Optimal Balancing of Spatial Suspended Cable Robot in Point-to-Point Motion using Indirect Approach
الموضوعات :Mojtaba Riyahi Vezvari 1 , Amin Nikoobin 2
1 - Robotics lab, Faculty of Mechanical Engineering,
University of Semnan, Iran
2 - Robotics lab, Faculty of Mechanical Engineering,
University of Semnan, Iran
الکلمات المفتاحية: Point-to-Point motion, Cable robot, Counterweights, Optimal balancing,
ملخص المقالة :
In this paper, a method based on the indirect solution of optimal control problem is presented to specify the optimal trajectory of spatially suspended cable robot in point to point motion with considering the counterweights. In fact, an optimal trajectory planning problem is outlined in which states, controls and the values of counterweights must be calculated simultaneously in order to minimize the given performance index. The value of the pulley torques is considered for the performance index (objective function). Using the fundamental theorem of a calculus of variations, the necessary conditions for optimality of cable robot are achieved. For the three-cable spatial robot, a two-point boundary value problem is achieved which can be solved with bvp4c command in MATLAB. The obtained results show that optimal balancing in comparison with the unbalancing method can reduce the performance index significantly.
[1] Betts, J. T., “Survey of Numerical Methods for Trajectory Optimization”, Journal of Guidance, Control and Dynamics, Vol. 21, No. 2, 1998, pp. 193–207.
[2] Rivin, E. I., “Mechanical Design of Robotsˮ, McGraw-Hill, New York, 1988.
[3] Chettibi, T., Lehtihet, H. E., Haddad, M., and Hanchi, S., “Minimum Cost Trajectory Planning for Industrial Robots”, European Journal of Mechanics, Vol. 23, No. 4, 2004, pp. 703–715.
[4] Chen, Y. C., “Solving Robot Trajectory Planning Problems with Uniform Cubic B-splines”, Optimal Control Applications and Methods, Vol. 12, No. 4, 1991, pp. 247–262.
[5] Ravichandran, T., Wang, D., and Heppler, G., “Simultaneous Plant-Controller Design Optimization of a Two-link Planar Manipulator”, Mechatronics, Vol. 16, No. 3, 2006, pp. 233–242.
[6] Lahouar, S., Ottaviano, E., Zeghoul, S., Zomdhane, L., and Ceccarelli, L., “Collision Free Path-planning for Cable-driven Parallel Robots”, Robotics and Autonomous Systems, Vol. 57, 2009, pp. 1083-1093.
[7] Kirk, D. E., “Optimal Control Theory, an Introductionˮ, Prentice-Hall, Englewood Cliffs, New Jersey, 1970.
[8] Shiller, Z., Dubowsky, S., “Robot Path Planning with Obstacles, Actuators, Gripper and Payload Constraints”, The International Journal of Robotics Research, Vol. 8, No. 6, 1986, pp. 3–18.
[9] Shiller, Z., “Time-energy Optimal Control of Articulated Systems with Geometric Path Constraints”, Proceedings of IEEE International Conference on Robotics and Automation, Vol. 4, 1994, pp. 2680–2685.
[10] Furuno, S., Yamamoto, M., and Mohri, A., “Trajectory Planning of Mobile Manipulator with Stability Considerations”, Proceedings of IEEE International Conference on Robotics and Automation, Vol. 3, 2003, pp. 3403–3408.
[11] Korayem, M. H., Nikoobin, A., “Maximum Payload for Fexible Joint Manipulators in Point-to-point Task using Optimal Control Approach”, The International Journal of Advanced Manufacturing Technology, Vol. 38, No. 9, 2008, pp. 1045-1060.
[12] Korayem, M. H., Nikoobin, A., and Azimirad, V., “Trajectory Optimization of Fexible Link Manipulators in Point-to-point Motion”, Robotica, Vol. 27, No. 6, 2009, pp. 825–840.
[13] Korayem, M. H., Nikoobin, A., “Maximum-payload Path Planning for Redundant Manipulator using Indirect Solution of Optimal Control Problem”, The International Journal of Advanced Manufacturing Technology, Vol. 44, 2009, pp. 725–736.
[14] Korayem, M. H., Bamdad, M., and Akbareha, A., “Trajectory Optimization of Cable Parallel Manipulators in Point-to-point Motion”, Journal of Industrial Engineering, Vol. 5, 2010, pp. 29-34.
[15] Korayem, M. H., Rahimi, H. N., and Nikoobin, A., “Path Planning of Mobile Elastic Robotic Arms by Indirect Approach of Optimal Control”, International Journal of Advanced Robotic Systems, Vol. 8, 2011, pp. 10-20.
[16] Saravanan, R., Ramabalan, S., and Babu, P. D., “Optimum Static Balancing of an Industrial Robot Mechanism”, Engineering Applications of Artificial Intelligence, Vol. 21, No. 6, 2008, pp. 824-834.
[17] Coelho, T. A. H., Yong, L., and Alves, V. F. A., “Decoupling of Dynamic Equations by Means of Adaptive Balancing of 2-dof Open-loop Mechanism”, Mechanism and Machine Theory, Vol. 39, 2004, pp. 871-881.
[18] Nikoobin, A., Moradi, M., and Esmaili, A., “Optimal Spring Balancing of Robot Manipulators in Point-to-point Motion”, Robotica, Vol. 31, 2013, pp. 611-621.
[19] Perreault, S., Cardou, P., and Gosselin, C., “Approximate Static Balancing of a Planar Parallel Cable-driven Mechanism Based on Four-bar Linkages and Springs”, Mechanism and Machine Theory, Vol. 79, 2014, pp. 64–79.
[20] Nikoobin, A., Moradi, M., “Optimal Balancing of Robot Manipulators in Point-to-point Motion”, Robotica, Vol. 29, 2011, pp. 233–244.
[21] Nikoobin, A., Vezvari, M. R., and Ahmadieh, M., “Optimal Balancing of Planar Cable Robot in Point to Point Motion using the Indirect Approach”, 3rd RSI International Conference on Robotics and Mechatronics, 2015, pp. 499-504.
[22] Arora, J., “Introduction to Optimum Designˮ, 2nd ed., Elsevier Academic Press, San Diego, 2004.
[23] Bertolazzi, E., Biral, F., and Lio, M. D., “Symbolic–numeric Indirect Method for Solving Optimal Control Problems for Large Multibody Systems”, Multibody System Dynamics, Vol. 13, No. 2, 2005, pp. 233–252.
[24] Sentinella, M. R., Casalino, L., “Genetic Algorithm and Indirect Method Coupling for Low-thrust Trajectory Optimization”, 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Sacramento, California, 2006.
[25] Williams, R. L., Gallina, P., “Planar Cable-Direct-Driven Robots, Part I: Kinematics and Statics”, Proceedings 27th Design Automation Conference of the ASME, 2001.
[26] Williams, R. L., Gallina, P., “Planar Cable-direct-Driven Robots, Part II: Dynamics and Control”, Proceedings 27th Design Automation Conference of the ASME, 2001.
[27] Korayem, M. H., Jalali, M., and Tourajizadeh, H., “Dynamic Load Carrying Capacity of Spatial Cable Suspended Robot: Sliding Mode Control Approach”, Int J of Advanced Design and Manufacturing Technology, Vol. 5, No. 3, 2012, pp. 73–81.
