Motion planning in order to optimize the length and clearance applying a Hopfield neural network Mehdi Ghatee a,b, * , Ali Mohades a,c a Department of Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15875-4413, Iran b Laboratory of Network and Optimization Research Center (NORC), Tehran, Iran c Laboratory of Algorithms and Computational Geometry Group, Tehran, Iran article info Keywords: Multi-objective Online routing Neural network Parallel implementation abstract This paper deals with motion planning in plane for a mobile robot with two freedom degrees through some polygonal unmoved obstacles. Applying Minkowski sum, we can represent the robot as a point. Then, by using traditional approaches such as visibility graphs, simple and generalized Voronoi diagrams, decomposition methods, etc, it is possible to provide a graph covering obstacles, say roadmap. In order to find a real-time collision-free robot motion planning between two arbitrary source and target configura- tions through the roadmap, an adoptive Hopfield neural network is considered. Maximizing the clearance of path together with minimizing the length of path are pursued in a bi-objective framework. For treating with multiple objectives TOPSIS method, as a kind of goal programming techniques, is provided to find the efficient solutions. Because of capability of parallel computation through hardware implementation of neural networks, the presented approach is a reasonable technique in mobile robot navigation and traveler guidance systems. The advantages of the proposed system are confirmed by simulation experi- ments. This approach can be directly extended in unknown environment including time-varying conditions. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Over the last decade there has been considerable progress in motion planning techniques and their application (Ahuactzin & Gupta, 1998; Chou, Chou, & Chen, 2008). Classic path planning ap- proaches including roadmap, cell decomposition and potential field use global methods to search the possible paths in the work- space. These models deal with static environment only and are computationally complicated. This paper considers a robot with two freedom degrees in the plane among polygonal obstacles, i.e., the robot can only transformed not rotate in the plane. Motion planning consist of a natural looking collision-free path for a robot. This means the path should be short as well as it should have a guaranteed amount of clearance, that is any point on the path is possibly far from the closest obstacle. In Wein, van den Berg, and Halperin (2007) some other objectives such as smoothness and not containing any sharp turns, were also introduced. Usually there is some confliction between these objective functions, for instance it is possible to considerably shorten the path by taking a shortcut through a narrow passage. The motion planning problem can be efficiently solved by com- puting a complete representation of the free configuration space. This approach was simplified, by decomposing the configuration space into pseudo-trapezoidal cells and constructing a roadmap of the free cells (Wein et al., 2007). Another popular approach is to use Probabilistic Roadmaps (Kavraki, Svestka, Latombe, & Over- mars, 1996). But the output paths in this case are also piecewise linear and may be far from the shortest possible paths. As the infra- structure of motion route design, some methods can be pursued in order to create a graph considering the place of obstacles (Berg, van Kreveld, Overmars, & Schwarzkopf, 2000; LaValle, 2006; Plaku, Bekris, Chen, Ladd, & Kavraki, 2005). After this preprocessing, a query phase should be done to connect the source and target con- figurations through the edges of the provided graph. In this phase a single objective or multiple objectives may be considered (Bu & Cameron, 2002; Min, Zhu, & Zheng, 2005). Most of the techniques implemented for this aim, generate locally optimal paths not nec- essarily with online response. To provide online shortest path in Sadati and Taheri (2002) a neural network architecture is devel- oped. Some neural network models were proposed for realtime ro- bot motion planning through learning and obtaining dynamic navigation of a mobile robot with obstacle avoidance, however, 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.06.040 * Corresponding author. Address: Department of Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15875-4413, Iran. Tel.: +98 21 64542542; fax: +98 21 66497930. E-mail addresses: ghatee@aut.ac.ir (M. Ghatee), mohades@aut.ca.ir (A. Mo- hades). Expert Systems with Applications 36 (2009) 4688–4695 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa