Kernel principal component analysis
Advances in kernel methods
Robot Motion Planning
A dimensionality reduction approach to modeling protein flexibility
Proceedings of the sixth annual international conference on Computational biology
On the Probabilistic Foundations of Probabilistic Roadmap Planning
International Journal of Robotics Research
Recursive principal components analysis using eigenvector matrix perturbation
EURASIP Journal on Applied Signal Processing
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In this paper we present a method to control random sampling in motion planning algorithms. The principle of the method is to use online the results of a probabilistic planner to describe the free space in which the planning takes place, by computing a principal component analysis (PCA). This method identifies the locally free directions of the free space. Given that description, our algorithm accelerates the progression along these favored directions. In this way, if the free space appears as a small volume around a sub-manifold of a high-dimensional configuration space, the method overcomes the usual limitations of probabilistic motion planning algorithms and finds a solution quickly. The presented method is theoretically analyzed and experimentally compared with known motion planners.