On the Effect of the End-effector Point Trajectory on the Joint ‎Jerk of the Redundant Manipulators

Document Type : Research Paper


Advanced Technology Center, Le Quy Don Technical University, Hoang Quoc Viet, Hanoi, 84, Vietnam


This paper is focused on investigating the joints jerk of industrial serial redundant manipulators with 6 degrees of freedom (6-DOF) under the variation of the end-effector point (EEP) trajectory in the workspace. The EEP trajectories are initially built in the basic planes because of their simplicity, verification and experimentation are smooth, and most of the actual welded structures are performed on these basic planes. The jerk is determined by solving the inverse kinematics problem of the redundant system. This problem is solved based on the algorithm which is used for adjusting the increments of the generalized coordinate vector (AGV). The efficiency of this algorithm is shown through the error between a given trajectory and the recalculated trajectory through the forward kinematics problem. The result of this study allows us to evaluate the effect of the change of the trajectory on the kinematics characteristics of the robot in general and the jerk of the joints in particular. On the other hand, these results can be used as the basis for planning the EEP trajectory for redundant robots, developing algorithms to reduce joint jerky, increase the life of robot systems, and improve the accuracy of the redundant robot movement.


Main Subjects

‎[1]‎ Homayoun, S., Configuration control of redundant manipulators: theory and implementation, IEEE Transactions on Robotics and Automation, 5, ‎‎1989, 472-490.‎
‎[2]‎ Siciliano, B., Kinematic control of redundant robot manipulators: A tutorial, Journal of Intelligent and Robotic Systems, 3, 1990, 201-212.‎
‎[3]‎ Chiaverini, S., Singularity robust task priority redundancy resolution for real time kinematic control of robot manipulators, IEEE Transactions on ‎Robotics and Automation, 13, 1997, 398–410.‎
‎[4]‎ Chiaverini, S., Oriono, G., Walker, I. D., Kinematically Redundant Manipulators, Springer Handbook of Robotics, Berlin, Heidenberg, 11, 2008, 245–‎‎268.‎
‎[5]‎ Zlajpah. L., Petric, T., Obstacle avoidance for redundant manipulators as control problem, IntechOpen, 11, 2012, 203–230.‎
‎[6]‎ Lian, S., Han, Y., Wang, Y., Bao, Y., Xiao, H., Li, X., Sun, N., Accelerating Inverse Kinematics for High-DOF Robots, In: Proceedings of the 54th ‎Annual Design Automation Conference, Austin, USA, 2017.‎
‎[7]‎ Yoshikawa, T., Dynamic manipulability of robot manipulators, Journal of Robotic Systems, 2, 1985, 113–124.‎

‎[8]‎ Wampler, C. W., Manipulator inverse kinematic solutions based on vector formulations and damped least squares methods, IEEE Transactions ‎on Systems, Man, and Cybernetics, 16, 1986, 93–101.‎
‎[9]‎ Wang, L. C. T., Chen, C. C., A combined optimization method for solving the inverse kinematics problem of mechanical manipulators, IEEE ‎Transactions on Robotics and Automation, 7, 1991, 489–499. ‎
‎[10]‎ Zhao, J., Badler, N. I., Inverse kinematics positioning using nonlinear programming for highly articulated figures, ACM Transactions on Graphics, ‎‎13, 1994, 313–336.‎
‎[11]‎ Sciavicco, L., Siciliano, B., A Solution Algorithm to the Inverse Kinematic Problem for Redundant Manipulators, Journal of Robotics and ‎Automation, 4, 1988, 403-410.‎
‎[12]‎ Antonelli, G., Chiaverini, S., Fusco, G., Kinematic control of redundant manipulators with online end-effector path tracking capability under ‎velocity and acceleration constraints, In: IFAC Robot Control, Austria, 2000, 183-188.‎
‎[13]‎ Wang, J., Li, Y., Zhao, X., Inverse kinematics and control of a 7 DOF redundant manipulator based on the closed loop algorithm, International ‎Journal of Advanced Robotics Systems, 7, 2010, 1-10.‎
‎[14]‎ My, C. A., Bien, D. X., Tung, H. B., Hieu, L. C., Cong, N. V., Hieu, T. V., Inverse kinematic control algorithm for a welding robot-positioner ‎system to trace a 3D complex curve, In: International Conference on Advanced Technologies for Communications, Hanoi, Vietnam, 2019, 319-323.‎
‎[15]‎ Aguilar, O. A., Huegel, J. C., Inverse Kinematics Solution for Robotic Manipulators Using a CUDA-Based Parallel Genetic Algorithms, Mexican ‎International Conference on Artificial Intelligence, 1, 2011, 490-503.‎
‎[16]‎ Bingul, Z., Ertunc, H. M., Oysu, C., Comparison of inverse kinematics solutions using neural network for 6R robot manipulator with offset, ‎Computational Intelligence Methods and Applications, 2005, 1–5.‎
‎[17]‎ Feng, Y., Yaonan, W., Yimin, Y., Inverse kinematics solution for robot manipulator based on Neural Network under joint subspace, International ‎Journal of Computer and Communications, 7, 2012, 459-472.‎
‎[18]‎ Xu, H. L., Xie, X. R., Zhuang, J., Wang, S. A., Global time-energy optimal planning of industrial robot trajectories, Chinese Journal of Mechanical ‎Engineering, 46, 2010, 19-25.‎
‎[19]‎ Osgouie, K. G., Gard, B., Using the matrix method to compute the degrees of freedom of mechanism, Journal of Applied and Computational ‎Mechanics, 3(3), 2017, 158–170.‎
‎[20]‎ Alessandro, G., Zanotto, V., A technique for time-jerk optimal planning of robot trajectories, Robotics and Computer-Integrated Manufacturing, 24, ‎‎2008, 415-426.‎
‎[21]‎ Palleschi, A., Garabini, M., Caporale, D., Pallottino, L., Time-Optimal Path Tracking for Jerk Controlled Robots, IEEE Robotics and Automation ‎Letters, 2019, 1-8.‎
‎[22]‎ Pierre-Jean, B., Richard, B., Pierre, B., Eric, D., Influence of a Jerk Controlled Movement Law on the Vibratory Behaviour of High-Dynamics ‎Systems, Journal of Intelligent & Robotic Systems, 42, 2005, 275-293.

‎[23]‎ Friedrich, L., Michael, S., Trajectory Generation for Immediate Path-Accurate Jerk-Limited Stopping of Industrial Robots, Proceeding in ‎International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 2015.‎
‎[24]‎ Piazzi, A., Visioli, A., Global Minimum-Jerk Trajectory Planning of Robot Manipulators, IEEE Transactions on Industrial Electronics, 47, 2000, 140-‎‎149.‎
‎[25]‎ Gabor, V., Bela, L., Shahram, P., Real-time optimized robot trajectory planning with jerk, IFAC Robot Control, Wroclaw, Poland, 2003, 265-270. ‎
‎[26]‎ Lin, H., Liu, Y., Minimum-Jerk Robot Joint Trajectory Using Particle Swarm Optimization, In: First International Conference on Robot, Vision and ‎Signal Processing, 2011, 118-121.‎
‎[27]‎ Vanni, Z., Alessandro, G., Albano, L., Paolo, B., Renato, V., Experimental Validation of Minimum Time-jerk Algorithms for Industrial Robots, ‎Journal of Intelligent Robot Systems, 64, 2011, 197–219.‎
‎[28]‎ Rubio, F., Valero, F., Suñer, J. L., Cuadrado, J. I., Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed ‎constraints, Industrial Robot: An International Journal, 29, 2012, 92-100.‎
‎[29]‎ Chengkai, D., Sylvain, L., Kai-Ming, Y., Jo, M. P. G., Charlie, C., Wang, L., Planning Jerk-Optimized Trajectory with Discrete-Time Constraints for ‎Redundant Robots, IEEE Transactions on Automation Science and Engineering, 17, 2020, 1711-1724.

‎[30]‎ Kazem, K., Zhaoyu, W., Global versus Local Optimization in Redundancy Resolution of Robotic Manipulators, The International Journal of Robotics ‎Research, 7, 1988, 1-10. ‎
‎[31]‎ Spong, M. W., Hutchinson, Vidyasagar, S. M., Robot modeling and Control, First edition, New York, USA, John Wiley and Sons, 2001.‎
‎[32]‎ Philip, F., Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots, Ph.D. Thesis, School of Engineering and Applied Science, ‎Department of Electrical and Systems Engineering, Washington University in St. Louis, Saint Louis, Missouri, USA, 2012.

‎[33]‎ Ying, W., Xiaogang, Y., Liangyu, H., Hongzhou, T., Yunong, Z., Inverse-Free Solution of ZIGI Type to Acceleration-Level Inverse Kinematics of ‎Redundant Robot Manipulators, 7th International Conference on Advanced Computational Intelligence Mount Wuyi, Fujian, China; March 27-29, 2015, ‎‎57-62. ‎
‎[34]‎ Macfarlane, S., Croft, E. A., Jerk-Bounded Manipulator Trajectory Planning: Design for Real-Time Applications, IEEE Transactions on Robotics and ‎Automation, 1, 2003, 42-52.‎
‎[35]‎ Vass, G., Lantos, B., Payandeh, S., Real-time optimized robot trajectory planning with jerk, In: IFAC Robot Control, Wroclaw, Poland, 2003, 265-‎‎270.‎
‎[36]‎ Zhao, R., Sidobre, D., Trajectory Smoothing using Jerk Bounded Shortcuts for Service Manipulator Robots, In: International Conference on Intelligent ‎Robots and Systems (IROS), 2015, 4929-4934. ‎
‎[37]‎ Lu, S., Zhao, J., Jiang, L., Liu, H., Solving the Time-Jerk Optimal Trajectory Planning Problem of a Robot Using Augmented Lagrange Constrained ‎Particle Swarm Optimization, Mathematical Problems in Engineering, 2017, 1-11.‎
‎[38]‎ Dai, C., Lefebvre, S., Yu, K., Geraed, J. M. P., Wang, C. C. L., Planning Jerk-Optimized Trajectory with Discrete-Time Constraints for Redundant ‎Robots, IEEE Transactions on Automation Science and Engineering, 2020, 1-14.‎
‎[39]‎ Cao, Z. Y., Wang, H., Wu, W. R., Xie, H. J., Time-jerk optimal trajectory planning of shotcrete manipulators, Journal of Central South University, ‎‎44, 2013, 114-121.‎
‎[40]‎ Zhong, G. L., Kobayashi, Y., Emaru, T., Minimum time-jerk trajectory generation for a mobile articulated manipulator, Journal of the Chinese ‎Society of Mechanical Engineers, 35, 2014, 287-296.‎
‎[41]‎ Liu, F., Lin, F., Time-jerk optimal planning of industrial robot trajectories, International Journal Robotics Automation, 31, 2016, 1-7.‎
‎[42]‎ FD-V8 robot from https://www.daihen-usa.com/product/fd-v8-robot-6kg-payload-1-4m-reach/ (Access: August 2020).‎
‎[43]‎ Khang, N. V., Dien, N. P., Vinh, N. V., Nam, T. H., Inverse kinematic and dynamic analysis of redundant measuring manipulator BKHN-MCX-04, ‎Vietnam Journal of Mechanics, 32, 2010, 15-26.‎
‎[44]‎ Raunhardt, D., Boulic, R., Progressive clamping, IEEE International Conference on Robotics and Automation (ICRA), 2007, 4414–4419.‎