We introduce a functional gradient descent trajectory optimization algorithm for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs). Functional gradient algorithms are a popular choice for motion planning in complex many-degree-of-freedom robots, since they (in theory) work by directly optimizing within a space of continuous trajectories to avoid obstacles while maintaining geom...

We present a generalization of the RBF-FD method that allows full control of the overlap between RBF-FD stencils. We accomplish this by introducing a continuous overlap parameter δ ∈ [0, 1] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of the RBF-FD stencils. We show with a simple example that global interpolation with both RBFs and RBFs augmented wi...

A new fault tolerant control (FTC) problem via the output probability density functions (PDFs) for non-Gaussian stochastic distribution control systems (SDC) is investigated. The PDFs can be approximated by the radial basis functions (RBFs) of neural networks. Differently from the conventional FTC problems, the measured information is in the form of probability distributions of the system outpu...

A treecode is presented for evaluating sums defined in terms of the multiquadric radial basis function (RBF), φ(x) = (|x|2 + c2)1/2, where x ∈ R3 and c ≥ 0. Given a set of N nodes, evaluating an RBF sum directly requires CPU time that scales like O(N2). For a given level of accuracy, the treecode reduces the CPU time to O(N logN) using a far-field expansion of φ(x). We consider two options for ...

We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are formulated entirely in Cartesian coordinates, thus avoiding any irregular clustering of nodes at artificial boundaries on the sphere and naturally bypassing any apparent artificial singularities associated with surfac...

Best-first search (BFS) expands the fewest nodes among all admissible algorithms using the same cost function, but typically requires exponential space. Depth-first search needs space only linear in the maximumsearch depth, but expands more nodes than BFS. Using a random tree, we analytically show that the expected number of nodes expanded by depth-first branch-and-bound (DFBnB) is no more than...

Radial Basis Function Neural Networks (RBFNNs) have been successfully employed in several function approximation and pattern recognition problems. The use of different RBFs in RBFNN has been reported in the literature and here the study centres on the use of the Generalized Radial Basis Function Neural Networks (GRBFNNs). An interesting property of the GRBF is that it can continuously and smoot...

For estimation of monthly precipitation, considering the intricacy and lack of accurate knowledge about the physical relationships, black box models usually are used because they produce more accurate values. In this article, a hybrid black box model, namely ANN-RBF, is proposed to estimate spatiotemporal value of monthly precipitation. In the first step a Multi Layer Perceptron (MLP) network i...

This paper has made some significant advances in the boundary-only and domain-type RBF techniques. The proposed boundary knot method (BKM) is different from the standard boundary element method in a number of important aspects. Namely, it is truly meshless, exponential convergence, integration-free (of course, no singular integration), boundary-only for general problems, and leads to symmetric ...

In this paper a multi-step learning algorithm for creating a Growing Radial Basis Function Network (RBFN) Model is presented and analyzed. The main concept of the algorithm is to gradually increase by one the number of the Radial Basis Function (RBF) units at each learning step thus gradually improving the total model quality. The algorithm stops automatically, when a predetermined (desired) ap...