    Weekend 42.1±39.0 43.3±35.5 −1.22 0.353
    Reading books
    Weekday 18.2±22.6 17.6±19.4 0.64 0.389
    Weekend 26.9±32.9 26.1±30.8 0.83 0.463
    Helping with family/housework
    Weekday 10.5±12.6 11.0±12.2 −0.47 0.280
    Weekend 15.6±20.8 15.8±17.6 −0.19 0.781
    Playing outside
    Weekday 28.8±35.5 32.3±36.6 −3.50 0.006
    Weekend 73.4±85.9 78.0±89.7 −4.65 0.136
    Doing hobbies
    Weekday 8.4±22.6 10.0±22.0 −1.64 0.038
    Weekend 17.8±40.7 21.6±44.7 −3.74 0.014

    *Note: Values in table: mean ± standard deviation, values in minutes; *Difference of the mean of the low-scoring group minus the mean of the high-scoring group; #Welch t-test.

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    Table 3.  Results of odds ratios of time spent by children with high HL group parents/guardians.
    No. in HL group
    Crude OR
    (95%CI)
    P Adjusted OR
    (95%CI)
    P
    Low High
    Watching television
    Weekday <30 min 87 107 1.00 (ref.) 1.00 (ref.)
    ≥30 min 1602 1392 0.71 (0.53–0.95) 0.020 0.71 (0.53–0.95) 0.022
    Weekend <30 min 104 108 1.00 (ref.) 1.00 (ref.)
    ≥30 min 1585 1391 0.85 (0.64–1.12) 0.237 0.86 (0.65–1.14) 0.304
    Playing video games
    Weekday <30 min 729 701 1.00 (ref.) 1.00 (ref.)
    ≥30 min 960 798 0.86 (0.75–0.99) 0.041 0.86 (0.75–0.99) 0.038
    Weekend <30 min 413 440 1.00 (ref.) 1.00 (ref.)
    ≥30 min 1276 1059 0.78 (0.67–0.91) 0.002 0.78 (0.66–0.91) 0.002
    Studying
    Weekday <30 min 165 133 1.00 (ref.) 1.00 (ref.)
    ≥30 min 1520 1362 1.11 (0.87–1.41) 0.387 1.11 (0.87–1.41) 0.396
    Weekend <30 min 474 378 1.00 (ref.) 1.00 (ref.)
    ≥30 min 1214 1121 1.16 (0.99–1.36) 0.068 1.16 (0.99–1.36) 0.064
    Reading books
    Weekday <30 min 1111 988 1.00 (ref.) 1.00 (ref.)
    ≥30 min 576 511 1.00 (0.86–1.16) 0.974 0.99 (0.86–1.15) 0.904
    Weekend <30 min 903 779 1.00 (ref.) 1.00 (ref.)
    ≥30 min 786 720 1.06 (0.92–1.22) 0.399 1.05 (0.91–1.21) 0.482
    Helping with family/housework
    Weekday <30 min 1465 1296 1.00 (ref.) 1.00 (ref.)
    ≥30 min 223 203 1.03 (0.84–1.26) 0.784 1.05 (0.86–1.29) 0.632
    Weekend <30 min 1280 1124 1.00 (ref.) 1.00 (ref.)
    ≥30 min 409 375 1.04 (0.89–1.23) 0.600 1.06 (0.90–1.25) 0.486
    Playing outside
    Weekday <30 min 864 683 1.00 (ref.) 1.00 (ref.)
    ≥30 min 825 816 1.25 (1.09–1.44) 0.002 1.24 (1.08–1.43) 0.003
    Weekend <30 min 524 425 1.00 (ref.) 1.00 (ref.)
    ≥30 min 1165 1074 1.14 (0.98–1.32) 0.100 1.14 (0.97–1.33) 0.105
    Doing hobbies
    Weekday <30 min 1445 1208 1.00 (ref.) 1.00 (ref.)
    ≥30 min 244 291 1.43 (1.18–1.72) <0.001 1.39 (1.15–1.68) 0.001
    Weekend <30 min 1270 1049 1.00 (ref.) 1.00 (ref.)
    ≥30 min 419 450 1.30 (1.11–1.52) 0.001 1.27(1.09–1.49) 0.003

    *Note: Abbreviations in the table: OR = odds ratio, CI = confidence interval, ref. = reference; Adjustment variables as follows: position of parent/guardian from child's side, age group of parent/guardian, type of employment of parent/guardian, number of family members, number of children, major source of household income, feeling of financial leeway.

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    Table 3 shows the odds ratios for child time spent for more than 30 minutes compared to less than 30 minutes in the group with high parental/guardian HL. The ORs of spending more than 30 minutes for watching television and video game playing were lower in the higher HL group. The adjusted ORs were 0.71 (95% CI = 0.53–0.95, P = 0.002) for weekday television watching, 0.86 (95% CI = 0.75–0.99, P = 0.038) for weekday video game playing and 0.78 (95% CI = 0.66–0.91, P = 0.002) for weekend video game playing. The ORs were close to 1.00 for study time, reading time and helping with family/housework either on weekdays or weekends. The ORs of spending more than 30 minutes playing outside and doing hobbies were higher in the higher HL group. The adjusted ORs were 1.24 (95% CI = 1.08–1.43, P = 0.003) for weekday playing outside, 1.39 (95% CI = 1.15–1.68, P = 0.001) for weekday hobby time and 1.27 (95% CI = 1.09–1.49, P = 0.003) for weekend hobby time. In a detailed analysis, significant differences in weekday television watching, weekday playing video games, weekend playing video games and weekday outside playing were even more noticeable for the more than 120 minutes time (not shown in the result table). The adjusted ORs were 0.65 (95% CI = 0.46–0.92, P = 0.041) for weekday television watching, 0.64 (95% CI = 0.47–0.88, P = 0.006) for weekday playing video games, 0.67 (95% CI = 0.55–0.82, P < 0.001) for weekend playing video games and 1.46 (95% CI = 1.05–2.04, P = 0.026) for weekday outside playing.

    We examined the association between parental/guardian health literacy and child's time spent at home, based on data of approximately 3000 Japanese schoolchildren. Overall, parental/guardian HL was strongly associated with the following four behavioral categories of time spent by children: watching television, playing video games, playing outside and doing hobbies. Our results for TV time and game time are consistent with previous studies, and regarding outdoor play as a physical activity, the direction of the results of the present study agrees with other previous studies [1],[3],[6][8].

    The largest difference in terms of number of hours was found for weekend watching television, which was approximately 10.6 minutes/day longer in the low parent/guardian HL group. The second largest time difference was found for weekend time playing video games, which was about 8.5 minutes/day longer in the low parent/guardian HL group. Children in the high parent/guardian HL group spent approximately 4.6 minutes more time playing outside on weekends and 3.7 minutes more time doing hobbies on weekends than children in the low parent/guardian HL group. The differences were measured in minutes and appeared small; however, this difference would be larger with long-term cumulation. Elementary schools in Japan have roughly 200 school days in a year. It is estimated that a difference of 7 min/day in children's weekday TV watching amounts to a difference of 1400 min/year, that is, about 23 hours.

    The results of the logistic analysis indicated that higher parental/guardian HL may reduce the probability of children spending more than 30 minutes watching TV on weekdays and playing games on weekdays and weekends. Higher parent/guardian HL indicated that the probability of children spending more than 30 minutes outside on weekdays and on weekday and weekend hobbies increased. Sub-analyses also suggested that higher parental/guardian HL, less likely for children to spend more than 2 hours watching TV on weekdays and playing games on weekdays and weekends while more likely for children to spend more than 2 hours playing outside. These results suggest that if parents/guardians have a high level of HL, it might be possible to reduce the amount of time children spend watching TV and playing games to less than 30 minutes or less than 120 minutes and to increase the amount of time they spend playing outside and enjoying their hobbies to more than 30 minutes or more than 120 minutes.

    In recent years, reports have also accumulated on children's screen time, sedentary time and their health disadvantages [3],[5],[15],[16]. The TV watching and video gaming time collected in this study could be substituted as total screen time or sitting time, although use of computers, mobile phones and smartphones was not included. Hence, screen time and sitting time were not estimated in this study. Our study also has some limitations. First, the data on children's time spent at home was based on questionnaire responses by parents/guardians and not actual measurement data, so some response errors were unavoidable. There may also be differences in content-specific time by child age and by sex. Our present study has not fully examined the variables. The information such as the child's sex/gender, year of age and class could not be added to the questionnaire due to concerns about the possibility of identifying the child. In particular, the time spent playing outside may differ by gender and age group. This remains an issue for future surveys. It has been also reported that parenting style could be significantly related to children's daily life and health behaviors [17][20]. The present study may not have adequately adjusted for parental parenting attitudes. It may also be insufficient for SES indicators, but the impact of SES as a predictor of health literacy appears to be limited [21].

    The present study focused on the relationship between parental/guardian HL and seven behavioral categories of child's time spent at home. There are few reports investigating the time spent by Japanese schoolchildren and the parents' HL, so the results of this study are very meaningful. Many factors, including the parental/guardian HL focused on in this study, have direct and indirect or combinatory influences on children's health behaviors and health outcomes. Further findings are expected from comprehensive and continuing epidemiological study.

    Our study conducted in Japanese schoolchildren showed that parental/guardian HL was associated with some contents of child's time spent at home. High parental/guardian HL was negatively associated with children's time spent watching TV and playing games, while times spent playing outside and doing hobbies were positively associated.



    [1] Y. Chen, L. Li, Collision-free trajectory planning for dual-robot systems using B-splines, Int. J. Adv. Rob. Syst., 14 (2017). https://doi.org/10.1177/1729881417728021 doi: 10.1177/1729881417728021
    [2] R. Marco, C. Fabio, S. Marco, A. Alessandra, A new framework for joint trajectory planning based on time-parameterized B-splines, Comput.-Aided Des., 154 (2023), 103421. https://doi.org/10.1016/j.cad.2022.103421 doi: 10.1016/j.cad.2022.103421
    [3] Y. Li, H. Tian, D. G. Chetwynd, An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines, Mech. Mach. Theory, 126 (2018), 479–490. https://doi.org/10.1016/j.mechmachtheory.2018.04.026 doi: 10.1016/j.mechmachtheory.2018.04.026
    [4] H. Wang, W. Heng, J. Huang, B. Zhao, L. Quan, Smooth point-to-point trajectory planning for industrial robots with kinematical constraints based on high-order polynomial curve, Mech. Mach. Theory, 139 (2019), 284–293. https://doi.org/10.1016/j.mechmachtheory.2019.05.002 doi: 10.1016/j.mechmachtheory.2019.05.002
    [5] H. Wang, Q. Zhao, H. Li, R. Zhao, Polynomial-based smooth trajectory planning for fruit-picking robot manipulator, Inf. Process. Agric., 9 (2022), 112–122. https://doi.org/10.1016/j.inpa.2021.08.001 doi: 10.1016/j.inpa.2021.08.001
    [6] X. Li, H. Lv, D. Zeng, Q. Zhang, An improved multi-objective trajectory planning algorithm for kiwifruit harvesting manipulator, IEEE Access, 11 (2023), 65689–65699. https://doi.org/10.1109/ACCESS.2023.3289207 doi: 10.1109/ACCESS.2023.3289207
    [7] Ü. Dinçer, M. Çevik, Improved trajectory planning of an industrial parallel mechanism by a composite polynomial consisting of Bézier curves and cubic polynomials, Mech. Mach. Theory, 132 (2019), 248–263. https://doi.org/10.1016/j.mechmachtheory.2018.11.009 doi: 10.1016/j.mechmachtheory.2018.11.009
    [8] F. Lin, L. Shen, C. Yuan, Z. Mi, Certified space curve fitting and trajectory planning for CNC machining with cubic B-splines, Comput.-Aided Des., 106 (2019), 13–29. https://doi.org/10.1016/j.cad.2018.08.001 doi: 10.1016/j.cad.2018.08.001
    [9] S. Lu, B. Ding, Y. Li, Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation, Adv. Mech. Eng., 12 (2020). https://doi.org/10.1177/1687814020913667 doi: 10.1177/1687814020913667
    [10] X. Zhao, M. Wang, N. Liu, Y. Tang, Trajectory planning for 6-DOF robotic arm based on quintic polynormial, in Proceedings of the 2017 2nd International Conference on Control, Automation and Artificial Intelligence (CAAI 2017), 2017. https://doi.org/10.2991/CAAI-17.2017.23
    [11] G. Wu, S. Zhang, Real-time jerk-minimization trajectory planning of robotic arm based on polynomial curve optimization, Proc. Inst. Mech. Eng., Part C: J. Mech., 236 (2022), 10852–10864. https://doi.org/10.1177/09544062221106632 doi: 10.1177/09544062221106632
    [12] M. Dupac, Smooth trajectory generation for rotating extensible manipulators, Math. Methods Appl. Sci., 41 (2018), 2281–2286. https://doi.org/10.1002/mma.4210 doi: 10.1002/mma.4210
    [13] P. Boscariol, D. Richiedei, Energy-efficient design of multipoint trajectories for Cartesian robots, Int. J. Adv. Manuf. Technol., 102 (2019), 1853–1870. https://doi.org/10.1007/s00170-018-03234-4 doi: 10.1007/s00170-018-03234-4
    [14] A. E. Ezugwu, A. K. Shukla, R. Nath, A. A. Akinyelu, J. O. Agushaka, H. Chiroma, Metaheuristics: a comprehensive overview and classification along with bibliometric analysis, Artif. Intell. Rev., 54 (2021), 4237–4316. https://doi.org/10.1007/s10462-020-09952-0 doi: 10.1007/s10462-020-09952-0
    [15] J. Zhang, Q. Meng, X. Feng, H. Shen, A 6-DOF robot-time optimal trajectory planning based on an improved genetic algorithm, Rob. Biomimetics, 5 (2018), 3. https://doi.org/10.1186/s40638-018-0085-7 doi: 10.1186/s40638-018-0085-7
    [16] K. Shi, Z. Wu, B. Jiang, H. R. Karimi, Dynamic path planning of mobile robot based on improved simulated annealing algorithm, J. Franklin Inst., 360 (2023), 4378–4398. https://doi.org/10.1016/j.jfranklin.2023.01.033 doi: 10.1016/j.jfranklin.2023.01.033
    [17] X. Zhang, F. Xiao, X. Tong, J. Yun, Y. Liu, Y. Sun, et al., Time optimal trajectory planing based on improved sparrow search algorithm, Front. Bioeng. Biotechnol., 10 (2022), 852408. https://doi.org/10.3389/fbioe.2022.852408 doi: 10.3389/fbioe.2022.852408
    [18] T. Wang, Z. Xin, H. Miao, H. Zhang, Z. Chen, Y. Du, Optimal trajectory planning of grinding robot based on improved whale optimization algorithm, Math. Probl. Eng., 2020 (2020), 3424313. https://doi.org/10.1155/2020/3424313 doi: 10.1155/2020/3424313
    [19] I. Carvajal, E. A. Martínez-García, R. Lavrenov, E. Magid, Robot arm planning and control by τ-Jerk theory and vision-based recurrent ANN observer, in 2021 International Siberian Conference on Control and Communications (SIBCON), (2021), 1–6. https://doi.org/10.1109/SIBCON50419.2021.9438857
    [20] E. Ö zge, A. Bekir, Trajectory planning for a 6-axis robotic arm with particle swarm optimization algorithm, Eng. Appl. Artif. Intell., 122 (2023), 106099. https://doi.org/10.1016/j.engappai.2023.106099 doi: 10.1016/j.engappai.2023.106099
    [21] G. Chen, W. Peng, Z. Wang, J. Tu, H. Hu, D. Wang, et al., Modeling of swimming posture dynamics for a beaver-like robot, Ocean Eng., 279 (2023), 114550. https://doi.org/10.1016/j.oceaneng.2023.114550 doi: 10.1016/j.oceaneng.2023.114550
    [22] G. Chen, Y. Xu, C. Yang, X. Yang, H. Hu, X. Chai, et al., Design and control of a novel bionic mantis shrimp robot, IEEE/ASME Trans. Mechatron., 28 (2023), 3376–3385. https://doi.org/10.1109/TMECH.2023.3266778 doi: 10.1109/TMECH.2023.3266778
    [23] K. Wu, L. Chen, K. Wang, M. Wu, W. Pedrycz, K. Hirota, Robotic arm trajectory generation based on emotion and kinematic feature, in 2022 International Power Electronics Conference (IPEC-Himeji 2022-ECCE Asia), (2022), 1332–1336. https://doi.org/10.23919/IPEC-Himeji2022-ECCE53331.2022.9807205
    [24] G. Hu, Y. Guo, G. Wei, L. Abualigah, Genghis Khan shark optimizer: a novel nature-inspired algorithm for engineering optimization, Adv. Eng. Inf., 58 (2023), 102210. https://doi.org/10.1016/j.aei.2023.102210 doi: 10.1016/j.aei.2023.102210
    [25] R. V. Ram, P. M. Pathak, S. J. Junco, Inverse kinematics of mobile manipulator using bidirectional particle swarm optimization by manipulator decoupling, Mech. Mach. Theory, 131 (2019), 385–405. https://doi.org/10.1016/j.mechmachtheory.2018.09.022 doi: 10.1016/j.mechmachtheory.2018.09.022
    [26] P. Golla, S. Ramesh, S. Bandyopadhyay, Kinematics of the Hybrid 6-Axis (H6A) manipulator, Robotica, 41 (2023), 2251–2282. https://doi.org/10.1017/S0263574723000334 doi: 10.1017/S0263574723000334
    [27] A. V. Antonov, A. S. Fomin, Inverse kinematics of a 5-DOF hybrid manipulator, Autom. Remote Control, 84 (2023), 281–293. https://doi.org/10.1134/S0005117923030037 doi: 10.1134/S0005117923030037
    [28] J. Q. Gan, E. Oyama, E. Rosales, H. Hu, A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm, Robotica, 23 (2005), 123–129. https://doi.org/10.1017/S0263574704000529 doi: 10.1017/S0263574704000529
    [29] G. Zhong, B. Peng, W. Dou, Kinematics analysis and trajectory planning of a continuum manipulator, Int. J. Mech. Sci., 222 (2022), 107206. https://doi.org/10.1016/j.ijmecsci.2022.107206 doi: 10.1016/j.ijmecsci.2022.107206
    [30] C. Wang, F. Ding, L. Ling, S. Li, Design of a teat cup attachment robot for automatic milking systems, Agriculture, 13 (2023), 1273. https://doi.org/10.3390/agriculture13061273 doi: 10.3390/agriculture13061273
    [31] A. Messaoudi, R. Sadaka, H. Sadok, Matrix recursive polynomial interpolation algorithm: An algorithm for computing the interpolation polynomials, J. Comput. Appl. Math., 373 (2020), 112471. https://doi.org/10.1016/j.cam.2019.112471 doi: 10.1016/j.cam.2019.112471
    [32] M. Ivan, V. Neagos, A representation of the interpolation polynomial, Numerical Algorithms, 88 (2021), 1215–1231. https://doi.org/10.1007/s11075-021-01072-2 doi: 10.1007/s11075-021-01072-2
    [33] X. Liu, G. Lin, W. Wei, Adaptive transition gait planning of snake robot based on polynomial interpolation method, Actuators, 11 (2022), 222. https://doi.org/10.3390/act11080222 doi: 10.3390/act11080222
    [34] A. Shrivastava, V. K. Dalla, Multi-segment trajectory tracking of the redundant space robot for smooth motion planning based on interpolation of linear polynomials with parabolic blend, Proc. Inst. Mech. Eng., Part C: J. Mech., 236 (2022), 9255–9269. https://doi.org/10.1177/09544062221088723 doi: 10.1177/09544062221088723
    [35] D. Wang, D. Tan, L. Liu, Particle swarm optimization algorithm: an overview, Soft Comput., 22 (2017), 387–408. https://doi.org/10.1007/s00500-016-2474-6 doi: 10.1007/s00500-016-2474-6
    [36] V. Trivedi, P. Varshney, M. Ramteke, A simplified multi-objective particle swarm optimization algorithm, Swarm Intell., 14 (2020), 83–116. https://doi.org/10.1007/s11721-019-00170-1 doi: 10.1007/s11721-019-00170-1
    [37] Y. Zhang, X. Liu, F. Bao, J. Chi, C. Zhang, P. Liu, Particle swarm optimization with adaptive learning strategy, Knowledge-Based Syst., 196 (2020), 105789. https://doi.org/10.1016/j.knosys.2020.105789 doi: 10.1016/j.knosys.2020.105789
    [38] A. G. Gad, Particle swarm optimization algorithm and its applications: a systematic review, Arch. Comput. Methods Eng., 29 (2022), 2531–2561. https://doi.org/10.1007/s11831-021-09694-4 doi: 10.1007/s11831-021-09694-4
    [39] J. Zheng, Y. Gao, H. Zhang, Y. Lei, J. Zhang, OTSU multi-threshold image segmentation based on improved particle swarm algorithm, Appl. Sci., 12 (2022), 11514. https://doi.org/10.3390/app122211514 doi: 10.3390/app122211514
    [40] L. Yu, Y. Han, L. Mu, Improved quantum evolutionary particle swarm optimization for band selection of hyperspectral image, Remote Sens. Lett., 11 (2020), 866–875. https://doi.org/10.1080/2150704X.2020.1782501 doi: 10.1080/2150704X.2020.1782501
    [41] S. Obukhov, A. Ibrahim, A. A. Z. Diab, A. S. Al-Sumaitim, R. Aboelsaud, Optimal performance of dynamic particle swarm optimization based maximum power trackers for stand-alone PV system under partial shading conditions, IEEE Access, 8 (2020), 20770–20785. https://doi.org/10.1109/ACCESS.2020.2966430 doi: 10.1109/ACCESS.2020.2966430
    [42] X. Li, B. Tian, S. Hou, X. Li, Y. Li, C. Liu, et al., Path planning for mount robot based on improved particle swarm optimization algorithm, Electronics, 12 (2023), 3289. https://doi.org/10.3390/electronics12153289 doi: 10.3390/electronics12153289
    [43] P. Qu, F. Du, Improved particle swarm optimization for laser cutting path planning, IEEE Access, 11 (2023), 4574–4588. https://doi.org/10.1109/ACCESS.2023.3236006 doi: 10.1109/ACCESS.2023.3236006
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