Abstract
How to plan the optimal trajectory of nonholonomic mobile manipulators in dynamic environments is a significant and challenging task, especially in the system with a moving target. This paper presents trajectory optimization of a nonholonomic mobile manipulator in dynamic environment pursuing a moving target. Full nonlinear dynamic equations of the system considering the nonholonomic constraints of wheels are presented. Then, dynamic motion planning of the system is formulated as an optimal control problem considering moving obstacle avoidance conditions. Accordingly, a new formulation of dynamic potential function was proposed based on the dynamic distance between colliding objects. In addition, an appropriate boundary value for a moving target was defined, and the resulted boundary value problem was solved to optimize the trajectory of the system. To solve the problem, an indirect solution of optimal control was applied which leads to transform the optimal control problem into a set of coupled differential equations. To demonstrate the efficiency and applicability of the method a number of simulations and experiments was performed for a spatial nonholonomic mobile manipulator.
Similar content being viewed by others
References
Sun Ch. H., Wang Y.H., Chang Ch. Ch.: Fuzzy model-based guaranteed cost control for two-wheeled mobile robots. Int. J. Innov. Comput. I 8, 3015–3028 (2012)
Wu W., Chen H., Woo P.Y.: Time optimal path planning for a wheeled mobile robot. J. Robot. Syst. 17, 585–591 (2000)
Gariblu H., Korayem M.H.: Trajectory optimization of flexible mobile manipulator. Robotica 24, 333–335 (2006)
Haddad, M., Chettibi, T., Hanchi, S., Lehtihet, H.E.: Optimal motion planner of mobile manipulators in generalized point-to-point task. In: 9th IEEE International Workshop on Advanced Motion Control, pp. 300–306 (2006)
Gracia L., Tornero J.: Optimal trajectory planning for wheeled mobile robots based on kinematics singularity. J. Intell. Robot. Syst. 53, 145–168 (2008)
Korayem M.H., Rahimi H.N., Nikoobin A.: Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joint. Appl. Math. Model. 36, 29–3244 (2012)
Yan Zh., Sun Y., Wang W.: Mobile robot hybrid path planning in an obstacle-cluttered environment based on steering control and improved distance propagating. Int. J. Innov. Comput. I 8, 4095–4109 (2012)
Bolandi H., Ehyaei A.F.: Trajectory planning of two cooperative mobile manipulators under closed-chain and differential constraints. Int. J. Innov. Comput. I 8, 1077–1102 (2012)
Korayem M.H., Nazemizadeh M., Rahimi H.N.: Smooth jerk-bounded optimal path planning of tricycle wheeled mobile manipulators in the presence of environmental obstacles. Int. J. Adv. Robot. Syst. 9, 1–13 (2012)
Korayem, M.H., Nazemizadeh, M., Binabaji, H., Azimirad, V.: Optimal motion planning of non-holonomic mobile robots in presence of multi obstacles. In: International Conference on Emerging Trends in Robotics and Communication Technologies, pp. 269–272 (2010)
Khatib O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Rob. Res. 5, 90–98 (1996)
Massari, M., Giardini, G., Bernelli-Zazzera, F.: Autonomous navigation system for planetary exploration rover based on artificial potential fields. In: Proceedings of Conference of Dynamics and Control of Structures in Space (2004)
Hamner B., Singh S., Roth S., Takahashi T.: An efficient system for combined route traversal and collision avoidance. Auton. Robots 24, 365–385 (2008)
Zhang, Q., Chen, D., Chen, T.: An obstacle avoidance method of soccer robot based on evolutionary artificial potential field. Energy Procedia 16, Part C, pp. 1792–1798 (2012)
Koren, Y., Borenstein, J.: Potential field methods and their inherent limitations for mobile robot navigation. In: Proceedingsof International Conference on Robotics and Automation, pp. 1398–1404 (1999)
Papadopoulos E., Poulakakis I., Papadimitriou I.: On path planning and obstacle avoidance for non-holonomic mobile manipulators: a polynomial approach. Int. J. Robot. Res. 21, 367–383 (2002)
Yamashita A., Arai T., Ota Asama H.J.: Motion planning of multiple mobile robots for cooperative manipulation and transportation. IEEE Trans. Robot. Autom. 19, 223–237 (2003)
Qu Z., Wang J., Plaisted C.E.: A new analytical solution to mobile robot trajectory generation in the presence of moving obstacles. IEEE Trans. Robot. 20, 978–993 (2003)
Fink, J., Hsieh, M.A., Kumar, V.: Multi-robot manipulation via caging in environments with obstacles. In: IEEE International Conference on Robotics, pp. 1471–1476 (2008)
Zhang, B., Chen, W., Fei, M.: An optimized method for path planning based on artificial potential field. In: Proceedings of Conference Intelligent System Design Application pp. 35-39 (2006)
Yamamoto Y., Yun X.: Coordinating locomotion and manipulation of a mobile manipulator. Trans. Auto. Contr. 39, 1326–1332 (1994)
Yamamoto Y., Yun X.: Effect of the dynamic interaction on coordinated control of mobile manipulators. IEEE Trans. Robot. Autom. 12, 816–824 (1996)
Kirk D.E.: Optimal Control Theory: an Introduction. Prentice- Hall Inc., New Jersey (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Korayem, M.H., Nazemizadeh, M. & Rahimi, H.N. Trajectory optimization of nonholonomic mobile manipulators departing to a moving target amidst moving obstacles. Acta Mech 224, 995–1008 (2013). https://doi.org/10.1007/s00707-012-0799-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-012-0799-5