Robotic path planning in static environment using hierarchical multi-neuron heuristic search and probability based fitness

Abstract

Path Planning is a classical problem in the field of robotics. The problem is to find a path of the robot given the various obstacles. The problem has attracted the attention of numerous researchers due to the associated complexities, uncertainties and real time nature. In this paper we propose a new algorithm for solving the problem of path planning in a static environment. The algorithm makes use of an algorithm developed earlier by the authors called Multi-Neuron Heuristic Search (MNHS). This algorithm is a modified A^⁎ algorithm that performs better than normal A^⁎ when heuristics are prone to sharp changes. This algorithm has been implemented in a hierarchical manner, where each generation of the algorithm gives a more detailed path that has a higher reaching probability. The map used for this purpose is based on a probabilistic approach where we measure the probability of collision with obstacle while traveling inside the cell. As we decompose the cells, the cell size reduces and the probability starts to touch 0 or 1 depending upon the presence or absence of obstacles in the cell. In this approach, it is not compulsory to run the entire algorithm. We may rather break after a certain degree of certainty has been achieved. We tested the algorithm in numerous situations with varying degrees of complexities. The algorithm was able to give an optimal path in all the situations given. The standard A^⁎ algorithm failed to give results within time in most of the situations presented.

Introduction

Robotics is a highly multi-disciplinary field that incorporates inputs from wireless systems, networks, cognition, image processing, AI, electrical, electronics and other related fields [21]. The highly multi-disciplinary nature makes it an exciting playground for people from various fields to collaborate and contribute. The whole problem of robotics include taking input from sensors, making of robotic world map, path planning, robot control [20], multi-robot coordination, high-end planning, etc. [7]. The application of AI and Soft Computing techniques in the recent years deserves a special mention.

Path Planning [18] is a specific problem in case of robots where we are given a map of the world. Through this we can come to know about the various paths and obstacles. The problem is to compute a path for the robot that can make it reach a specific goal starting from a specific position. The solution of this problem is a path using which the robot can reach its goal without colliding with any of the obstacles. The problem is usually studied in two separate heads. These are path planning in static environment and path planning in dynamic environment. In static environment the obstacles are static and do not change their position with respect to time. On the other hand, in dynamic path planning the position of obstacles may change with time. A path planning algorithm must ensure that if a solution is possible, it is found and returned. This is called as completeness of the algorithm [2]. It must also ensure that the algorithm gives its result within the specified amount of time [16].

The problem of path planning takes its input a map. A robotic map is a representation of the world of the robot [23]. The map depicts the traversable path, obstacles, surface and other information. Various types of paths may be drawn depending upon the problem and solution requirements. Some of the commonly used maps include topological maps [34], voronoi maps [4], [33], hybrid maps [4], etc. The map is built using the results of the various sensors along with the output of the recognition systems [7].

Path planning usually gives its output to the robotic control. This consists of a robotic controller, which is supposed to move the robot in the desired path. Various robot controllers have been designed. Some of them are built using the Adaptive Neuro-Fuzzy architecture [24].

The problem of path planning has been a very active area of research especially during the last decade. The problem has seen numerous methods and means that solve the prevalent research issues to varying extents. A class of algorithms uses the potential method approach to navigate a robot [28]. In this approach, whenever the robot collides with a robot, a large potential is given. The potential increases if robot moves too close to the obstacle. The aim is the minimization of the potential.

Pozna et al. [28] solved the problem using a potential field approach for obstacle avoidance. Other potential field methods include [35]. Hui and Pratihar [11] gave a comparison between the Potential Field and the Soft Computing solutions. Various statistical approaches have also been used. This includes the work of Jolly et al. [14] who used Bezier Curve for path planning. Goel et al. [8] solved the problem for dynamic obstacles using an adaptive strategy. Quad tree [17], mesh [12], pyramid [36] are representations that have been tried for better performance. Another good amount of work exists using the Soft Computing approaches especially Genetic Algorithms [1], [15], [37], [22], A^⁎ Algorithms [32] and artificial neural networks (ANN) [16]. Shibata et al. [30] used Fuzzy Logic for fitness evaluation of the paths generated. Various other approaches [6], [26] have also been proposed.

Zhu and Latombe [38] used the concepts of cell decomposition and hierarchal planning. Here they represented the cells in a similar concept of grayness denoting the obstacles. Urdylis et al. [36] used a multi-level probability based pyramid for solving the path planning problem. Hierarchical Planning can also be found in the work of Lai et al. [19] and Shibata et al. [30].

Along with the problem of path planning, the researchers have also studied the degrees of freedom and dimensionality as they have a deep impact on the problem. Jan et al. [13] presented his work for solving in 3 degrees of freedom.

Chen and Chiang [5] made an adaptive intelligent system and implemented using a Neuro-Fuzzy Controller and Performance Evaluator. Their system explored new actions using GA and generated new rules. In the field of multi-robot systems, Carpin and Pagello [3] used an approximation algorithm to solve the problem of robotic coordination using the space–time data structures. They showed a compromise between speed and quality. Pradhan et al. [29] solved a similar problem for unknown environments using Fuzzy Logic. Peasgood et al. [27] solved the multi-robot planning problem ensuring completeness using Spanning Trees. Hazon and Kaminka [9] analyzed the completeness of the multi-robot coverage problem. O' Hara et al. [25] gave the idea of using embedded networks as sensors for solving the problem.

It was earlier shown by the authors that A^⁎ generates the best results for the problem of path planning [32]. However, the algorithm was found to be computationally very expensive. It was also earlier shown by the authors that A^⁎ algorithm does not perform well in problems like maze solving [31]. The motivation behind this work is to adapt A^⁎ algorithm in such a way that it becomes more scalable and performs well in finite time. We do this with the application of probability based map representation [17].

In this paper we have proposed the use of Multi-Neuron Heuristic Search (MNHS) for the purpose of solving the path planning problem [31]. This was an algorithm proposed earlier by the authors as an improvement over the standard A^⁎ algorithm. This algorithm was found to perform better in situations where the heuristic function may fluctuate very quickly between adjacent nodes in the graph. The MNHS improves performance in situations where the heuristic function behavior is uncertain by expanding multiple heuristic nodes simultaneously, in place of the node with the best heuristic as was the case with conventional A^⁎ algorithm.

The map in this paper has been modeled in a way similar to the quad tree approach as used by [17]. In this model the graph was divided into a set of nodes of varying sizes. All nodes are arranged in layered manner from top to bottom, each with different size of nodes, and different level of uncertainty. Here, at the top, the nodes have high degree of uncertainty regarding the presence or absence of the obstacles. This uncertainty is measured in terms of ‘greyness’ of the cell. A completely white cell denotes the absence of any kind of obstacle from the entire region. On the other hand full black color denotes the conformation of presence of obstacles in the cell. The grey denotes the intermediate values with the intensity denoting the probability of the cell being free from obstacles.

In practical problems, the map may be too large for the standard MNHS algorithm to perform. This problem is solved by making a hierarchical solution to the problem. The first little iterations are supposed to find the initial vague solutions with lesser details. The probability of collision with obstacles is undetermined to a large extent in the first little iteration. The size of the cells is quite large. Towards the later iterations of the algorithm the cells lying on the possibly optimal path are decomposed. As a result path keeps adding details. Also the presence or absence of the obstacles keeps getting clear.

This paper is organized as follows. Section 2 introduces the MNHS algorithm. In Section 3 we introduce the general outline of the algorithm. The hierarchical approach is introduced in Section 4. The concept of probability based fitness is discussed in Section 5. In Section 6 we discuss the simulation model and the results. Section 7 gives the comparative analysis and Section 8 presents the results.