Adaptive motion planning with high-dimensional mixture models

Recent progress in motion planning has made it possible to determine homotopy inequivalent trajectories between an initial and terminal configuration in a robot configuration space. Current approaches have however either assumed the knowledge of differential one-forms related to a skeletonization of the collision space, or have relied on a simplicial representation of the free space. Both of these approaches are currently however not yet practical for higher dimensional configuration spaces. We propose 2D topological task projections (TTPs): mappings from the configuration space to 2-dimensional spaces where simplicial complex filtrations and persistent homology can identify topological properties of the high-dimensional free configuration space. Our approach only requires the availability of collision free samples to identify winding centers that can be used to determine homotopy inequivalent trajectories. We propose the Winding Augmented RRT and RRT* (WA-RRT/RRT*) algorithms using which homotopy inequivalent trajectories can be found. We evaluate our approach in experiments with configuration spaces of planar linkages with 2–10 degrees of freedom. Results indicate that our approach can reliably identify suitable topological task projections and our proposed WA-RRT and WA-RRT* algorithms were able to identify a collection of homotopy inequivalent trajectories in each considered configuration space dimension.

As tropical forests are complex systems, they tend to be modelled either roughly via scaling relationships or in a detailed manner as high-dimensional systems with many variables. We propose an approach which lies between the two whereby succession in a tropical forest is viewed as a trajectory in the configuration space of a dynamical system with just three dependent variables, namely, the mean leaf-area index (LAI) and its standard deviation (SD) or coefficient of variation along a transect, and the mean diameter at breast height (DBH) of trees above the 90th percentile of the distribution of tree DBHs near the transect. Four stages in this forest succession are identified: (I) naturally afforesting grassland: the initial stage with scattered trees in grassland; (II) very young forest: mostly covered by trees with a few remaining gaps; (III) young smooth forest: almost complete cover by trees of mostly similar age resulting in a low SD; and (IV) old growth or mature forest: the attracting region in configuration space characterized by fluctuating SD from tree deaths and regrowth. High-resolution LAI measurements and other field data from Khao Yai National Park, Thailand show how the system passes through these stages in configuration space, as do simple considerations and a crude cellular automaton model.

In the present paper, we develop a method to calculate the rate of homogeneous bubble nucleation within a superheated L-J liquid based on the (n,v) equilibrium embryo free energy surface introduced in the first paper (DOI: 10.1021/jp404149n). We express the nucleation rate as the product of the concentration of critical nuclei within the metastable liquid phase and the relevant forward rate coefficient. We calculate the forward rate coefficient of the critical nuclei from their average lifetime as determined from MD simulations of a large number of embryo trajectories initiated from the transitional region of the metastable liquid configuration space. Therefore, the proposed rate coefficient does not rely on any predefined reaction coordinate. In our model, the critical nuclei belong to the region of the configuration space where the committor probability is about one-half, guaranteeing the dynamical relevance of the proposed embryos. One novel characteristic of our approach is that we define a limit for the configuration space of the equilibrium metastable phase and do not include the configurations that have zero committor probability in the nucleation free energy surface. Furthermore, in order to take into account the transitional degrees of freedom of the critical nuclei, we develop a simulation-based approach for rigorously mapping the free energy of the (n,v) equilibrium embryos to the concentration of the critical nuclei within the bulk metastable liquid phase.

Mixture modeling is a major paradigm for clustering in statistics. In this article, we develop a new block-wise variable selection method for clustering by exploiting the latent states of the hidden Markov model on variable blocks or the Gaussian mixture model. The variable blocks are formed by depth-first-search on a dendrogram created based on the mutual information between any pair of variables. It is demonstrated that the latent states of the variable blocks together with the mixture model parameters can represent the original data effectively and much more compactly. We thus cluster the data using the latent states and select variables according to the relationship between the states and the clusters. As true class labels are unknown in the unsupervised setting, we first generate more refined clusters, namely, semi-clusters, for variable selection and then determine the final clusters based on the dimension reduced data. Experiments on simulated and real data show that the new method is highly competitive in terms of clustering accuracy compared with several widely used methods. Supplementary materials for this article are available online.

Generating a dataset that is representative of the accessible configuration space of a molecular system is crucial for the robustness of machine-learned interatomic potentials. However, the complexity of molecular systems, characterized by intricate potential energy surfaces, with numerous local minima and energy barriers, presents a significant challenge. Traditional methods of data generation, such as random sampling or exhaustive exploration, are either intractable or may not capture rare, but highly informative configurations. In this study, we propose a method that leverages uncertainty as the collective variable (CV) to guide the acquisition of chemically relevant data points, focusing on regions of configuration space where ML model predictions are most uncertain. This approach employs a Gaussian Mixture Model-based uncertainty metric from a single model as the CV for biased molecular dynamics simulations. The effectiveness of our approach in overcoming energy barriers and exploring unseen energy minima, thereby enhancing the dataset in an active learning framework, is demonstrated on alanine dipeptide and bulk silica.

The scalar form factor describes modifications induced by the pion over the quark condensate. Assuming that representations produced by chiral perturbation theory can be pushed to high values of negative-t, a region in configuration space is reached (r < R ∼ 0.5 fm) where the form factor changes sign, indicating that the condensate has turned into empty space. A simple model for the pion incorporates this feature into density functions. When supplemented by scalar-meson excitations, it yields predictions close to empirical values for the mean square radius (⟨r2⟩πS = 0.59 fm2) and for one of the low energy constants , with no adjusted parameters.

A note on topology of isoenergy manifold of n-degree natural Hamiltonian systems and existence of global Poincaré section

Motion planning for robotic manipulation of clothing is a challenging problem as clothing articles have high-dimensional configuration spaces and are computationally expensive to simulate. We present an algorithm for robotic cloth folding that, given a sequence of desired folds, outputs a motion plan consisting of a sequence of primitives for a robot to fold the cloth. Previous work on cloth folding does not take into account the constraints of the robot, and thus produces plans which are often infeasible given the kinematics of robots like the Willow Garage PR2. In this paper we introduce a class of motion primitives that start and end in a subset of the cloth’s state space. To find a sequence of primitives that achieves all required folds, the algorithm takes advantage of the partial ordering inherent in folding, and produces a time-optimal motion plan (given the set of primitives) for the robot if one exists. We describe experiments with a general purpose mobile robotic platform, the PR2, folding articles that require dragging and base motion in addition to folding. Our experiments show that (1) many articles of clothing conform well enough to the assumptions made in our model and (2) this approach allows our robot to perform a wide variety of folds on articles of various sizes and shapes.

In rarefied gas flows, discontinuity phenomena such as velocity slip and temperature jump commonly appear in the gas layer adjacent to a solid boundary. Due to the physical complexity of the interactions at the gas-solid interface, particularly in the case of systems with local nonequilibrium state, boundary models with limited number of parameters cannot completely describe the reflection of gas molecules at the boundary. In this work, the Gaussian mixture (GM) model, which is an unsupervised machine learning technique, is employed to construct a statistical gas-solid surface scattering model based on the collisional data obtained from molecular dynamics (MD) simulations. The GM model is applied to study Couette flow for different inert gases (Ar and He) confined between two parallel infinite gold walls at different temperatures. A direct comparison between the results obtained from the GM model and the Cercignani-Lampis-Lord (CLL) scattering kernel against the MD collisional data in terms of the distribution of the predicted postcollisional velocities, and accommodation coefficients has shown that the results from the GM model are an excellent match with the MD results outperforming the CLL scattering kernel. As an example, for He gas, while the predicted energy accommodation coefficient by the CLL model is more than two times higher than the MD predictions, the value computed by the GM model is in excellent agreement with the MD results. This superior performance of the GM model confirms its high potential to derive a generalized boundary condition in systems encountered with highly nonequilibrium and complex gas flow conditions.

In this work we present and apply a new Hyperspectral image classification method based on Dirichlet Process Gaussian mixture models (also known as infinite Gaussian mixture models - IGMMs). Since this approach is a non-parametric Bayesian method, we circumvent the problem of model selection which is unavoidable and often difficult when employing traditional parametric Gaussian mixture models (GMM). In order to infer model parameters from observations, we adopt a Gibbs Sampling method to sample the posterior distributions of these parameters. In the preprocessing step, we use Local Fisher's Discriminant Analysis (LFDA) for dimension reduction since we expect it to preserve the multi-modal, non-Gaussian structure of the hyperspectral data. We compared our proposed IGMM based classification method to the existing state-of-the-art classification methods using popular hyperspectral imagery datasets. To simulate challenging real-world sensing environment, we mix every pixel with background and study the performance of these classification approaches. Our experiments show that the proposed LFDA-IGMM method and GMM method have almost the same performance for most cases, given “pure” data - with mixed pixels, LFDA-IGMM outperformed GMM for sub-pixel classification. Both methods outperformed the other commonly used classification approaches when the training sample size is relatively large. Also, the IGMM based method is less sensitive to pixel mixing than other methods.

The light collection and concentration subsystem (LCCS) of any concentrating solar thermal (CST) system is composed of the surfaces that collect and concentrate the sunlight and of the input surfaces of the receivers, or receivers’ envelopes, where the light is concentrated. For all commercial CST technologies the LCCS is, together with the power block, the subsystem that has more influence in the overall performance and cost. Thus, its optimization is critical to increase the cost-competitiveness of these systems. This optimization requires, in many cases, the optimization of the position, geometry and size of a very large number of solar collecting and concentrating surfaces as well as the optimization of the shape and size of the input surfaces of the receivers where the sunlight is concentrated. Because a full optimization requires the exploration of a configuration space with a very large number of dimensions, the traditional approach consist in making many initial assumptions to drastically reduce the number of dimensions of the configuration space to a handful, so that the optimization can be carried out using conventional high-end workstations in a matter of hours. However, to achieve relevant breakthroughs and to substantially increase the cost-competitiveness of CST systems a bolder approach is needed, where sophisticated design and analysis tools, engineered from the start to be used in High Performance Computers (HPC), will be combined with sophisticated optimization strategies targeted to explore and find optimal solutions in very high dimensional configuration spaces. This paper presents the first of a series of such design and analysis tools. The tool, call Flux Tracer, partitions the three-dimensional space in which the LCC subsystem under analysis is immersed into volumetric pixels (voxels) and computes the radiant energy flux that traverses each voxel as a function of time. It integrates the energy density in every voxel overtime, providing detailed information regarding how the radiant energy flows in space in a given LCC subsystem and in a given period of time. This information is the cornerstone of the highly sophisticated computational LCC subsystem optimization framework The Cyprus Institute (CYI) is developing, in collaboration with the Australian National University (ANU), targeted to be used in HPC’s.

In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices.

Traditional motion planning can be computationally burdensome for practical robots, due to extensive collision checking and considerable iterative propagation of cost values. We present a novel neural network architecture which can directly generate the cost-to-go (c2g) function for a given configuration space and a goal configuration. The output of the network is a continuous function whose gradient in configuration space can be directly used to generate trajectories in motion planning without the need for protracted iterations or extensive collision checking. This higher order function (i.e. a function generating another function) representation lies at the core of our motion planning architecture, c2g-HOF, which can take a workspace as input, and generate the cost-to-go function over the configuration space map (C-map). Simulation results for 2D and 3D environments show that c2g-HOF can be orders of magnitude faster at execution time than methods which explore the configuration space during execution. We also present an implementation of c2g-HOF which generates trajectories for robot manipulators directly from an overhead image of the workspace.

When robots perform manipulation tasks, they need to determine their own movement, as well as how to grasp and release an object. Reasoning about the motion of the robot and the object simultaneously leads to a multi-modal planning problem in a high-dimensional configuration space. In this paper we propose an asymptotically optimal manipulation planner. Our approach extends optimal sampling-based roadmap planners to efficiently explore the configuration space of the robot and the object. We prove probabilistic completeness and global, asymptotic optimality. Extensive simulations of a typical pick-and-place scenario show that our approach significantly outperforms a (nonoptimal) state-of-the-art approach. We implemented our planner on a real manipulator and were able to compute high quality solutions in less than a second.

Efficient similarity search for uncertain data is a challenging task in many modern data mining applications like image retrieval, speaker recognition and stock market analysis. A common way to model the uncertainty of data objects is using probability density functions in the form of Gaussian Mixture Models (GMMs), which have an ability to approximate arbitrary distribution. However, due to the possible unequal length of mixture models, the use of existing index techniques has serious problems for the objects modeled by GMMs. Either the techniques cannot handle GMMs or they have too many limitations. Hence, we propose a dynamic index structure, Gaussian Component based Index (GCI), for GMMs. GCI decomposes GMMs into the single, pairs, or n-lets of Gaussian components, stores these components into well studied index trees such as U-tree and Gauss-Tree, and refines the corresponding GMMs in a conservative but tight way. GCI supports both k-most-likely queries and probability threshold queries by means of Matching Probability. Extensive experimental evaluations of GCI demonstrate a considerable speed-up of similarity search on both synthetic and real-world data sets.