Showing papers on "Configuration space published in 2023"

Uncertainty-driven dynamics for active learning of interatomic potentials

Abstract: Abstract Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces.

Abstract: Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Assessing quantum thermalization in physical and configuration spaces via many-body weak values

Abstract: We explore the origin of the arrow of time in an isolated quantum system described by the Schroedinger equation. We provide an explanation from weak values in the configuration space, which are understood as operational properties obtained in the laboratory following a well-defined protocol. We show that quantum systems satisfying the eigenstate thermalization hypothesis can simultaneously provide thermalized ensemble expectation values and nonthermalized weak values of the momentum, both from the same operational probability distribution. The reason why weak values of the momentum may escape from the eigenstate thermalization hypothesis is because they are linked only to off-diagonal elements of the density matrix in the energy representation. For indistinguishable particles, however, operational properties can not be defined in the configuration space. Therefore, we state that the origin of the arrow of time in isolated quantum systems described by the Schroedinger equation comes from dealing with properties obtained by averaging (tracing out) some degrees of freedom of the configuration space. We then argue that thermalization does not occur in the properties defined in the configuration space, and our argument is compatible with defending that thermalization is a real phenomenon in the properties defined in the physical space. All of these conclusions are testable in the laboratory through many-body weak values.

Constraint reduction based on virtual feature in assembly model

Abstract: With kinematic analyses of assembly, it is difficult to derive the motion of the assembly because many constraints make the kinematic model of assembly complex. In order to derive an equivalent minimum model of the kinematic model of assembly, and to decrease the computational complexity, a constraint reduction procedure for the kinematic model of assembly in configuration space is proposed as follows: first, mapping rules of the kinematic model are proposed in order to realize the mapping from a feature-based kinematic model to a kinematic model in configuration space. Second, constraint reduction procedure in configuration space and a method for deriving the minimum kinematic model in configuration space are proposed. Third, based on the constraint reduction procedure in configuration space, feature-based constraint reduction is proposed by introducing virtual feature; it is confirmed that TTRS reduction rules are valid feature-based constraint reduction rules. Using this reduction procedure, a method for deriving the feature-based minimum kinematic model is proposed. Fourth, using the feature-based minimum kinematic model and the mapping rule of the kinematic model, a method for deriving the minimum kinematic model in configuration space is proposed. Finally, in order to confirm the usefulness of the proposed constraint reduction, it is applied to an example of the kinematic model of assembly.

A sampling and learning framework to prove motion planning infeasibility

Abstract: We present a learning-based approach to prove infeasibility of kinematic motion planning problems. Sampling-based motion planners are effective in high-dimensional spaces but are only probabilistically complete. Consequently, these planners cannot provide a definite answer if no plan exists, which is important for high-level scenarios, such as task-motion planning. We apply data generated during multi-directional sampling-based planning (such as PRM) to a machine learning approach to construct an infeasibility proof. An infeasibility proof is a closed manifold in the obstacle region of the configuration space that separates the start and goal into disconnected components of the free configuration space. We train the manifold using common machine learning techniques and then triangulate the manifold into a polytope to prove containment in the obstacle region. Under assumptions about the hyper-parameters and robustness of configuration space optimization, the output is either an infeasibility proof or a motion plan in the limit. We demonstrate proof construction for up to 4-DOF configuration spaces. A large part of the algorithm is parallelizable, which offers potential to address higher dimensional configuration spaces.

An Atlas-Based Approach to Planar Variable-Structure Cable-Driven Parallel Robot Configuration-Space Representation

Abstract: Variable-structure cable-driven parallel robots (VSCR) are a new class of cable robots that are able to cover nonconvex installation spaces by permitting collisions between cables and fixed objects in the environment. In this article, we show how the configuration space of a general planar VSCR can be represented as an organized set of partially overlapping regions of constant structure. The benefit of this representation, which we refer to as the “structure atlas,” is that it allows any techniques from the established cable-driven parallel robot literature to be applied locally, greatly simplifying the modeling complexity associated with VSCRs. A complete method for how such a representation can be constructed is provided, which includes identifying the set of reachable kinematic structures for a given VSCR and the area where each structure is active. We then give specific examples of how this new representation can be used for performing VSCR workspace analysis and directly solving the VSCR inverse kinematics problem. Our results are demonstrated with the aid of simulated and experimental results.

Quantum Monte Carlo calculations in configuration space with three-nucleon forces

Abstract: Neutron matter, through its connection to neutron stars as well as systems like cold atom gases, is one of the most interesting yet computationally accessible systems in nuclear physics. The Configuration-Interaction Monte Carlo (CIMC) method is a stochastic many-body technique allowing to tackle strongly coupled systems. In contrast to other Quantum Monte Carlo methods employed in nuclear physics, the CIMC method can be formulated directly in momentum space allowing for an efficient use of non-local interactions. In this work we extend CIMC method to include three-nucleon interactions through the normal-ordered two-body approximation. We present results for the equation of state of neutron matter in line with other many-body calculations that employ low resolution chiral interactions, and provide predictions for the momentum distribution and the static structure factor.

Spin-Orbit Couplings of Open-Shell Systems with Restricted Active Space Configuration Interaction.

Abstract: In this work we perform electronic structure calculations to unravel the origin of spin-orbit couplings (SOCs) in open-shell molecules. For that, we select systems displaying di or polyradical character, e.g., trimethylene, and analyze the changes in the magnitude of SOC constants along molecular distortions of ethylene and in the presence of intermolecular interactions between open and closed-shell moieties in the O2-C2H4 system. Calculations were performed by using nonrelativistic wave functions obtained with the restricted active space configuration interaction (RASCI) method, in conjunction with a recent implementation for the calculation of SOC based on the spin-orbit mean field approximation. Our results demonstrate the suitability of RASCI in the calculation of SOCs of open-shell systems, while providing a deep understanding of the relationship between couplings and the nature of the electronic states. Moreover, we introduce a new definition of the SOC constant for the study of molecular aggregates.

A Smooth Orientation Planner for Trajectories in the Cartesian Space

Abstract: Trajectories in the operational space, when conceived for manipulators with more then three degrees of freedom, impose the adoption of an orientation primitive for the end-effector. The planning complexity increases if smoothness represents one of the motion requirements and the trajectory is obtained through the combination of several basic primitives. In this eventuality, vibrations and mechanical solicitations can be reduced by avoiding motion stops at the end of each segment. Good tracking performances can be conversely achieved by guaranteeing jerk-continuous reference signals for the actuators. The orientation planner proposed in this paper allows the smart generation of smooth trajectories. As experimentally proved in the work, the novel planning primitive is characterized by very short computational times.

Comparison of Data-Driven Approaches to Configuration Space Approximation

Abstract: Configuration spaces (C-spaces) are an essential component of many robot path-planning algorithms, yet calculating them is a time-consuming task, especially in spaces involving a large number of degrees of freedom (DoF). Here we explore a two-step data-driven approach to C-space approximation: (1) sample (i.e., explicitly calculate) a few configurations; (2) train a machine learning (ML) model on these configurations to predict the collision status of other points in the C-space. We studied multiple factors that impact this approximation process, including model representation, number of DoF (up to 42), collision density, sample size, training set distribution, and desired confidence of predictions. We conclude that XGBoost offers a significant time improvement over other methods, while maintaining low error rates, even in C-Spaces with over 14 DoF.

Mechanism Evolution and Analysis of a Novel Space Manipulator

Abstract: With the continuous development of aerospace industry in recent years, space manipulator has attracted much attention because of its excellent performance in aerospace operation. In this work, the topology of space manipulator is obtained through configuration evolution based on the Canadarm2 serving in the international space station. By analyzing the configuration characteristics, a new topological configuration of space manipulator is further optimized, then the structural design and prototype construction are completed. The kinematic model of space manipulator is established by D-H method. By comparing the theoretical calculation results with simulation data obtained from SolidWorks and MATLAB, the effectiveness of the established kinematic model is verified. Based on the kinematic model, the workspace analysis of the new space manipulator is completed by Monte Carlo method.

Certified Polyhedral Decompositions of Collision-Free Configuration Space

Abstract: Understanding the geometry of collision-free configuration space (C-free) in the presence of task-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-IRIS (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake. We furthermore provide examples of our algorithm in interactive Python notebooks.

Nudged elastic bands and lightly bound skyrmions

Abstract: It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5\leq B\leq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.

A minimum swept-volume metric structure for configuration space

Abstract: Borrowing elementary ideas from solid mechanics and differential geometry, this presentation shows that the volume swept by a regular solid undergoing a wide class of volume-preserving deformations induces a rather natural metric structure with well-defined and computable geodesics on its configuration space. This general result applies to concrete classes of articulated objects such as robot manipulators, and we demonstrate as a proof of concept the computation of geodesic paths for a free flying rod and planar robotic arms as well as their use in path planning with many obstacles.

Semiclassical Theory and the Koopman-van Hove Equation

Abstract: The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton-Jacobi equation for the complex phase factor and the transport equation for the amplitude. These two equations can be combined to form a nonlinear semiclassical version of the KvH equation in configuration space. Every solution of the configuration space KvH equation satisfies both the semiclassical phase space KvH equation and the Hamilton-Jacobi constraint. For configuration space solutions, this constraint resolves the paradox that there are two different conserved densities in phase space. For integrable systems, the KvH spectrum is the Cartesian product of a classical and a semiclassical spectrum. If the classical spectrum is eliminated, then, with the correct choice of Jeffreys-Wentzel-Kramers-Brillouin (JWKB) matching conditions, the semiclassical spectrum satisfies the Einstein-Brillouin-Keller quantization conditions which include the correction due to the Maslov index. However, semiclassical analysis uses different choices for boundary conditions, continuity requirements, and the domain of definition. For example, use of the complex JWKB method allows for the treatment of tunneling through the complexification of phase space. Finally, although KvH wavefunctions include the possibility of interference effects, interference is not observable when all observables are approximated as local operators on phase space. Observing interference effects requires consideration of nonlocal operations, e.g. through higher orders in the asymptotic theory.

Homological monotonicity for configuration spaces of manifolds

Abstract: Consider the configuration spaces of manifolds. An influential theorem of McDuff, Segal and Church shows that the (co)homology of the unordered configuration space is independent of number of points in a range of degree called the stable range. We study the another important (and general) property of unordered configuration spaces of manifolds (not necessarily orientable, and not necessarily admitting non-vanishing vector field) that is homological monotonicity in unstable part. We show that the homological dimension of unordered configuration spaces of manifolds in each degree is monotonically increasing. Our results show that the monotonicity property is not depend on the differential structure and orientiability of manifold.

Geometric conjecture about phase transitions

Abstract: As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach the steady state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and $\ensuremath{\epsilon}$-mixing time of the configuration spaces of hard-disk and hard-sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems and numerical evidence suggests that a discontinuity in the $\ensuremath{\epsilon}$-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.

Thermodynamic Interpretaion of Entanglement in Canonical Nonlinearity

Abstract: For classical discrete system under constant composition, typically reffered to as substitutional alloys, canonical average acts as nonlinear map F from a set of potential energy surface U to that of microscopic configuration in thermodynamic equilibrium, Q, which is called canonical nonlinearity (CN). On statistical manifold, at any given configuration, F can be divided into the sum of local and non-local contribution in terms of Kullback-Leibler (KL) divergence, where the former has strong positive correlation with time evolution of the nonlinearity (NOL) on configuration space (called anharmonicity in structural degree of freedoms (ASDF), while the latter, corresponding to entanglement in SDFs, does exhibit clear correlation with the ASDF. On the other hand, our recent work bridge the different concepts of NOL on configuration space and statistical manifold through stochastic thermodynamics. While the work successfully provides clear relationships between the changes in total NOL through system transition and heat transfer, thermodynamic interpretation of how the entanglment in SDFs contributes to thermodynamic functions, is totally unclear due mainly to its non-trivial, non-local character. The present study tackle this problem, deriving upper bound for the entanglement for any given transition in terms of the mutual information, heat transfer and free energy. The present thermodynamic interpretaion will provide quantitative description of how the entanglement in SDFs is dominated by configuration of ground-state structures on configuration space.

Sample-Driven Connectivity Learning for Motion Planning in Narrow Passages

Abstract: Sampling-based motion planning works well in many cases but is less effective if the configuration space has narrow passages. In this paper, we propose a learning-based strategy to sample in these narrow passages, which improves overall planning time. Our algorithm first learns from the configuration space planning graphs and then uses the learned information to effectively generate narrow passage samples. We perform experiments in various 6D and 7D scenes. The algorithm offers one order of magnitude speed-up compared to baseline planners in some of these scenes.

Hybrid Safety Certificate for Fast Collision Checking in Sampling-Based Motion Planning

Abstract: Safety certificates in robot configuration space have been shown as an efficient collision checking method. However, this method can only be applied to very simple problems since constructing the configuration space obstacles is often intractable. In this paper we propose a hybrid safety certificate (HSC) approach in both the configuration space and the workspace to increase collision checking efficiency for large-scale complex motion planning problems. Specifically, the collision-free certificate regions are constructed as random spheres in the configuration space. While the in collision certificate regions are constructed using the inside spheres of the workspace obstacles. In fact, the HSC method realizes collision checking as a straightforward sphere-sphere overlapping test which is widely regarded as the simplest way for collision detection. Besides the lazy collision checking strategy can be naturally combined with our high efficient HSC method. The HSC method combining with the lazy planning strategy is applied to both the feasible and the optimal motion planning problems. And we present a feasible motion planner BiHSC and an optimal motion planner BiHSC*. Simulations demonstrate that the computation speed is much faster than that of the state-of-the-art algorithms.

CaRE: Finding Root Causes of Configuration Issues in Highly-Configurable Robots

Abstract: Robotic systems have subsystems with a combinatorially large configuration space and hundreds or thousands of possible software and hardware configuration options interacting non-trivially. The configurable parameters are set to target specific objectives, but they can cause functional faults when incorrectly configured. Finding the root cause of such faults is challenging due to the exponentially large configuration space and the dependencies between the robot's configuration settings and performance. This paper proposes CaRE -- a method for diagnosing the root cause of functional faults through the lens of causality. CaRE abstracts the causal relationships between various configuration options and the robot's performance objectives by learning a causal structure and estimating the causal effects of options on robot performance indicators. We demonstrate CaRE's efficacy by finding the root cause of the observed functional faults and validating the diagnosed root cause by conducting experiments in both physical robots (Husky and Turtlebot 3) and in simulation (Gazebo). Furthermore, we demonstrate that the causal models learned from robots in simulation (e.g., Husky in Gazebo) are transferable to physical robots across different platforms (e.g., Husky and Turtlebot 3).

Enhanced Sampling of Configuration and Path Space in a Generalized Ensemble by Shooting Point Exchange

Abstract: The computer simulation of many molecular processes is complicated by long time scales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path sampling with enhanced exploration of configuration space. The method relies on exchange moves between configuration and trajectory space, carried out based on a generalized ensemble. This scheme substantially enhances the efficiency of the transition path sampling simulations, particularly for systems with multiple transition channels, and yields information on thermodynamics, kinetics and reaction coordinates of molecular processes without distorting their dynamics. The method is illustrated using the isomerization of proline in the KPTP tetrapeptide.

Round twin groups on few strands

Abstract: We study the fundamental group of the configuration space of $n$ ordered points on the circle no three of which are equal. We compute it for $n<6$ and describe its homology for $n=6$. We also show how, for arbitrary $n$, this group can be assembled from planar braid groups, relate it to the pure cactus group and construct a cubical complex homotopy equivalent to its classifying space.

Direct Robot Configuration Space Construction using Convolutional Encoder-Decoders

Abstract: Intelligent robots must be able to perform safe and efficient motion planning in their environments. Central to modern motion planning is the configuration space. Configuration spaces define the set of configurations of a robot that result in collisions with obstacles in the workspace, C-clsn, and the set of configurations that do not, C-free. Modern approaches to motion planning first compute the configuration space and then perform motion planning using the calculated configuration space. Real-time motion planning requires accurate and efficient construction of configuration spaces. We are the first to apply a convolutional encoder-decoder framework for calculating highly accurate approximations to configuration spaces. Our model achieves an average 97.5% F1-score for predicting C-free and C-clsn for 2-D robotic workspaces with a dual-arm robot. Our method limits undetected collisions to less than 2.5% on robotic workspaces that involve translation, rotation, and removal of obstacles. Our model learns highly transferable features between robotic workspaces, requiring little to no fine-tuning to adapt to new transformations of obstacles in the workspace.

A quantum pseudo-integrable Hamiltonian impact system

Abstract: Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties. It is demonstrated that the energy levels statistics are similar to those of pseudointegrable billiards. Yet, here, the density of wavefunctions which concentrate on projections of classical level sets to the configuration space does not disappear at large energies, suggesting that there is no equidistribution in the configuration space in the large energy limit; this is shown analytically for some limit symmetric cases and is demonstrated numerically for some nonsymmetric cases.

Improving Path Planning Performance through Multimodal Generative Models with Local Critics

Abstract: This paper presents a novel method for accelerating path planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of the free conditioned configuration space. Our proposed approach involves conditioning the WGAN-GP with a Variational Auto-Encoder in a continuous latent space to handle multimodal datasets. However, training a Variational Auto-Encoder with WGAN-GP can be challenging for image-to-configuration-space problems, as the Kullback-Leibler loss function often converges to a random distribution. To overcome this issue, we simplify the configuration space as a set of Gaussian distributions and divide the dataset into several local models. This enables us to not only learn the model but also speed up its convergence. We evaluate the reconstructed configuration space using the homology rank of manifolds for datasets with the geometry score. Furthermore, we propose a novel transformation of the robot's configuration space that enables us to measure how well collision-free regions are reconstructed, which could be used with other rank of homology metrics. Our experiments show promising results for accelerating path planning tasks in unknown scenes while generating quasi-optimal paths with our WGAN-GP. The source code is openly available.

Growing Convex Collision-Free Regions in Configuration Space using Nonlinear Programming

Abstract: One of the most difficult parts of motion planning in configuration space is ensuring a trajectory does not collide with task-space obstacles in the environment. Generating regions that are convex and collision free in configuration space can separate the computational burden of collision checking from motion planning. To that end, we propose an extension to IRIS (Iterative Regional Inflation by Semidefinite programming) [5] that allows it to operate in configuration space. Our algorithm, IRIS-NP (Iterative Regional Inflation by Semidefinite & Nonlinear Programming), uses nonlinear optimization to add the separating hyperplanes, enabling support for more general nonlinear constraints. Developed in parallel to Amice et al. [1], IRIS-NP trades rigorous certification that regions are collision free for probabilistic certification and the benefit of faster region generation in the configuration-space coordinates. IRIS-NP also provides a solid initialization to C-IRIS to reduce the number of iterations required for certification. We demonstrate that IRIS-NP can scale to a dual-arm manipulator and can handle additional nonlinear constraints using the same machinery. Finally, we show ablations of elements of our implementation to demonstrate their importance.