Rapidly exploring random graphs: motion planning of multiple mobile robots

Rahul Kala
2013 Advanced Robotics  
Rapidly Exploring Random Trees (RRT) and Probabilistic Roadmaps (PRM) are sampling based techniques being extensively used for robot path planning. In this paper the tree structure of the RRT is generalized to a graph structure which enables a greater exploration. Exploration takes place simultaneously from multiple points in the map, all explorations fusing at multiple points producing well-connected graph architecture. Initially, in a typical RRT manner, the search algorithm attempts to reach
more » ... the goal by expansions, and thereafter furtherer areas are explored. With some additional computation cost, as compared to RRT with a single robot, the results can be significantly improved. The so formed graph is similar to roadmap produced by PRM. However as compared to PRM, the proposed algorithm has a more judicious search strategy and is adaptable to the number of nodes as a parameter. Experimental results are shown with multiple robots planned using prioritization scheme. Results show the betterment of the proposed algorithm as compared to RRT and PRM techniques. Advanced Robotics (RSJ) or decentralized [1]. Centralized planning techniques construct a complex configuration space consisting of all the robots and attempt to generate an optimal plan. Decentralized approaches plan each robot separately in their own configuration space. A coordination technique may be used to avoid collisions between the robots. Prioritization [2-3] is a commonly used coordination technique. Due to the nature of the problem, sampling based techniques are increasingly being used where some samples are taken to represent the entire configuration space. Sampling may hence lead to loss of completeness and optimality with the advantage of computational time. The two frequently used sampling based techniques are Rapidly-exploring Random Trees (RRT) [4-5] and Probabilistic Road Maps (PRM) [6-7]. In RRT [4-5] the search begins with the source as the root of a search tree. At every iteration the algorithm generates a random point in the configuration space, searches for the closest point in the tree and extends this point to the random sample by a magnitude of stepsize. The algorithm stops when the exploration results in reaching the goal. Algorithm may be made biased to explore towards the goal. RRT-Connect algorithm checks if travelling straight in the line of expanded point reaches the goal, in which case the algorithm terminates. Bi-directional variant of RRT expands two trees, one each from the source and goal, and terminates when the two trees meet. RRTs are computationally efficient, but sub-optimal. Sub-optimality here may be global or local. Global optimality indicates the strategy to avoid obstacles (whether to go from left of an obstacle, or right of an obstacle, or in-between obstacles) while local optimality indicates distances to maintain from obstacles. RRT paths may be passed through local optimization which is computationally expensive. In a multi-robot scenario, each robot may have its own RRT instance which makes the search process time consuming. PRM [6-7] is another widely used technique. In this technique a number of random points are sampled out of the configuration space and a local planning algorithm is used to determine which states are connected to which other states, producing a graph structure called roadmap. In Lazy PRM [8] collision checking is performed using a coarser to finer strategy which is more efficient. The construction of the roadmap is a computationally expensive step. Samples are taken from the entire configuration space, which may consist of a large number of areas which are visibly unnecessary for any robot to go from its source to its goal. This is especially true when a small number of robots navigate in sections of dynamic maps. Unlike RRT, PRM is less likely to miss being near the global optima. The key contributions of the work are (a) A graph variant of RRT is proposed which is a completely new domain of thought. (b) The proposed algorithm can have multi-directional multi-strategized exploration with multiple initiation points. (c) In terms of path length, the proposed algorithm is better in terms of both global and local optimality as compared to RRT and its variants. (d) While the proposed algorithm is computationally more expensive as compared to RRT (and variants) with every robot's path computed independently by an independent processor, the total processing required is smaller in case of the proposed algorithm. (c) The proposed algorithm is better than PRM and similar
doi:10.1080/01691864.2013.805472 fatcat:ir5gea6vcbhubgmalggxv5fxpy