Classic and Heuristic Approaches in Robot Motion Planning – A Chronological Review Ellips Masehian, and Davoud Sedighizadeh Abstract—This paper reviews the major contributions to the Motion Planning (MP) field throughout a 35-year period, from classic approaches to heuristic algorithms. Due to the NP-Hardness of the MP problem, heuristic methods have outperformed the classic approaches and have gained wide popularity. After surveying around 1400 papers in the field, the amount of existing works for each method is identified and classified. Especially, the history and applications of numerous heuristic methods in MP is investigated. The paper concludes with comparative tables and graphs demonstrating the frequency of each MP method’s application, and so can be used as a guideline for MP researchers. Keywords—Robot motion planning, Heuristic algorithms. I. INTRODUCTION considerable amount of research exists in the field of Robot Motion Planning (RMP). The discipline launched at mid 60’s, but it was not until Lozano-Pérez’s revolutionary contribution [42] on spatial planning that MP drew most researchers’ attention. It is proved that the path planning problem is NP-complete [7]. The current developed classic methods are variations of a few general approaches: Roadmap, Cell Decomposition, Potential fields, and mathematical programming. Most classes of MP problems can be solved using these approaches. These approaches are not necessarily mutually exclusive, and a combination of them is often used in developing a motion planner [46]. In the roadmap approach, the free C-space, i.e., the set of feasible motions, is retracted, reduced to, or mapped onto a network of one-dimensional lines. This approach is also called the Retraction, Skeleton, or Highway approach. The search for a solution is limited to the network, and MP becomes a graph-searching problem. The well-known roadmaps are Visibility graph, Voronoi diagram, Silhouette, and the Subgoal Network. The Visibility Graph (VG) is the collection of lines in the free space that connects a feature of an object to that of another. In its principal form, these features are vertices of polygonal obstacles, and there are O(n 2 ) edges in the visibility graph, which can be constructed in O(n 2 ) time and space in 2D, where n is the number of features. The idea of using Visibility graph for RMP was used in [4]. The Voronoi diagram (VD) of a collection of geometric objects is a partition of space into cells, each of which consists of the points closer to one particular object Authors are with Faculty of Engineering, Tarbiat Modares University, Tehran, Iran. than any others. The idea of using Voronoi diagram for RMP was used in [8]. The other approach is Silhouette. In [6, 7], a general method of constructing a roadmap in arbitrary dimensions is presented. It projects an object in a higher dimensional space to a lower dimensional space and then traces out the boundary curves of the projection, which is called silhouette. The Subgoal Network (SN) method does not build an explicit representation of the configuration obstacles. Instead, the list of reachable configurations from the start configuration is maintained. When the goal configuration is reachable, the MP is solved. The reachability of one configuration from another is decided by a rather simple local MP algorithm called local operator, such as that moving the robot in a straight line between the configurations [17]. In Cell Decomposition (CD) Algorithm, the free C-space is decomposed into a set of simple cells, and the adjacency relationships among the cells are computed. A collision-free path between the start and the goal configuration of the robot is found by first identifying the two cells containing the start and the goal and then connecting them with a sequence of connected cells. The idea of using Cell decomposition for RMP was used in [34]. The Potential Fields (PF) concept was first introduced by Oussama Khatib [36]. A robot in Potential Fields method is treated as a point represented in configuration space as a particle under the influence of an artificial potential field U whose local variations reflect the ‘structure’ of the free space. The potential function can be defined over free space as the sum of an Attractive potential pulling the robot toward the goal configuration, and a Repulsive potential pushing the robot away from the obstacles [40]. The Mathematical programming approach represents the requirement of obstacle avoidance with a set of inequalities on the configuration parameters. MP is formulated then as a mathematical optimization problem that finds a curve between the start and goal configurations minimizing a certain scalar quantity. A comprehensive review on Classic MP methods can be found in [29]. II. HEURISTIC METHODS The abovementioned classic approaches suffer from many drawbacks, such as high time complexity in high dimensions, and trapping in local minima, which makes them inefficient in practice. In order to improve the efficiency of Classic methods, Probabilistic algorithms have been developed, including Probabilistic Roadmaps (PRM) and Rapidly- A World Academy of Science, Engineering and Technology International Journal of Mechanical, Industrial Science and Engineering Vol:1 No:5, 2007 255 International Science Index Vol:1, No:5, 2007 waset.org/Publication/10300