Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

Abstract

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange’s principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

Keywords

mobile robot / trajectory planning / nonlinear dynamic / optimal control

References

[1] Ma Q Z, Lei X J. Dynamic path planning of mobile robots based on ABC algorithm. Artificial Intelligence and Computational Intelligence, 2010, 6320: 267–274

[2] Zhou T, Fan X P, Yang Sh Y, Qu Zh H. Path planning for mobile robots based on hybrid architecture platform. Computer and Information Science, 2010, 3(3): 117–121

[3] Castillo O, Trujillo L, Melin P. Multiple objective genetic algorithms for path-planning optimization in autonomous mobile robots. Soft Computing, 2007, 11(3): 269–279

[4] Yamaguchi H, Kanbo Y, Kawakami A. Formation vector control of nonholonomic mobile robot groups and its experimental verification. International Journal of Vehicle Autonomous Systems, 2011, 9(1,2): 26–45

[5] Dierks T, Brenner B, Jagannathan S. Discrete-time optimal control of nonholonomic mobile robot formations using linearly parameterized neural networks. International Journal of Robotics and Automation, 2011, 26(1)

[6] Park B S, Yoo S J, Park J B, Choi Y H. A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots. IEEE Transactions on Control Systems Technology, 2010, 18(5): 1199–1206

[7] Campion G, Bastin G, Dandrea-Novel B. Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE Transactions on Robotics and Automation, 1996, 12(1): 47–62

[8] Morin P, Samson C. Handbook of Robotics. New York: Springer, 2008

[9] Dixon W E, Dawson D M, Zergeroglu E, Zhang F. Robust tracking and regulation control for mobile robots. International Journal of Robust and Nonlinear Control, 2000, 10(4): 199–216

[10] Kanayama Y, Kimura Y, Miyazaki F, Noguchi T. A stable tracking control method for an autonomous mobile robot. In: Proceedings of IEEE International Conference on Robotics and Automation, 1990, 1: 384–389

[11] de Wit C C, Sordalen O J. Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Transactions on Automatic Control, 1992, 37(11): 1791–1797

[12] Jiang Zh P, Nijmeijer H. Tracking control of mobile robots: a case study in backstepping. Automatica, 1997, 33(7): 1393–1399

[13] Jiang Zh P, Lefeber E, Nijmeijer H. Saturated stabilization and tracking of a nonholonomic mobile robot. Systems & Control Letters, 2001, 42(5): 327–332

[14] Wu Y Q, Wang B, Zong G D. Finite-time tracking controller design for nonholonomic systems with extended chained form. IEEE Transactions on Circuits and Systems II: Express Briefs, 2005, 52(11): 798–802

[15] Wu J B, Xu G H, Yin Zh P. Robust adaptive control for a nonholonomic mobile robot with unknown parameters. Journal of Control Theory and Applications, 2009, 7(2): 212–218

[16] Wu W G, Chen H T, Woo P Y. Time optimal path planning for a wheeled mobile robot. Journal of Robotic Systems, 2000, 17(11): 585–591

[17] Korayem M H, Ghariblu H, Basu A. Dynamic load-carrying capacity of mobile-base flexible joint manipulators. The International Journal of Advanced Manufacturing Technology, 2005, 25(1-2): 62–70

[18] Dos Santos R R, Steffen V, Saramago S F P. Robot path planning in a constrained workspace by using optimal control techniques. Multibody System Dynamics, 2008, 19(1-2): 159–177

[19] Korayem M H, Rahimi H N, Nikoobin A. Path planning of mobile elastic robotic arms by indirect approach of optimal control. International Journal of Advanced Robotic Systems, 2011, 8(1): 10–20

[20] Korayem M H, Rahimi H N, Nikoobin A. Dynamic analysis, simulation and trajectory planning of mechanical mobile manipulators with flexible links and joints. Applied Mathematical Modelling, 2012

[21] Yamamoto Y, Yun X. Coordinating locomotion and manipulation of a mobile manipulator. IEEE Transactions on Automatic Control, 1994, 39(6): 1326–1332

[22] Kirk D E. Optimal Control Theory: An Introduction. New Jersey: Prentice-Hall Inc., Upper Saddle River, 1970

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg