Quantitatively Evaluating Performance of RRTs

Rapidly-Exploring Random Trees (RRTs) [LaValle98] have been the focus of a significant amount of research recently. This simple algorithm provides an efficient randomized technique to tackle the difficult problem of motion planning involving high dimensional spaces. Various extensions and modifications have also been proposed to the basic algorithm [LaValle01]. While results regarding the probabilistic completeness (assurance of finding a path if one exists as the number of nodes approaches infinity) and the convergence rate of the RRT planner exist [LaValle01], there has been very little quantitative evaluation of the RRTs with respect to path quality, number of nodes required to find a solution, and scaling power with increase in dimensionality. This project aims to rectify this deficit through an empirical study of RRTs applied to various environments and differing non-holonomic constraints. This project applies RRTs to a variety of robots, starting with the holonomic case of a point robot operating in 2-DOF, to a car robot with three trailers operating with non-holonomic constraints in a 7-DOF state space. The variation of the number of nodes required to find a path and the time to find a solution with an increase in state-space dimensionality are studied by making all the robots operate in the same environment. For the 2-DOF case the path quality obtained by use of RRTs is compared against the optimal path length. In addition, the performance of the RRT algorithm in environments with narrow passages or tight confines is also considered. The bi-directional variant is the RRT algorithm used for all experiments in this project, unless otherwise specified. All experiments are performed in simulation. The report is laid out as follows. The next section gives an introduction to motion planning with an emphasis on non-holonomic planning. Previous work in this field is also described here. The subsequent section decribes the RRT algorithm along with its various variants. Following this, models of the robots used in the simulations are presented. A description of the experiments and results, and a discussion of the results obtained comprise the latter part of the report.