Analysis of the Evolution of C-Space Models built through Incremental Exploration

Abstract

Many sampling methods for motion planning explore the robot's configuration space (C-space) starting from a set of configuration(s) and incrementally explore surrounding areas to produce a growing model of the space. Although there is a common understanding of the strengths and weaknesses of these techniques, metrics for analyzing the incremental exploration process and for evaluating the performance of incremental samplers have been lacking. We propose the use of local metrics that provide insight into the complexity of the different regions in the model and global metrics that describe the process as a whole. These metrics only require local information and can be efficiently computed. We illustrate the use of our proposed metrics to analyze representative incremental strategies including the Rapidly-exploring Random Trees, Expansive Space Trees, and the original Randomized Path Planner. We show how these metrics model the efficiency of C-space exploration and help to identify different modeling stages. In addition, these metrics are ideal for adapting space exploration to improve performance.

Structural Improvement Filtering Strategy for PRM

“…These classifications have been used to compare the quality of samples generated by different sampling strategies. As a quick summary, each new sample X is classified as follows: (See [15], [17] for more details.) • cc-create -A new component CC with X as its only node is created as seen in Figure 1(c).…”

“…Estimating the potential before edge pairs are tested is what differentiates this work from previous work [15], [17] or VISPRM [12]. Previously, expensive local planners for the edge pairs were needed to make reliable classifications or to calculate the improvement of a new sample.…”

“…It is important to note that delaying the sample acceptance policy for an initial time period is necessary. During the initial phase of roadmap building the model is in a "Quick Learning" stage [15], [17]. Here, estimations and classifications of samples are not accurate due to the primitive knowledge in the model.…”

“…Both a rise and a fall in the component's diameter signify an improvement: a rise corresponds to an addition of connected C-Space, and a fall corresponds to improvements in shorter pathways. We also show when the point at which the query for the environment is solved, although this is a poor metric for comparisons [15], [17], [24]. Additionally, tables of average statistics gathered when solving the queries are shown for: Maze in Table V, Hook in Table VI, and Walls in Table VII. All sample acceptance policies for a given planner provide some level of improvement over Pure; the amount of improvement depends on the type of planner.…”

“…In our previous work, we have developed online metrics [15], [17] to monitor the sampling process to estimate the performance of the model building process at three levels of detail: at the sample level, how "good" and efficient are the samples created? At a small region level, how well are the small locally-homogeneous regions in the large highdimensional space being explored?…”