Waveform based Inverse Kinematics Algorithm of Kinematically Redundant 3-DOF Manipulator

  • Setyamartana Parman Universiti Teknikal Malaysia Melaka, 75450 Ayer Keroh, Melaka, Malaysia
  • Affiani Machmudah Universitas Airlangga, Jalan Mulyosari, Surabaya 60115, Indonesia
Keywords: Waveform, sinusoidal function, inverse kinematics algorithm, kinematically redundant manipulator

Abstract

This paper presents a new approach to the problem of inverse kinematics by modelling robot arm movements as signals generated from algebra-based solutions. The inverse kinematics of point P(xP,yP) are modelled as sinusoidal functions with mechanical constraints. Unique wave forms occur at each point in the workspace. There are four types of inverse kinematic waves depending on how sinusoidal waves cross the value of mechanical constraints. In terms of tracking the path, the robot's arm produces complex waves that produce the desired movement. Due to mechanical constraints, many points in the workspace have the bandwidth where the signal is produced only at limited intervals from the angular domain. Tracks must be stored at these appropriate intervals, which build bandwidth tunnels, completely from the initial configuration to the final configuration. Simulations will be carried out using 3-DOF series planar robots to track highly complex mathematical curves. With a wave-based approach, the solution of the IK problem can benefit from wave characteristics such as the superposition principle.

References

[1] Hormaza LA, Mohammed WM, Ferrer BR, Bejarano R and Lastra JLM. On-line Training and Monitoring of Robot Tasks through Virtual Reality. In: 2019 IEEE 17th International Conference on Industrial Informatics (INDIN), Helsinki, Finland, 22-25 July 2019.
[2] Ovchinnikov I, Kovalenko P. Predictive Model to Simulate Humanoid Gait. In: International Journal of Innovative Technology and Interdisciplinary Sciences, 2018, Vol 1(1), pp. 9-17.
[3] Pac MR, Popa DO. Interval analysis of kinematic error in serial manipulator using product of exponential formula. In: IEEE Trans. Autom. Sci. Eng., 2013, Vol. 10, pp. 525-535.
[4] Almarkhi AA, Maciejewski AA. Singularity Analysis for Redundant Manipulators of Arbitrary Kinematic Structure. In: Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2019) - Volume 2, pages 42-49.
[5] Wampler CW. Inverse kinematic function for redundant manipulators. In: Proceedings IEEE Conf. Robotics and Automat., 1987, pp. 610–617.
[6] Baillieul J. Kinematic programming alternatives for redundant manipulators. In: Proceedings IEEE Conf. Robotics and automation, 1985. pp. 722–8.
[7] Baker DR, Wampler CW. On the inverse kinematics of redundant robot manipulators. In: Int. J. Robot. Res., 1988, vol 7, pp. 3-21.
[8] Burdick JW. On the inverse kinematics of redundant manipulators: characterization of the self-motion manifolds. In: Proc. IEEE Conf. Robotics and Automat. Scottsdale, Arizona, 1989, pp. 264-270.
[9] Ahuactzin JM, Gupta K. A motion planning based approach for inverse kinematics of redundant robots: the kinematic roadmap. In: Int. J. Robot. Res., 1998, vol 14, pp. 159-167.
[10] Nerchou AC. Solving the inverse kinematics problem of redundant robots operating in complex environments via modified genetic algorithm. In: Mech. Mach. Theory, 1998, vol 33, pp. 273-292.
[11] Marcos MG, Machado JAT, Azavedo-Perdicoulis TP. Trajectory planning of redundant manipulators using genetic algorithms. In: Commun. Nonlinear Sciences, 2009, vol 14, pp. 2858-2869.
[12] Rao RS, Asaithambi A, Agraval SK. Inverse kinematic solution of robot manipulators using interval analysis. In: J. Mech. Des., 1998, vol 120, pp. 147-150.
[13] Pac MR, Popa DO. Interval analysis of kinematic error in serial manipulator using product of exponential formula. In: IEEE Trans. Autom. Sci. Eng., 2013, Vol. 10, pp. 525-535.
[14] Wei Y, Jian S, He S, Wang Z. General approach for inverse kinematics of nR robots. In: Mech. Mach. Theory, 2014, vol 75, pp. 97-106.
[15] Rudny T. Solving inverse kinematics by fully automated planar curves intersecting. In: Mech. Mach. Theory, 2014, vol 74, pp. 310-318.
[16] Toz M. Chaos-based Vortex Search algorithm for solving inverse kinematics problem of serial robot manipulators with offset wrist. In: Applied Soft Computing Volume 89, April 2020, 106074.
[17] Erleben K, Andrews S. Solving inverse kinematics using exact Hessian matrices. In: Computers & Graphics, 2019, Volume 78, pp. 1-11.
[18] Dereli S, Köker R. A meta-heuristic proposal for inverse kinematics solution of 7-DOF serial robotic manipulator: quantum behaved particle swarm algorithm. In: Artificial Intelligence Review, 2020, volume 53, pages949–964.
[19] Pan X, Polden J, Larkin N, Duin SV, and Norrish J. Recent progress on programming methods for industrial robots. In: Robot. Comput.-Integr. Manuf, 2012, vol. 28, pp. 87-94.
[20] Orfanidis SJ. Introduction to Signal Processing. Pearson Education, Inc. 2010.
[21] Machmudah A, Parman S, Zainuddin A, Chacko S. Polynomial joint angle arm robot motion planning in complex geometrical obstacles. In: Applied Soft Computing, 2013, vol 13, pp. 1099-1109.
[22] Merlet JP. A generic trajectory verifier for the motion planning of parallel robot. In: Journal of Mechanical Design, 2001, vol. 123, pp. 510-515.
Published
2020-04-14
How to Cite
Parman, S., & Machmudah, A. (2020). Waveform based Inverse Kinematics Algorithm of Kinematically Redundant 3-DOF Manipulator. International Journal of Innovative Technology and Interdisciplinary Sciences, 3(2), 407-428. https://doi.org/10.15157/IJITIS.2020.3.2.407-428