Meta-Heuristics Based Inverse Kinematics of Robot Manipulator’s Path Tracking Capability Under Joint Limits

  • Ganesan Kanagaraj Department of Mechatronics Engineering, Thiagarajar College of Engineering, Anna University, Madurai, Tamil Nadu, India
  • SAR Sheik Masthan Department of Mechatronics Engineering, Thiagarajar College of Engineering, Anna University, Madurai, Tamil Nadu, India
  • Vincent F Yu Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, Taiwan
Keywords: Inverse Kinematics, Redundant Robot Manipulator, Path Tracking, Meta-Heuristic Algorithm, BAT, Particle Swarm optimization, Gravitational Search, Whale Optimization


In robot-assisted manufacturing or assembly, following a predefined path became a critical aspect. In general, inverse kinematics offers the solution to control the movement of manipulator while following the trajectory. The main problem with the inverse kinematics approach is that inverse kinematics are computationally complex. For a redundant manipulator, this complexity is further increased. Instead of employing inverse kinematics, the complexity can be reduced by using a heuristic algorithm. Therefore, a heuristic-based approach can be used to solve the inverse kinematics of the robot manipulator end effector, guaranteeing that the desired paths are accurately followed. This paper compares the performance of four such heuristic-based approaches to solving the inverse kinematics problem. They are Bat Algorithm (BAT), Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and Whale Optimization Algorithm (WOA). The performance of these algorithms is evaluated based on their ability to accurately follow a predefined trajectory. Extensive simulations show that BAT and GSA outperform PSO and WOA in all aspects considered in this work related to inverse kinematic problems.


Andreev, A., and Peregudova, O. Trajectory tracking control for robot manipulators using only position measurements. International Journal of Control 92, 7 (2019), 1490–1496.

Ayyıldız, M., and Cetinkaya, K. Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-dof serial robot manipulator. Neural Computing and Applications 27, 4 (2016), 825–836.

Baek, J., Cho, S., and Han, S. Practical timedelay control with adaptive gains for trajectory tracking of robot manipulators. IEEE Transactions on Industrial Electronics 65, 7 (2017), 5682–5692.

Bayati, M. Using cuckoo optimization algorithm and imperialist competitive algorithm to solve inverse kinematics problem for numerical control of robotic manipulators. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 229, 5 (2015), 375–387.

Beyer, U., and Smieja, F. A heuristic approach to the inverse differential kinematics problem. Journal of Intelligent and Robotic Systems 18, 4 (1997), 309–327.

Chen, C.-Y., Her, M.-G., Hung, Y.-C., and Karkoub, M. Approximating a robot inverse kinematics solution using fuzzy logic tuned by genetic algorithms. The International Journal of Advanced Manufacturing Technology 20, 5 (2002), 375–380.

Chen, D., Zhang, Y., and Li, S. Tracking control of robot manipulators with unknown models: A jacobian-matrix-adaption method. IEEE Transactions on Industrial Informatics 14, 7 (2017), 3044–3053.

Cheng, J., Zhang, G., Caraffini, F., and Neri, F. Multicriteria adaptive differential evolution for global numerical optimization. Integrated Computer-Aided Engineering 22, 2 (2015), 103–107.

Chin, K. M., Teh, S.-H., Ho, J.-H., and Ng, H. K. Controller design and trajectory tracking of a two-link robotic orthosis via sinusoidal-input describing function model. International Journal of Mechanical Engineering and Robotics Research 8, 6 (2019).

Chyan, G. S., and Ponnambalam, S. Obstacle avoidance control of redundant robots using variants of particle swarm optimization. Robotics and Computer-Integrated Manufacturing 28, 2 (2012), 147–153.

DeMers, D., and Kreutz-Delgado, K. Inverse kinematics of dextrous manipulators. In Neural Systems for Robotics. Elsevier, 1997, pp. 75–116.

Denavit, J., and Hartenberg, R. S. A kinematic notation for lower-pair mechanisms based on matrices.

Eberhart, R., and Kennedy, J. A new optimizer using particle swarm theory. In MHS’95. Proceedings of the sixth international symposium on micro machine and human science (1995), Ieee, pp. 39–43.

El-Sherbiny, A., Elhosseini, M. A., and Haikal, A. Y. A new abc variant for solving inverse kinematics problem in 5 dof robot arm. Applied Soft Computing 73 (2018), 24–38.

Emami, S. A., and Banazadeh, A. Simultaneous trajectory tracking and aerial manipulation using a multi-stage model predictive control. Aerospace Science and Technology 112 (2021), 106573.

Fang, J., Mei, T., Zhao, J., and Li, T. A dual-mode online optimization method for trajectory tracking of redundant manipulators. Industrial Robot: An International Journal (2016).

Funda, J., Taylor, R. H., and Paul, R. P. On homogeneous transforms, quaternions, and computational efficiency. IEEE transactions on Robotics and Automation 6, 3 (1990), 382–388.

Gan, D., Liao, Q., Wei, S., Dai, J., and Qiao, S. Dual quaternion-based inverse kinematics of the general spatial 7r mechanism. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, 8 (2008), 1593–1598.

Geradin, M., and Cardona, A. Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra. Computational Mechanics 4, 2 (1988), 115–135.

Gharehchopogh, F. S., and Gholizadeh, H. A comprehensive survey: Whale optimization algorithm and its applications. Swarm and Evolutionary Computation 48 (2019), 1–24.

Guo, J., Qiu, B., Hu, C., and Zhang, Y. Discrete-time nonlinear optimization via zeroing neural dynamics based on explicit linear multistep methods for tracking control of robot manipulators. Neurocomputing 412 (2020), 477–485.

Hernandez-Barragan, J., Lopez-Franco, C., Arana-Daniel, N., Alanis, A. Y., and Lopez-Franco, A. A modified firefly algorithm for the inverse kinematics solutions of robotic manipulators. Integrated Computer-Aided Engineering 28, 3 (2021), 257–275.

Houcine, L., Bouzbida, M., and Chaari, A. Improved fuzzy clustering algorithm using adaptive particle swarm optimization for nonlinear system modeling and identification. Iranian Journal of Fuzzy Systems 18, 3 (2021), 179–196.

Houssein, E. H., Gad, A. G., Hussain, K., and Suganthan, P. N. Major advances in particle swarm optimization: theory, analysis, and application. Swarm and Evolutionary Computation 63 (2021), 100868.

Huang, H.-C., Xu, S. S.-D., and Hsu, H.-S. Hybrid taguchi dna swarm intelligence for optimal inverse kinematics redundancy resolution of sixdof humanoid robot arms. Mathematical Problems in Engineering 2014 (2014).

Husty, M. L., Pfurner, M., and Schrocker, H.-P. A new and efficient algorithm for the inverse kinematics of a general serial 6r manipulator. Mechanism and machine theory 42, 1 (2007), 66–81.

Joo, D., and Yeom, K. Improved hybrid trajectory tracking algorithm for a 3-link manipulator using artificial neural network and kalman filter [j]. International Journal of Mechanical Engineering and Robotics Research 10, 2 (2021), 60–66.

Kanagaraj, G., Masthan, S. A. R. S., and Vincent, F. Y. Inverse kinematic solution of obstacle avoidance redundant robot manipulator by batalgorithms. International Journal of Robotics and Automation 36, 1 (2021).

Karimi, J., and Pourtakdoust, S. H. Optimal maneuver-based motion planning over terrain and threats using a dynamic hybrid pso algorithm. Aerospace Science and Technology 26, 1 (2013), 60–71.

Lafmejani, A. S., Masouleh, M. T., and Kalhor, A. Trajectory tracking control of a pneumatically actuated 6-dof gough–stewart parallel robot using backstepping-sliding mode controller and geometry-based quasi forward kinematic method. Robotics and Computer-Integrated Manufacturing 54 (2018), 96–114.

MathWorks India. Import rigid body tree model from urdf file, text, or simscape multibody model - matlab importrobot, (Accessed 06/2022).

Mirjalili, S., and Lewis, A. The whale optimization algorithm. Advances in engineering software 95 (2016), 51–67.

Motoman. Motoman mh5ls ii robot for assembly & handling — 5.0 kg, https://www.motoman. com/en-us/products/robots/industrial/assembly-handling/mh-series/mh5ls-ii (Accessed 06/2022).

Nearchou, A. C. Solving the inverse kinematics problem of redundant robots operating in complex environments via a modified genetic algorithm. Mechanism and machine theory 33, 3 (1998), 273–292.

Pluhacek, M., Kazikova, A., Kadavy, T., Viktorin, A., and Senkerik, R. Relation of neighborhood size and diversity loss rate in particle swarm optimization with ring topology. Mendel 27, 2 (2021), 74–79.

Ram, R., Pathak, P. M., and Junco, S. Inverse kinematics of mobile manipulator using bidirectional particle swarm optimization by manipulator decoupling. Mechanism and Machine Theory 131 (2019), 385–405.

Rashedi, E., Nezamabadi-Pour, H., and Saryazdi, S. Gsa: a gravitational search algorithm. Information sciences 179, 13 (2009), 2232–2248.

Rokbani, N., Casals, A., and Alimi, A. M. Ik-fa, a new heuristic inverse kinematics solver using firefly algorithm. In Computational intelligence applications in modeling and control. Springer, 2015, pp. 369–395.

Sadat Asl, A., Fazel Zarandi, M., Sotudian, S., and Amini, A. A fuzzy capacitated facility location-network design model: A hybrid firefly and invasive weed optimization (fiwo) solution. Iranian Journal of Fuzzy Systems 17, 2 (2020), 79–95.

Setayandeh, M., and Babaei, A. A novel method for multi-objective design optimization based on fuzzy systems. Iranian Journal of Fuzzy Systems 18, 5 (2021), 181–198.

Shen, D., Tang, L., Hu, Q., Guo, C., Li, X., and Zhang, J. Space manipulator trajectory tracking based on recursive decentralized finitetime control. Aerospace Science and Technology 102 (2020), 105870.

Tarokh, M., and Zhang, X. An adaptive genetic algorithm for real-time robotic trajectory tracking. IFAC Proceedings Volumes 39, 15 (2006), 199–204.

Theodoridis, D. C., Boutalis, Y. S., and Christodoulou, M. A. A new adaptive neurofuzzy controller for trajectory tracking of robot manipulators. International Journal of Robotics and Automation 26, 1 (2011), 64.

Thomas, M. J., Sanjeev, M. M., Sudheer, A., and Joy, M. Comparative study of various machine learning algorithms and denavit–hartenberg approach for the inverse kinematic solutions in a 3-ppss parallel manipulator. Industrial Robot: the international journal of robotics research and application 47, 5 (2020), 683–695.

Van Cuong, P., and Nan, W. Y. Adaptive trajectory tracking neural network control with robust compensator for robot manipulators. Neural Computing and Applications 27, 2 (2016), 525–536.

Wang, G.-G., Chu, H. E., and Mirjalili, S. Three-dimensional path planning for ucav using an improved bat algorithm. Aerospace Science and Technology 49 (2016), 231–238.

Yang, X.-S., and Gandomi, A. H. Bat algorithm: a novel approach for global engineering optimization. Engineering computations (2012).

Yarza, A., Santibanez, V., and Moreno-Valenzuela, J. Uniform global asymptotic stability of an adaptive output feedback tracking controller for robot manipulators. IFAC Proceedings Volumes 44, 1 (2011), 14590–14595.

Yin, X., and Pan, L. Enhancing trajectory tracking accuracy for industrial robot with robust adaptive control. Robotics and Computer-Integrated Manufacturing 51 (2018), 97–102.

Yin, X., Pan, L., and Cai, S. Robust adaptive fuzzy sliding mode trajectory tracking control for serial robotic manipulators. Robotics and Computer-Integrated Manufacturing 72 (2021),101884.

Younis, M. T., and Yang, S. Genetic algorithm for independent job scheduling in grid computing. In Mendel (2017), vol. 23, pp. 65–72.

Zhao, Y. M., Lin, Y., Xi, F., and Guo, S. Calibration-based iterative learning control for path tracking of industrial robots. IEEE Transactions on industrial electronics 62, 5 (2014), 2921–2929.

Zoric, N. D., Lazarevic, M. P., and Simonovi ´c, A. M. Multi-body kinematics and dynamics in terms of quaternions: Langrange formulation in covariant form: Rodriguez approach. FME Transactions 38, 1 (2010), 19–28.

How to Cite
Kanagaraj, G., Sheik Masthan, S. and Yu, V.F. 2022. Meta-Heuristics Based Inverse Kinematics of Robot Manipulator’s Path Tracking Capability Under Joint Limits. MENDEL. 28, 1 (Jun. 2022), 41-54. DOI:
Research articles