# A meta-heuristic proposal for inverse kinematics solution of 7-DOF serial robotic manipulator: quantum behaved particle swarm algorithm

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## Abstract

In this study, a quantum behaved particle swarm algorithm has used for inverse kinematic solution of a 7-degree-of-freedom serial manipulator and the results have been compared with other swarm techniques such as firefly algorithm (FA), particle swarm optimization (PSO) and artificial bee colony (ABC). Firstly, the DH parameters of the robot manipulator are created and transformation matrices are revealed. Afterward, the position equations are derived from these matrices. The position of the end effector of the robotic manipulator in the work space is estimated using Quantum PSO and other swarm algorithms. For this reason, a fitness function which name is Euclidian has been determined. This function calculates the difference between the actual position and the estimated position of the manipulator end effector. In this study, the algorithms have tested with two different scenarios. In the first scenario, values for a single position were obtained while values for a hundred different positions were obtained in the second scenario. In fact, the second scenario confirms the quality of the QPSO in the inverse kinematic solution by verifying the first scenario. According to the results obtained; Quantum behaved PSO has yielded results that are much more efficient than standard PSO, ABC and FA. The advantages of the improved algorithm are the short computation time, fewer iterations and the number of particles.

## Keywords

Quantum particle swarm optimization Inverse kinematics 7-DOF robotic manipulator Particle swarm optimization Swarm algorithms## Notes

## References

- Almusawi A, Dülger LC, Kapucu S (2016) A new artificial neural network approach in solving inverse kinematics of robotic arm (Denso VP6242). Comput Intell Neurosci. https://doi.org/10.1155/2016/5720163 Google Scholar
- Aristidou A, Lasenby J (2011) FABRIK: a fast, iterative solver for the inverse kinematics problem. Graph Models 73:243–260CrossRefGoogle Scholar
- Ayyıldız M, Çetinkaya K (2015) Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator. Neural Comput Appl 27:825–836Google Scholar
- Bai Q (2010) Analysis of particle swarm optimization algorithm. Comput Inf Sci 3:180–184Google Scholar
- Çavdar T, Alavi M (2012) A new heuristic approach for inverse kinematics of robot arms. J Comput Theor Nanosci 19:329–333Google Scholar
- Dereli S, Koker R (2017) Design and analysis of multi-layer artificial neural network used for training in inverse kinematic solution of 7-DOF serial robot. Gaziosmanpasa J Sci Res 6:60–71Google Scholar
- Dereli S, Köker R (2018) IW-PSO approach to the inverse kinematics problem solution of a 7-DOF serial robot manipulator. Sigma J Eng Nat Sci 36:77–85Google Scholar
- Durmuş B, Temurtaş H, Gün A (2011) An inverse kinematics solution using particle swarm optimization. In: International advanced technologies symposium, 16–18 May 2011, Elazig, TurkeyGoogle Scholar
- Dutra MS, Lengerke O, Carreno EA, Tavara MJM (2014) A hybrid solution for the inverse kinematic on a seven DOF robotic manipulator. IEEE Lat Am Trans 12:212–218CrossRefGoogle Scholar
- El-Sherbiny A, Elhosseini MA, Haikal AY (2017) A comparative study of soft computing methods to solve inverse kinematics problem. Ain Shams Eng J 9:2535–2548CrossRefGoogle Scholar
- Huang HC, Xu SSD, Wu CH (2016) A hybrid swarm intelligence of artificial immune system tuned with Taguchi–genetic algorithm and its field-programmable gate array realization to optimal inverse kinematics for an articulated industrial robotic manipulator. Adv Mech Eng 8:1–10Google Scholar
- Iliukhin VN, Mitkovskii KB, Bizyanova DA, Akopyan AA (2013) The modeling of inverse kinematics for 5 DOF manipulator. Proc Eng 176:498–505CrossRefGoogle Scholar
- Köker R (2005) Reliability-based approach to the inverse kinematics solution of robots using Elman’s networks. Eng Appl Artif Intell 18:685–693CrossRefGoogle Scholar
- Köker R (2013) A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators. Eng Comput 29:507–515CrossRefGoogle Scholar
- Köker R, Çakar T (2016) A neuro–genetic–simulated annealing approach to the inverse kinematics solution of robots: a simulation based study. Eng Comput 32:553–565CrossRefGoogle Scholar
- Köker R, Öz C, Çakar T, Ekiz H (2004) A study of neural network based inverse kinematics solution for a three-joint robot. Rob Auton Syst 49:227–234CrossRefGoogle Scholar
- Kucuk S (2013) Energy minimization for 3-RRR fully planar parallel manipulator using particle swarm optimization. Mech Mach Theory 62:129–169CrossRefGoogle Scholar
- Kucuk S, Bingul Z (2005) The inverse kinematics solutions of fundemantal robot manipulators with offset wrists. In: IEEE international conference on mechatronics, 10–12 July, Taipei, TaiwanGoogle Scholar
- Küçük S, Bingül Z (2014) Inverse kinematics solutions for industrial robot manipulators with offset wrists. Appl Math Model 38:1983–1999MathSciNetCrossRefzbMATHGoogle Scholar
- Lee CSG, Ziegler M (1984) Geometric approach in solving inverse kinematics of PUMA robots. IEEE Trans Aerosp Electron Syst 6:695–706CrossRefGoogle Scholar
- Manocha D, Canny JF (1994) Efficient inverse kinematics for general 6R manipulators. IEEE Trans Robot Autom 10:648–657CrossRefGoogle Scholar
- Merlet JP (2016) A new generic approach for the inverse kinematics of cable-driven parallel robot with 6 deformable cables. Adv Robot Kinemat 2018:209–216Google Scholar
- Momani SM, Abo-Hammour Z, Alsmadi O (2016) Solution of inverse kinematics problem using genetic algorithms. Appl Math Inf Sci 10:1–9MathSciNetCrossRefGoogle Scholar
- Pant M, Thangaraj R, Abraham A (2008) A new quantum behaved particle swarm optimization. In: The 10th annual conference on genetic and evolutionary computation, ACMGoogle Scholar
- Pham DT, Castellani M, Fahmy AA (2008) Learning the inverse kinematics of a robot manipulator using the bees algorithm. In: IEEE international conference on industrial informatics, 13–16 July 2008, Daejeon, KoreaGoogle Scholar
- Pozna CR, Horvath E, Hollosi J (2016) The inverse kinematics problem, a heuristical approach. In: IEEE 14th international symposium on applied machine intelligence and informatics, 21–23 January 2016, Herlany, SlovakiaGoogle Scholar
- Qiao SG, Liao QZ, Wei SM (2010) Inverse kinematic analysis of the general 6R serial manipulators based on double quaternions. Mech Mach Theory 45:193–199CrossRefzbMATHGoogle Scholar
- Rokbani N, Alimi AM (2013) Inverse kinematics using particle swarm optimization, a statistical analysis. Proc Eng 64:1602–1611CrossRefGoogle Scholar
- Rokbani N, Casals A, Alimi AM (2015) IK-FA, a new heuristic inverse kinematics solver using firefly algorithm. Comput Intell Appl Model Control 575:553–565Google Scholar
- Shi Q, Xie J (2017) A research on inverse kinematics solution of 6-dof robot with offset-wrist based on adaboost neural network. In: IEEE international conference on CIS and RAM, 18–20 November, Ningbo, ChinaGoogle Scholar
- Sun J, Fang W, Palade V, Wu X, Xu W (2011) Quantum-behaved particle swarm optimization with Gaussian distributed local attractor point. Appl Math Comput 218:3763–3775zbMATHGoogle Scholar
- Sun JD, Cao GZ, Li WB, Liang YX, Huang SD (2017) Analytical inverse kinematic solution using the D–H method for a 6-DOF Robot. In: International conference on ubiquitous robots and ambient intelligence, 1 July–28 June 2017, Jeju, KoreaGoogle Scholar
- Tabandeh S, Clark C, Melek W (2006) Genetic algorithm approach to solve for multiple solutions of inverse kinematics using adaptive niching and clustering. In: IEEE congress on evolutionary computation, 16–21 July 2006, Vancouver, CanadaGoogle Scholar
- Tatum R, Lucas D, Weaver J, Perkins J (2015) Geometrically motivated inverse kinematics for an arm with 7 degrees of freedom. In: IEEE MTS Oceans, 19–22 October 2015, Washington, USAGoogle Scholar
- Ullah MI, Ajwad SA, Islam RU, Iqbal U, Iqbal J (2014) Modeling and computed torque control of a 6 degree of freedom robotic arm. In: International conference on robotics and emerging allied technologies in engineering, 22–24 April 2014, Islamabad, PakistanGoogle Scholar
- Vosniakos GC, Kannas Z (2009) Motion coordination for industrial robotic systems with redundant degrees of freedom. Robot Comput Integr Manuf 25:417–431CrossRefGoogle Scholar
- Wen X, Sheng D, Huang J (2008) A hybrid particle swarm optimization for manipulator inverse kinematics control. Adv Intell Comput Theor Appl 5226:784–791Google Scholar
- Zhang Y, Wang S, Ji G (2015) A comprehensive survey on particle swarm optimization algorithm and its applications. Math Prob Eng 2015:1–38MathSciNetzbMATHGoogle Scholar