Optimal Trajectory Planning of a Box Transporter Mobile Robot
الموضوعات :Hossein Barghi Jond 1 , Adel Akbarimajd 2 , Nurhan Gürsel Özmen 3 , Sonia Gharibzadeh 4
1 - Ahar Branch, Islamic Azad University, Ahar, Iran
2 - Faculty of Electrical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
3 - Department of Mechanical Engineering, Karadeniz Technical University, Trabzon, Turkey.
4 - Ahar Branch, Islamic Azad University, Ahar, Iran
الکلمات المفتاحية: Genetic algorithm, Trajectory Planning, Dynamic Grasp, Non-prehensile Manipulation, Mobile Robots,
ملخص المقالة :
This paper aims to discuss the requirements of safe and smooth trajectory planning of transporter mobile robots to perform non-prehensile object manipulation task. In non-prehensile approach, the robot and the object must keep their grasp-less contact during manipulation task. To this end, dynamic grasp concept is employed for a box manipulation task and corresponding conditions are obtained and are represented as a bound on robot acceleration. A trajectory optimization problem is defined for general motion where dynamic grasp conditions are regarded as constraint on acceleration. The optimal trajectory planning for linear, circular and curve motions are discussed. Optimization problems for linear and circular trajectories were analytically solved by previous studies and here we focused with curve trajectory where Genetic Algorithm is employed as a solver tool. Motion simulations showed that the resulted trajectories satisfy the acceleration constraint as well as velocity boundary condition that is needed to accomplish non-prehensile box manipulation task.
[1] Lynch, K. M. and Mason, M. T., 1999. Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments. International Journal of Robotics Research, 18 (1), pp. 64-92.
[2] Lynch, K. M., Northrop, M. and Pan, P., 2002. Stable limit sets in a dynamic parts feeder. IEEE Trans Robotics and Automation, 18 (4), pp. 608-615.
[3] Lynch, K. M. and Murphey, T. D., 2003. Control of nonprehensile manipulation. Control Problems in Robotics-Springer Tracts in Advanced Robotics, 4, pp. 39-57.
[4] Li, Q. and Payande, S., 2004. Planning Velocities of Free Sliding Objects as a Free Boundary Value Problem. International Journal of Robotics Research, 23 (1), pp. 69-87.
[5] Mason, M. T., Pai, D., Rus D., Taylor, R. L. et. al., 1999. A Mobile Manipulator. Proc. IEEE International Conf. on Robotics and Automation, Detroit, Michigan, pp. 2322 – 2327.
[6] Yamashita, A., Kawano, K., Ota, J., Arai, T. et. al., 1999. Planning method for cooperative manipulation by multiple mobile robots using tools with motion errors. Proc. IEEE/RSJ International Conf. on Intelligent Robots and Systems, Kyongju, pp. 978 – 983.
[7] Huang, W. H. and Holden G. F., 2001. Nonprehensile Palmar Manipulation with a Mobile Robot. Proc. IEEE/RSJ International Conf. on .Intelligent Robots and Systems, Maui, HI, USA.
[8] Gupta, A. and Huang, W. H., 2003. A carrying task for nonprehensile mobile manipulators. Proc. IEEE/RSJ International Conf. on Intelligent Robots and Systems, Las Vegas, USA.
[9] Liu, Y. and Liu, G., 2009. Mobile manipulation using tracks of a tracked mobile robot. Proc. IEEE/RSJ International Conf. on Intelligent Robots and Systems, St. Louis, MO.
[10] Kolhe, P., Dantam, N., Stilman, M., 2010. Dynamic Pushing Strategies for Dynamically Stable Mobile Manipulators. Proc. IEEE International Conf. on Robotics and Automation, Alaska, USA.
[11] Lepetic, M., Klancar, G. Skrjanc, I., Matko, D. et. al., 2003. Time optimal path planning considering acceleration limits. Robotics and Autonomous Systems, 45, pp. 199–210.
[12] Naguyen, K. D., Chen, I. M., Ng, T. C., 2007. Planning algorithms for s-curve trajectories. Proc. IEEE/ASME International conf. on Advanced Intelligent Mechatronics, Zurich.
[13] Kardos, E. S. and Kiss, B., 2009. Continuous-curvature paths for mobile robots. Periodica polytechnic Electrical Engineering, 53 (1-2), pp. 63-72.
[14] Korayem, M. H., Nazemizadeh, M., Rahimi, H. N., 2013. Trajectory optimization of nonholonomic mobile manipulators departing to a moving target amidst moving obstacles. Acta Mechanica, 224 (5), pp. 995-1008.
[15] Li, B. and Shao, Z., 2015. Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots. Advances in Engineering Software, 87, pp. 30–42.
[16] Sabelhaus, D., Lammers, P. S., Helligen, L. P., Röben, M. F., 2015. Path planning of headland turn manoeuvres. LANDTECHNIK ,70(4), pp. 123–131.
[17] Katrakazas, C., Quddus, M., Chen, W., Deka, L., 2015. Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions. Transportation Research Part C: Emerging Technologies, 60, pp. 416-442.
[18] Yang, G. J., Delgado, R., Choi, B. W., 2016. A Practical Joint-space Trajectory Generation Method Based on Convolution in Real-time Control. International Journal of Advanced Robotic Systems, International Journal of Advanced Robotic Systems, 13(56), pp. 1-12.
[19] Yang, K., Jung, D., Sukkarieh, S., 2013. Continuous curvature path-smoothing algorithm using cubic Bezier spiral curves for non-holonomic robots. Advanced Robotics, 27(4): pp. 247-258.
[20] Jolly, K. G., Sreerama-Kumar, R., Vijayakumar, R., 2009. A Bezier curve based path planning in a multi-agent robot soccer system without violating the acceleration limits. Robotics and Automation Systems, 57(1), pp. 23-33.
[21] Yang, G. J. and Choi, B. W., 2013. Smooth trajectory planning along Bezier curve for mobile robots with velocity constraints. International Journal of Control and Automation, 6(2), pp. 225-234.
[22] Barghijand, H., Akbarimajd, A., Keighobadi, J., 2011. Quasi-Static Object Manipulation by Mobile Robot: Optimal Motion Planning Using GA. International Conference on Intelligent Systems Design and Applications, Spain, pp. 202-207.
[23] Siciliano, B. and Khatib, O. (Eds.), 2008. Springer Handbook of Robotics, Springer, Springer-Verlag Berlin Heidelberg, Chaps. 5, 27.
[24] Sardain, P. and Bessonnet, G., 2004. Forces Acting on a Biped Robot. Center of Pressure—Zero Moment Point. IEEE Transactions on Systems, Man, and Cybernetics, 34 (5), pp. 630-637.
[25] Jond, H. B., Akbarimajd, A. and Ozmen, N. G., 2014. Time-Distance Optimal Trajectory Planning For Mobile Robots On Straight And Circular Paths. Journal of Advances in Computer Research, 5 (2), pp. 23-36.
[26] Gray, A., 1997. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press.
[27] Melanie, M., 1996. An Introduction to Genetic Algorithms, Fifth printing, Cambridge, MA: MIT Press., Chap. 2.
[28] Haupt, R. L. and Haupt, S. E., 2004. Practical Genetic Algorithms. 2nd ed. New York, USA, Wiley.