طراحی مسیر بهینه برای ربات فضایی شناور - آزاد در حرکت نقطه به نقطه به روش غیرمستقیم

نوع مقاله: مقاله پژوهشی

نویسندگان

1 عضو هیات علمی / دانشکدة مهندسی مکانیک، آزمایشگاه رباتیک و کنترل، دانشگاه سمنان

2 کارشناس ارشد مهنـدسی مکانیک / آزمایشگاه رباتیک و کنترل، دانشکدة مهندسی مکانیک، دانشگاه سمنان

چکیده

در این مقاله روشی جدید براساس حل غیرمستقیم مسئلة کنترل بهینه برای طراحی مسیر بهینة ربات فضایی شناور - آزاد، در حرکت نقطه به نقطه ارائه شده است. برای این منظور، معادلات دینامیکی سیستم در کنار قیود غیرهولونومیک ناشی از برقراری قانون بقای ممنتم زاویه‌ای در فرم فضای حالت استخراج می‌شود. سپس با استفاده از قضیة اساسی حساب تغییرات، شرایط لازم بهینگی به‌دست می‌آید. معادلات حاصل به یک مسئلة مقدار مرزی دونقطه‌ای منجر می‌شود که حل آنها مسیر بهینه و تابع کنترل بهینه را نتیجه خواهد داد. در روش ارائه‌شده می‌توان هم فضاپیما و هم منیپولاتور را از موقعیت اولیه به موقعیت نهایی به‌گونه‌ای رساند که علاوه بر برآوردن دقیق شرایط مرزی، معادلات دینامیکی و قیود غیرهولونومیک، یک تابع عملکرد همچون توان یا گشتاور مصرفی نیز کمینه شود. در این مقاله شبیه‌سازی برای یک ربات فضایی شناور - آزاد دو لینکی انجام شده، نتایج حاصل با کارهای قبلی مقایسه و نهایتاً کارایی روش پیشنهادی در کاهش حرکت پایه نمایش داده شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Optimal trajectory planning of free-floating space robot using indirect approach in point to point motion

نویسندگان [English]

  • Amin Nikoobin 1
  • Nastaran Samani 2
چکیده [English]

In this paper, a new method on the base of the indirect solution of optimal control problem is presented for trajectory planning of Free-Floating Space Robot (FFSR) in point to point motion. To this end, dynamic equations of the system beside the non-holonomic constraints due to angular momentum conservation low are derived in the state space form. Then the necessary conditions for optimality are derived using the fundamental theorem calculus of variations. The obtained equations lead to a two-point boundary value problem (BVP) which its solution result in optimal trajectory and optimal control function. In  the proposed method, both manipulator and base moves from the initial pose to the final pose in such a way that all the boundary conditions, dynamic equations and non-holonomic constraints are satisfied, and a given performance index such as consumed power or torque is also minimized. Simulations are performed for a two-link free-floating space manipulator and the obtained results are compared with the previous works, and the efficiency of proposed method to reduce the base movement is illustrated.

کلیدواژه‌ها [English]

  • free-floating space manipulator
  • optimal trajectory planning
  • point to point motion
  • optimal control
  • indirect method

[1] W. Xu, B. Liang, Y. Xu, “Survey of modeling, planning, and ground verification of space robotic systems.” Acta Astronautica, 68(11), 2011, pp. 1629-1649.

[2] From P. J., J. T. Gravdahl, K. Y. Pettersen, Vehicle-Manipulator Systems, Springer Link, Book chapter, 2014, pp. 325-354.

[3] Vafa, Z., S. Dubowsky. “The kinematics and dynamics of space manipulators: the virtual manipulator approach.” The Int Journal of Robotics Research, 9(4), 1990, pp. 3-21.

[4] Torres, M. A., S. Dubowsky. “Minimizing spacecraft attitude disturbances in space manipulator systems.” Journal of guidance, control, and dynamics, 15(4), 1992, pp. 1010-1017.

[5] Yoshida, K., K. Hashizume, S. Abiko. “Zero reaction maneuver: flight validation with ETS-VII space robot and extension to kinemati- cally redundant arm.” Proceedings of the IEEE International Conference on Robotics and Automation, Piscataway, USA, 2001, pp. 441-446.

[6] Papadopoulos, E., I. Tortopidis, K. Nanos. “Smooth planning for free -floating space robots using polynomials.” Proceedings of the IEEE Int. Conference on Robotics and Automation, Barcelona, Spain, 2005, pp. 4272-4277.

[7] Tortopidis, I., E. Papadopoulos. “On point-to-point motion planning for underactuated space manipulator systems.” Robotics and Autonomous Systems, 55(2), 2007, pp. 122-131.

[8] Huang, P., Y. Xu. “Pso-based time-optimal trajectory planning for space robot with dynamic constraints.” IEEE International Conference on Robotics and Biomimetics, 2006, pp. 1402-1407.

[9] Huang, P., Y. Xu, B. Liang. “Minimum-torque path planning of space robots using genetic algorithms.” International Journal of Robotics and Automation, 21(3), 2006, pp. 229-236.

[10] Oki, T., H. Nakanishi, K. Yoshid, “Time-optimal manipulator control of a free-floating space robot with constraint on reaction torque.” International Conference on Intelligent Robots and Systems, 2008, pp. 2828-2833.

[11] Kim, Y. M., B. K. Kim. “Energy-Efficient Trajectory Generation for Space Manipulators with Reaction Wheels under a Fixed Base Orientation.” Journal of Intelligent & Robotic Systems, 76(2), 2014, pp. 219-237.

[12] Xu, W., C., X. Li, Y. Wang, B. Liu, Y. Liang. “Study on non-holonomic cartesian path planning of a free-floating space robotic system.” Advanced Robotics, 23(1-2), 2009, pp. 113-143.

[13] Xu, W., et al. “The Cartesian path planning of free-floating space robot using particle swarm optimization.” International Journal of Advanced Robotic Systems, 5(3), 2008, pp. 301-310.

[14] Zhang, F., et al. “Point-to-point planning for free-floating space manipulator with zero-disturbance spacecraft attitude.” IEEE International Conference on Information and Automation, 2012, pp. 142-147.

[15] Moosavian, S. A. A, A. Daneshvar, M. Moradi. “Reactionless path planning for mobile robots.” modares mechanical engineering, 11(1), 2011, pp. 41-49 (in Persian).

[16] Zhuang, Y., H. Huang, “Time-optimal trajectory planning for under actuated spacecraft using a hybrid particle swarm optimization algorithm.” Acta Astronautica, 94(1), 2014, pp. 690-698.

[17] Wang, M., J. Luo, U. Walter. “Trajectory planning of free-floating space robot using Particle Swarm Optimization (PSO).” Acta Astronautica, 112(1), 2015, pp. 77-88.

[18] Chettibi, T., H. E. Lehtihet, M. Haddad, S. Hanchi, “Minimum cost trajectory planning for industrial robots.” European Journal of Mechanics A/Solids, 23(4), 2004, pp. 703-715.

[19] Callies, R., P. Rentrop. “Optimal Control of Rigid‐Link Manipulators by Indirect Methods.” GAMMMitteilungen, 31(1), 2008, pp. 27-58.

[20] Korayem, M. H., A. Nikoobin. “Maximum Payload for Flexible Joint Manipulators in Point-to-Point Task Using Optimal Control Approach.” The International Journal of Advanced Manufacturing Technology, 38 (9-10), 2008, pp. 1045-1060.

[21] Boscariol, P., A. Gasparetto. “Model-based trajectory planning for flexible-link mechanisms with bounded jerk.” Robotics and Computer-Integrated Manufacturing, 29(4), 2013, pp. 90-99.

[22] Mashadi, B., M. Majidi. “Global optimal path planning of an autonomous vehicle for overtaking a moving obstacle.” Latin American Journal of Solids and Structures, 11(14), 2014, pp. 2555-2572.

[23] Korayem, M. H., H. N. Rahimi, A. Nikoobin, “Mathematical Modeling and Trajectory Planning of Mobile Manipulators with Flexible Links and Joints.” Applied Mathematical Modelling, 36(7), 2012, pp. 3229-3244.

[24] Korayem, M. H., H. N. Rahimi, A. Nikoobin, “Path Planning of Mobile Elastic Robotic Arms by Indirect Approach of Optimal Control.” International Journal of Advanced Robotic Systems, 8(1), 2011, pp. 10-20.

[25] Jarzębowska, E., K. Pietrak. “Constrained mechanical systems modeling and control: A free-floating space manipulator case as a multi-constrained system.” Robotics and Autonomous Systems, 62(10), 2014, pp. 1353-1360.

[26] Kirk, D. E., Optimal control theory: an introduction, New York: Dover, 2004.