Robust path planning for mobile robot based on fractional attractive force

In path planning, potential fields introduce force constraints to ensure curvature continuity of trajectories and thus to facilitate path-tracking design. In previous works, a path planning design by fractional (or generalized) repulsive potential has been developed to avoid fixed obstacles: danger level of each obstacle was characterized by the fractional order of differentiation, and a fractional road was determined by taking into account danger of each obstacle. If the obstacles are dynamic, the method was extended to obtain trajectories by considering repulsive and attractive potentials taking into account position and velocity of the robot with respect to obstacles. Then, a new attractive force based on fractional potential was developed. The advantage of the generalized normalized force is the possibility to control its variation. The curve is continuously varying and depends only on one parameter, the non integer order of the generalized attractive potential. But, in case of robot parameter variations, these two previous attractive forces do not allow to obtain robust path planning. In this paper, a new fractional attractive force for robust path planning of mobile robot is defined. This method allows to obtain robust path planning despite robot mass variations. The robustness of the obtained trajectories is studied. A comparison between a classical method and the proposed approach is presented.

[1]  Shuzhi Sam Ge,et al.  Dynamic Motion Planning for Mobile Robots Using Potential Field Method , 2002, Auton. Robots.

[2]  Petros A. Ioannou,et al.  New Potential Functions for Mobile Robot Path Planning , 2000 .

[3]  JongSuk Choi,et al.  Sensor-Based Motion Planning for Mobile Robots , 2002 .

[4]  José António Tenreiro Machado,et al.  Fractional order electromagnetics , 2006, Signal Process..

[5]  Vijay Kumar,et al.  A potential field based approach to multi-robot manipulation , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[6]  Andrey Ronzhin,et al.  Control of a Mobile Robot Using Spoken Commands , 2004 .

[7]  I. Podlubny.  Fractional differential equations , 1998 .

[8]  A. Poty,et al.  Dynamic path planning by fractional potential , 2004, Second IEEE International Conference on Computational Cybernetics, 2004. ICCC 2004..

[9]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[10]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[11]  Mohamed Naceur Abdelkrim,et al.  Attractive force based on generalized potential for mobile robot path planning in dynamic environment. , 2009 .

[12]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[13]  O. Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[14]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[15]  Hyungpil Moon,et al.  Generation of quadratic potential force fields from flow fields for distributed manipulation , 2006, IEEE Transactions on Robotics.

[16]  A. Oustaloup.  La dérivation non entière , 1995 .

[17]  A. Oustaloup,et al.  Robust path planning for dynamic environment based on fractional attractive force , 2009, 2009 6th International Multi-Conference on Systems, Signals and Devices.

[18]  Andreas Petersson,et al.  Optimization of waypoint-guided potential field navigation using evolutionary algorithms , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[19]  Steffi Beckhaus,et al.  Guided Exploration with Dynamic Potential Fields: the Cubical Path System , 2001, Comput. Graph. Forum.

[20]  Alexandre Poty.  Planification de trajectoire dans un environnement dynamique et génération de mouvement d'ordre non entier , 2006 .

[21]  Mohamed Naceur Abdelkrim,et al.  Attractive Force Based on Fractional Potential in Dynamic Motion Planning for Mobile Robot , 2007 .

[22]  Jesus Savage,et al.  Creation of Virtual Environments Using Photographs with a Mobile Robot. , 2002 .

[23]  A. Poty,et al.  Dynamic path planning for mobile robots using fractional potential field , 2004, First International Symposium on Control, Communications and Signal Processing, 2004..

[24]  Hyungpil Moon,et al.  Prediction of Equilibria of Lifted Logarithmic Radial Potential Fields , 2004, Int. J. Robotics Res..

[25]  Meng Joo Er,et al.  Control of a mobile robot using generalized dynamic fuzzy neural networks , 2004, Microprocess. Microsystems.

[26]  N. Engheta.  On fractional calculus and fractional multipoles in electromagnetism , 1996 .