Skip to main content

Optimal trajectory planning for a redundant mobile manipulator with non-holonomic constraints performing push–pull tasks

  • José P. Puga (a1) and Luciano E. Chiang (a1)

This work presents a method to generate optimal trajectories for redundant mobile manipulators based on a weighted function that considers simultaneously joint torques, manipulability and preferred joint angle references. This method is applicable to a group of tasks, commonly known as push–pull tasks, in which a redundant mobile manipulator subject to non-holonomic constraints moves slowly while exerting a set of forces against the environment. In practice, this occurs when the manipulator is pulling against an object such as when opening a door or unearthing a buried object. Torque is computed in a quasi-static manner, mainly taking into consideration the effect of multiple external forces while neglecting dynamic effects. The formulation incorporates a criterion for optimizing a starting configuration, and special considerations are made to account for non-holonomic constraints. The application to an existing mobile manipulator is described.

Corresponding author
*Corresponding author. E-mail:
Hide All
1.Shugen, Ma, “A new formulation technique for local torque optimization of redundant manipulators,” Trans. Ind. Elec. 43 (4), 462468 (1996).
2.Cheng, Fan-Tian, Sheu, Rong-Jing and Chen, Tsing-Hua, “The improved compact QP method for resolving manipulator redundancy,” IEEE Trans. Syst. Man Cybern. 25 (11), 15211530 (1995).
3.Nedungadi, A. and Kazerouinian, K., “A local solution with global characteristics for the joint toque optimization of a redundant manipulator,” J. Rob. Syst. 6 (5), 631654 (1989).
4.Lee, Heow Pueh, “Motions with minimal joint torques for redundant manipulators,” J. Mech. Des. 115 (3), 599603 (1993).
5.Yoshikawa, T., “Manipulability of robot mechanisms,” Int. J. Robot. Res. 4 (2), 39 (1985).
6.Bowling, A. and Khatib, O., “The dynamic capability equations: a new tool for analyzing robotic manipulator performance,” IEEE Trans. Robot. 21 (1), 115123 (2005).
7.Hollerbach, J. M. and Suh, K. C., “Redundancy resolution of manipulators through torque optimization,” IEEE J. Robot. Autom. 3 (4), 308315 (1987).
8.Sekhavat, S., Svestka, P., Laumond, J. P. and Overmars, M. H., “Multilevel path Planing for nonholonomic robots using semiholonomic subsystems,” Int. J. Robot. Res. 17 (8), 840857 (1998).
9.Laumond, J. P., Jacobs, P. E., Taïx, M., and Murray, R. M., “A motion planner for nonholonomic mobile robots,” IEEE Trans. Robot. Autom. 10, 577593 (1994).
10.Carriker, W. F., Khosla, P. K. and Krogh, B. H., “Path planning for mobile manipulators for multiple task exceution,” IEEE Trans. Robot. 7 (3), 403408 (1991).
11.Pin, F. G., Culioli, J. C. and Reister, D. B., “Using minimax approaches to plan optimal task commutation configurations for combined mobile platform-manipulator system,” IEEE Trans. Robot. Autom. 10 (1), 4454 (1994).
12.Lee, J. K., Kim, S. H. and Cho, H. S., “Motion planing for a mobile manipulator to execute a multiple point-to-point task,” Proceedings IEEE/RSJ International Conference Intelligent Robots and Systems (1996) pp. 737–742.
13.Seraji, H., “A unified approach to motion control of mobile manipulators,” Int. J. Robot. Res. 17 (2), 107118 (1998).
14.Perrier, C., Dauchez, P. and Pierrot, F., “A global approach for motion generation of non-holonomic mobile manipulators,” IEEE Proceedings IEEE International Conference on Robotics and Automation (1998) pp. 2971–2976.
15.Foulon, G., Fourquet, J. Y. and Reanud, M.. “Planning point to point paths for nonholomic mobile manipulators,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (1998) pp. 374–379.
16.Tanner, H. G. and Kyriakopoulos, K. J., “Nonholonomic motion planning for mobile manipulators,” Proceedings of IEEE International Conference on Robotics and Automation (2000) pp. 1233–1238.
17.Desai, J. P. and Kumar, V. “Nonholonomic motion planning for mobile manipulators,” Proceedings of IEEE International Conference Robotics and Automation (1997) pp. 3409–3414.
18.Kurisu, M. and Yoshikawa, T., “Trajectory planning and dynamic control of a mobile manipulators,” Trans Jap. Soc. Mech. Eng. 62 (596-C), 242248 (1996).
19.Mohri, A., Furuno, S. and Yamamoto, M., “Trajectory planning of mobile manipulator with end-effectors's Specified path,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2001) pp. 2264–2269.
20.Padois, V., Fourquet, J. Y. and Chiron, P., “Kinematic and dynamic model-based control of wheeled mobile manipulators: A unified framework for reactive approaches,” Robotica 25 (2), 157173 (2007).
21.Liegeois, A., “Automatic supervisory control of the configuration and behavior of multibody mechanisms,” IEEE Trans. Syst. Man Cybern. SMC-7, 868–871 (1977).
22.Puga, J. P. and Chiang, L., “Desarrollo de un manipulador móvil redundante. Aspectos de diseño mecánico, control automático y configuración óptima,” XII Congreso Chileno de Ingeniería Mecánica, Curicó, Chile (Nov. 2006).
23.Nakamura, Y., Advanced Robotics: Redundancy and Optimization (Addison-Wesley Publishing Company, 1991).Boston, USA.
24.Strang, G., Introduction to Linear Algebra 3rd ed. (Wellesley-Cambridge Press, Massachussetts 1998).
25.Albert, A. E., Regression and the Moore–Penrose pseudoinverse (New York, Academic Press, 1972).
26.Whitney, D. E., “Resolved motion rate control of manipulators and human prostheses,” IEEE Trans. Man-Mac. Syst. MMS-10, 47–53 (1969).
27.Whitney, D. E., “The mathematics of coordinated control of prosthetic arms and manipulators”, ASME J. Dyn. Syst. Meas. Control pp. 303–309 (1972).
28.Chiang, L., Análisis Dinámico de Sistemas Mecánicos (Ediciones AlfaOmega, Ciudad de México, México, 1999).
29.White, G. D., Bhatt, R. M. and Krovi, V. N., “Dynamic redundancy resolution in a nonholonomic wheeled mobile manipulator,” Robotica 25 (2), 147156 (2007).
30.Sekhavat, S., Svestka, P., Laumond, J. P. and Overmars, M. H., “Probabilistic path planning for tractor trailer robots,” Technical Report 96007, LAAS/CNRS (Toulouse, France, 1996).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *