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Optimal path planning of redundant free-floating revolute-jointed space manipulators with seven links

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Abstract

The path planning of free-floating manipulators is of great interest in space operations. The manipulators in the free-floating mode exhibit nonholonomic characteristics due to the nonintegrability of the angular momentum, which makes the problem complicated. This paper analyzes the path planning of redundant, free-floating space manipulators with revolute joints and 7 degrees of freedom. The primary task of manipulators is to move the manipulator arms so that the desired end-effector position and orientation can be achieved. The motion of the manipulators can produce an attitude disturbance of the base, which has an adverse impact on the spacecraft operation. Thus, it is necessary to minimize the base attitude disturbance in order to reduce the fuel consumption for attitude maintenance. Practically, the path planning of redundant free-floating manipulators with higher degrees of freedom (7 degrees of freedom in this paper) in three-dimensional space is more complicated than path planning with fewer degrees of freedom, including planar or fixed base cases. This paper provides a tractable planning method to solve this problem, which could avoid the pseudo inverse of the Jacobian matrix. The sine functions, whose arguments are the polynomial functions with unknown coefficients, are used to specify the joint paths. The PSODE algorithm (particle swarm optimization combined with differential evolution) is applied to optimize the unknown coefficients of the polynomials in order to achieve the desired end-effector position and orientation and simultaneously minimize the base attitude disturbance. The simulations demonstrate that this method could provide satisfactory smooth paths for redundant free-floating space manipulators.

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References

  1. King, D.: Space servicing: past, present and future. In: Proceeding of the 6th International Symposium on Artificial Intelligence and Robotics & Automation in Space (2001)

    Google Scholar 

  2. Vafa, Z., Dubowsky, S.: The kinematics and dynamics of space manipulators: the virtual manipulator approach. Int. J. Robot. Res. 9(4), 3–21 (1990)

    Article  Google Scholar 

  3. Nakamura, Y., Mukherjee, R.: Nonholonomic path planning of space robots via a bidirectional approach. IEEE Trans. Robot. Autom. 7(4), 500–514 (1991)

    Article  Google Scholar 

  4. Papadopoulos, E., Dubowsky, S.: Dynamic singularities in free-floating space manipulators. J. Dyn. Syst. 115(1), 44–52 (1993)

    Article  Google Scholar 

  5. Dubowsky, S., Torres, M.A.: Path planning for space manipulator to minimize spacecraft attitude disturbances. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 3, Sacramento, California, April 1991, pp. 2522–2528 (1991)

    Chapter  Google Scholar 

  6. Yoshida, K., Hashizume, K., Abiko, S.: Zero reaction maneuver: flight validation with ETS-VII space robot and extension to kinematically redundant arm. In: Proceeding of the IEEE International Conference on Robotics and Automation, pp. 441–446 (2001)

    Google Scholar 

  7. Agrawal, O.P., Xu, Y.S.: On the global optimum path planning for redundant space manipulator. IEEE Trans. Syst. Man Cybern. 24(9), 1306–1316 (1994)

    Article  Google Scholar 

  8. Pandey, S., Agrawal, S.: Path planning of free-floating prismatic-jointed manipulators. Multibody Syst. Dyn. 1(1), 127–140 (1997)

    Article  MATH  Google Scholar 

  9. Papadopoulos, E., Tortopidis, I., Nanos, K.: Smooth planning for free-floating space robots using polynomials. In: Proceeding of the IEEE International Conference on Robotics and Automation, Barcelona, Spain, April 2005, pp. 4272–4277 (2005)

    Chapter  Google Scholar 

  10. Tortopidis, I., Papadopoulos, E.: On point-to-point motion planning for underactuated space manipulator systems. Robot. Auton. Syst. 55, 122–131 (2007). doi:10.1016/j.robot.2006.07.003

    Article  Google Scholar 

  11. Nenchev, D.N., Yoshida, K.: Singularity-consistent teleoperation techniques for redundant free-flying robots. Rev. Ciênc. Exatas 5–8, 7–20 (1999–2002)

    Google Scholar 

  12. Kreutz-Delgado, K., Long, M., Seraji, H.: Kinematic analysis of 7 DOF manipulators. Int. J. Robot. Res. 11, 469–481 (1992)

    Article  Google Scholar 

  13. Xu, W., Liu, Y., Liang, B., Wang, X., Xu, Y.: Unified multi-domain modelling and simulation of space robot for capturing a moving target. Multibody Syst. Dyn. 23(3), 293–331 (2010). doi:10.1007/s11044-009-9184-0

    Article  MathSciNet  MATH  Google Scholar 

  14. Xiang, Y., Arora, J.S., Rahmatalla, S., Marler, T., Bhatt, R., Abdel-Malek, K.: Human lifting simulation using a multi-objective optimization approach. Multibody Syst. Dyn. 23(4), 431–451 (2010). doi:10.1007/s11044-009-9186-y

    Article  MathSciNet  MATH  Google Scholar 

  15. Kim, J.H., Xiang, Y., Yang, J., Arora, J.S., Abdel-Malek, K.: Dynamic motion planning of overarm throw for a biped human multibody system. Multibody Syst. Dyn. 24(1), 1–24 (2010). doi:10.1007/s11044-010-9193-z

    Article  MathSciNet  MATH  Google Scholar 

  16. Santos, R.R., Steffen, V., Saramago, S.F.P.: Robot path planning in a constrained workspace by using optimal control techniques. Multibody Syst. Dyn. 19(1–2), 159–177 (2008). doi:10.1007/s11044-007-9059-1

    Article  MATH  Google Scholar 

  17. Kim, J.H., Yang, J., Abdel-Malek, K.: A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators in DH representation. Multibody Syst. Dyn. 19(4), 427–451 (2008). doi:10.1007/s11044-007-9100-4

    Article  MathSciNet  MATH  Google Scholar 

  18. Bertolazzi, E., Biral, F., Da Lio, M.: Real-time motion planning for multibody systems real life application examples. Multibody Syst. Dyn. 17(2–3), 119–139 (2007). doi:10.1007/s11044-007-9037-7

    Article  MathSciNet  MATH  Google Scholar 

  19. Bottasso, C.L., Croce, A.: Optimal control of multibody systems using an energy preserving direct transcription method. Multibody Syst. Dyn. 12(1), 17–45 (2004). doi:10.1023/B:MUBO.0000042931.61655.73

    Article  MathSciNet  MATH  Google Scholar 

  20. Bottasso, C.L., Croce, A., Ghezzi, L., Faure, P.: On the solution of inverse dynamics and trajectory optimization problems for multibody systems. Multibody Syst. Dyn. 11(1), 1–22 (2004). doi:10.1023/B:MUBO.0000014875.66058.74

    Article  MathSciNet  MATH  Google Scholar 

  21. Kielau, G., Maißer, P.: Nonholonomic multibody dynamics. Multibody Syst. Dyn. 9(3), 213–236 (2003). doi:10.1023/A:1022920709192

    Article  MathSciNet  MATH  Google Scholar 

  22. Lo, J., Huang, G., Metaxas, D.: Human motion planning based on recursive dynamics and optimal control techniques. Multibody Syst. Dyn. 8(4), 433–458 (2002). doi:10.1023/A:1021111421247

    Article  MathSciNet  MATH  Google Scholar 

  23. Niu, B., Li, L.: A novel PSO-DE-based hybrid algorithm for global optimization. In: Lecture Notes in Computer Science, vol. 5227, pp. 156–163. Springer, Berlin (2008). doi:10.1007/978-3-540-85984-0

    Google Scholar 

  24. Gibbs, G., Sachdev, S.: Canada and the international space station program: overview and status. Acta Astronaut. 51(1–9), 591–600 (2002)

    Article  Google Scholar 

  25. Licata, R., Parisch, M., Ruiz Urien, I.J., De Bartolomei, M., Grisoni, G., Didot, F.: Robotic assembly of large space structures: application to XEUS. In: 7th ESA Workshop on. Advanced Space Technologies for Robotics and Automation (2002)

    Google Scholar 

  26. Boumans, R., Heemskerk, C.: The European robotic arm for the international space station. Robot. Auton. Syst. 23, 17–27 (1998)

    Article  Google Scholar 

  27. Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices. J. Appl. Mech. 77(23), 215–221 (1955)

    MathSciNet  Google Scholar 

  28. Craig, J.J.: Introduction to Robotics: Mechanics and Control. Addison-Wesley, Boston (1986)

    Google Scholar 

  29. Roberson, R.E., Wittenburg, J.: A dynamical formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite attitude control. In: Proceedings of 3rd Congress, the International Federation Automatic Control. London, England, June 1966 (1966)

    Google Scholar 

  30. Wittenburg, J.: Dynamics of Systems of Rigid Bodies. Teubner, Stuttgart (1977)

    Book  MATH  Google Scholar 

  31. Watanabe, Y.: Acceleration-level control of a kinematically redundant manipulator on a free-flying space robot. In: AIAA Guidance, Navigation, and Control Conference and Exhibit (AIAA 2001-4226) (2001)

    Google Scholar 

  32. Huang, P., Chen, K., Xu, Y.: Optimal path planning for minimizing disturbance of space robot. In: Proceedings of the IEEE: 9th International Conference on Control, Automation, Robotics and Vision, Singapore, December 2006, pp. 1–6 (2006). doi:10.1109/ICARCV.2006.345055

    Chapter  Google Scholar 

  33. Liu, X., Baoyin, H., Ma, X.: Five special types of orbits around Mars. J. Guid. Control Dyn. 33(4), 1294–1301 (2010). doi:10.2514/1.48706

    Article  Google Scholar 

  34. Niu, B., Li, L.: Design of T-S fuzzy model based on PSODE algorithm. In: Lecture Notes in Computer Science, vol. 5227, pp. 384–390. Springer, Berlin (2008). doi:10.1007/978-3-540-85984-0_47

    Google Scholar 

  35. Zhu, K., Li, J., Baoyin, H.: Multi-swingby optimization of mission to Saturn using global optimization algorithms. Acta Mech. Sin. 25(6), 839–845 (2009). doi:10.1007/s10409-009-0299-6

    Article  MathSciNet  Google Scholar 

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Acknowledgement

This research was supported by the National Natural Science Foundation of China (No. 11072122).

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  1. School of Aerospace, Tsinghua University, Beijing, 100084, China

    Xiaodong Liu, Hexi Baoyin & Xingrui Ma

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  1. Xiaodong Liu
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  2. Hexi Baoyin
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  3. Xingrui Ma
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Correspondence to Hexi Baoyin.

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Liu, X., Baoyin, H. & Ma, X. Optimal path planning of redundant free-floating revolute-jointed space manipulators with seven links. Multibody Syst Dyn 29, 41–56 (2013). https://doi.org/10.1007/s11044-012-9323-x

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  • DOI: https://doi.org/10.1007/s11044-012-9323-x

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