A Random Sampling Scheme for Path Planning

Abstract

Several randomized path planners have been proposed dur ing the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empir ically observed success. In this article, we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot 's configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilis tically complete: if a path exists, they will find one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characteriz ing the "goodness" of the robot's free space, we show that the

Sampling and node adding in probabilistic roadmap planners

“…See the books of Latombe [25] and LaValle [27] for an extensive overview of the situation and for example the proceedings of the yearly IEEE International Conference on Robotics and Automation (ICRA) or the Workshop on Foundations of Robotics (WAFR) for many recent results. A popular motion planning technique is the Probabilistic Roadmap Method (PRM), developed independently at different sites [3,4,19,20,31,36]. It turns out to be very efficient, easy to implement, and applicable for many different types of motion planning problems (see e.g.…”

Combinatorial Motion Planning

“…Nevertheless, it is worthwhile to study the clever heuristics involved in this earlier method because they illustrate many interesting issues, and the method was very influential in the development of other sampling-based planning algorithms. 13 The most complicated part of the algorithm is the definition of a potential function, which can be considered as a pseudometric that tries to estimate the distance from any configuration to the goal. In most formulations, there is an attractive term, which is a metric on C that yields the distance to the goal, and a repulsive term, which penalizes configurations that come too close to obstacles.…”

“…Intuitively, ǫ(C f ree ) represents the small fraction of C f ree that is visible from any point. In terms of ǫ and the number of vertices in G, bounds can be established that yield the probability that a solution will be found [13]. The main difficulties are that the ǫ-goodness concept is very conservative (it uses worst-case analysis over all configurations), and ǫ-goodness is defined in terms of the structure of C f ree , which cannot be computed efficiently.…”

“…The basic idea from one of them [13] is briefly presented here. Consider problems such as the one in Figure 5.27, in which the connect method will mostly likely fail in the thin tube, even though a connection exists.…”

Reachability-based analysis for Probabilistic Roadmap planners

“…Although this planner was much faster than previous approaches, it could get stuck at a local minimum of the potential function. One year later, different researchers independently devised the Probabilistic Roadmap Method (PRM), which was successfully able to deal with many motion planning problems [6][7][8]. This success is due to its wide applicability and good performance: if a solution to a problem is easy, then it seems that the PRM can solve it very fast.…”