Showing papers on "Configuration space published in 2022"

A General Framework of Motion Planning for Redundant Robot Manipulator Based on Deep Reinforcement Learning

Abstract: Motion planning and its optimization is vital and difficult for redundant robot manipulator in an environment with obstacles. In this article, a general motion planning framework that integrates deep reinforcement learning (DRL) is proposed to explore the length-optimal path in Cartesian space and to derive the energy-optimal solution to inverse kinematics. First, based on the maximum entropy framework and Tsallis entropy, a DRL algorithm with clipped automatic entropy adjustment is proposed to make the agent to be qualified to cope with diverse tasks. Second, a path planning structure that combines traditional path planner and DRL is proposed, which integrates the powerful exploration capability of the former and exploitation of experience replay of the latter to enhance the planning performance. Third, based on the exploration ability of DRL and the nonlinear fitting ability of artificial neural networks, a structure is proposed to provide an energy-optimal inverse kinematics solution for redundant robot manipulators. Finally, experimental results on both simulated and real-world customized scenarios have verified the performance of the proposed work.

RRT*-Based Path Planning for Continuum Arms

Abstract: Continuum arms are bio-inspired devices that exhibit continuous, smooth bending and generate motion through structural deformation. Rapidly-exploring random trees (RRT) is a traditional approach for performing efficient path planning. RRT approaches are usually based on exploring the configuration space (C-Space) of the robot to find a desirable work space (W-Space) path. Due to the complex kinematics and the highly non-linear mapping between the C-Space and W-Space of continuum arms, a high-quality path in the C-Space (e.g., a linear path) may not correspond to a desirable path/movement in the W-Space. Consequently, the C-Space RRT approaches that are based on C-Space cost functions do not lead to reliable and effective path planning when applied to continuum arms. In this letter, we propose a RRT* path planning approach for continuum arms that is based on exploring the W-Space of the robot as opposed to its C-Space. We show the successful applications of the proposed W-Space RRT* path planner in performing path planning with obstacle avoidance and in performing trajectory tracking. In all the aforementioned tasks, the quality of the paths generated by the proposed planner is superior to that of previous approaches and to its counterpart C-Space based RRT* approach, while the paths are generated in substantially less time.

Robot Precision Assembly Combining With Passive and Active Compliant Motions

Abstract: Precision assembly is one of the primary goals of robots in manufacturing. Assembly strategies combining active and passive compliant control are presented herein. In this article, we construct a high-dimensional configuration space of robot assembly and then divide the configuration space to its subspaces. We further map the active compliant motion and the passive compliant motion of the manipulator into different subspaces. In one subspace, we construct the constraint function and design the passive compliant motion of the manipulator in the constraint region, where the uncertainties of the system should be eliminated by the environment constraints. In another subspace, we design a force controller based on the low-resolution force sensory information to control the position of the robot. The proposed method avoids the design of precision mechanism systems and the usage of high-quality sensors. Several experiments pertaining to peg-in-hole insertions are conducted to demonstrate the efficiency of the proposed method.

Closed-form Minkowski sums of convex bodies with smooth positively curved boundaries

Abstract: This article derives closed-form parametric formulas for the Minkowski sums of convex bodies in d -dimensional Euclidean space with boundaries that are smooth and have all positive sectional curvatures at every point. Under these conditions, there is a unique relationship between the position of each boundary point and the surface normal. The main results are presented as two theorems. The first theorem directly parameterizes Minkowski sum boundaries using the unit normal vector at each surface point. Although simple to express mathematically, such a parameterization is not always practical to obtain computationally. Therefore, the second theorem derives a more useful parametric closed-form expression using the gradient that is not normalized. In the special case of two ellipsoids, the proposed expressions are identical to those derived previously using geometric interpretations. In order to examine the results, numerical validations and comparisons of the Minkowski sums between two superquadric bodies are conducted. Applications to generate configuration space obstacles in motion planning problems and to improve optimization-based collision detection algorithms are introduced and demonstrated.

Bohmian quantum potential and chaos

Abstract: We study the quantum potential Q in a system of 2 degrees of freedom with emphasis on the regions where chaos is generated. Q goes to −∞ at the nodal points, where the wave function vanishes. But close to every nodal point, there is an unstable stagnant point in the frame of reference of the moving node, the X-point, which scatters the incoming trajectories and produces chaos. We first study the quantum potential of a wavefunction with a single nodal point, where we also give an analytical approximation of Q close to the node. Then we consider a wavefunction with infinitely many nodal points along a straight line and finally a system with a finite number of scattered nodal points in the configuration space. In all cases we find that the X-points are very close to the local maxima of Q. These maxima of Q form spikes at those times when the nodal points acquire large velocities, as they go to infinity in the inertial frame of reference (x, y).

Conceptual configuration design of line-foldable deployable space truss structures employing graph theory

Abstract: From the perspective of the truss as a whole, this research investigates the conceptual configuration design for deployable space truss structures that are line-foldable with the help of graph theory. First, the bijection between a truss and its graph model is established. Therefore, operations can be performed based on graph models. Second, by introducing Maxwell’s rule, maximum clique, and chordless cycle, the principle of conceptual configuration synthesis is analyzed. A corresponding procedure is formed and it is verified by a truss with seven nodes. Third, assisted by some theorems of graph theory, the simplified double-color topological graph of deployable space truss structures is acquired and it also displays the procedure with a case. Finally, based on the above analysis, it obtains the optimal conceptual configurations. This novel research lays the foundation for kinematic synthesis and geometric dimension designs.

Configuration space for quantum gravity in a locally regularized path integral

Abstract: We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parametrization of Euclidean metric fluctuations such that (i) the signature of the metric is preserved in all configurations that enter the gravitational path integral, and (ii) the parametrization provides a bijective map between full Euclidean metrics and metric fluctuations about a fixed background. For the case of foliatable manifolds, we show how to parametrize fluctuations in order to preserve foliatability of all configurations. Moreover, we show explicitly that preserving the signature on the configuration space for the Lorentzian quantum gravitational path integral is most conveniently achieved by inequality constraints. We discuss the implementation of these inequality constraints in a nonperturbative renormalization group setup.

Shannon Entropy in LS-Coupled Configuration Space for Ni-like Isoelectronic Sequence

Abstract: The Shannon entropy in an LS-coupled configuration space has been calculated through a transformation from that in a jj-coupled configuration space for a Ni-like isoelectronic sequence. The sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction have been presented for adjacent levels. It is shown that eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, and both of them are a sufficient condition for information exchange, which is the same as the case of the jj-coupled configuration space. It is found that the structure of sudden change from jj-coupled into LS-coupled configuration spaces through the LS-jj transformation is invariant for Shannon entropy along the isoelectronic sequence. What is more, in an LS-coupled configuration space, there are a large number of information exchanges between energy levels whether with or without strong configuration interaction, and most of the ground and single excited states of Ni-like ions are more suitable to be described by a jj-coupled or other configuration basis set instead of an LS-coupled configuration basis set according to the configuration mixing coefficients and their Shannon entropy. In this sense, Shannon entropy can also be used to measure the applicability of a configuration basis set or the purity of atomic state functions in different coupling schemes.

Solving the Schrödinger Equation in the Configuration Space with Generative Machine Learning.

Abstract: The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schrödinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.

Analogy among Center of Gravity, Center of Mass, and Centroid of Rigid body: Analysis of Formula for Their Respective Calculation as per Configuration of Body and Utilization in Composite Application

Abstract: The essential distinctions and similarities between the center of gravity, the center of mass, and the centroid of a rigid body in space are illustrated in this article. The use of an acceptable equation for a given configuration of the body situated at any location in a 3-D space is established and used in a composite application in the boiler lever safety valve.

Graphic Characterization and Clustering Configuration Descriptors of Determinant Space for Molecules.

Abstract: Quantum Monte Carlo approaches based on stochastic sampling of determinant space have evolved to be powerful methods to compute the electronic states of molecules. These methods not only calculate the correlation energy at an unprecedented accuracy but also provide insightful information on the electronic structures of computed states, for example, the population, connection, and clustering of determinants, which have not been fully explored. In this work, we devise a configuration graph for visualizing determinant space, revealing the nature of the molecule's electronic structure. In addition, we propose two analytical descriptors to quantify the extent of configuration clustering of multideterminant wave functions. The graph and descriptors provide us with a fresh perspective of the electronic structures of molecules and can assist with further development of configuration interaction-based electronic structure methods.

Nonholonomic Reorientation of Free-Flying Space Robots Using Parallelogram Actuation in Joint Space

Abstract: A robot with large-degree-of-freedom joints is a promising future space robot capable of adapting to various environments and can perform dexterous tasks with multiple manipulators. The attitude dynamics of a free-flying robot shows nonholonomy, which enables the robot to reorient its attitude by moving its body. However, previous studies were not generally able to handle the nonholonomy, especially for robots with large degrees of freedom of joints. In the present study, we analytically investigate a maneuver in which joints are actuated along a parallelogram trajectory in joint angle space and propose an analytical path modification method in joint angle space in order to achieve the target attitude. Parallelogram actuation guarantees that the body configuration is returned to the initial state after one set of maneuvers, and thus the attitude of the robot is independently reoriented to the target maintaining the body configuration. The analytical solution is provided by applying Magnus expansion to the kinematics equation of rotational matrices, and its Lie group structure contributes to concise mathematical expressions. In addition, the analytical solution does not cause numerical difficulties, such as combinatorial explosion, and so can fully make use of the reorientation ability of a robot with large degrees of freedom.

Configuration Transformation Planning Method of Unmanned Aerial Vehicle Cluster Based on Improved Hungarian Algorithm

Abstract: For the planning problem of Unmanned Aerial Vehicle (UAV) formation configuration transformation, a formation configuration transformation planning method based on the improved Hungarian algorithm is proposed. By selecting a straight-line path as the movement path of UAVs in configuration transformation, the configuration transformation problem is transformed into a multi-UAV position assignment problem with constraint handling in a dynamic environment. For the Hungarian algorithm efficiency matrix power function treatment, the improved algorithm can be simultaneously bivariate integrated optimization; Introduce the time axis in the configuration space to establish the configuration-time space, and analyze the collision constraints during the dynamic transformation process in this space, and finally, the feasibility of the method is verified by simulation.

Geometric interpretation for coupled-cluster theory. A comparison of accuracy with the corresponding configuration interaction model.

Abstract: Although coupled-cluster theory is well-known for its accuracy, the geometry associated with the manifold of wave functions reached by the coupled-cluster Ansatz has not been deeply explored. In this article, we look for an interpretation for the high accuracy of coupled-cluster theory based on how the manifold of coupled-cluster wave functions is embedded within the space of n-electron wave functions. We define the coupled-cluster and configuration interaction manifolds and measure the distances from the full-configuration interaction (FCI) wave function to these manifolds. We clearly observe that the FCI wave function is closer to the coupled-cluster manifold that is curved than to the configuration interaction manifold that is flat for the selected systems studied in this work. Furthermore, the decomposition of the distances among these manifolds and wave functions into excitation ranks gives insights into the failure of the coupled-cluster approach for multireference systems. The present results show a new interpretation for the quality of the coupled-cluster method, as contrasted to the truncated configuration interaction approach, besides the well-established argument based on size extensivity. Furthermore, we show how a geometric description of wave function methods can be used in electronic structure theory.

Quotient maps and configuration spaces of hard disks

Abstract: Hard disks systems are often considered as prototypes for simple fluids. In a statistical mechanics context, the hard disk configuration space is generally quotiented by the action of various symmetry groups. The changes in the topological and geometric properties of the configuration spaces effected by such quotient maps are studied for small numbers of disks on a square and hexagonal torus. A metric is defined on the configuration space and the various quotient spaces that respects the desired symmetries. This is used to construct explicit triangulations of the configuration spaces as $\alpha$-complexes. Critical points in a configuration space are associated with changes in the topology as a function of disk radius, are conjectured to be related to the configurational entropy of glassy systems, and could reveal the origins of phase transitions in other systems. The number and topological and geometric properties of the critical points are found to depend on the symmetries by which the configuration space is quotiented.

Navigation of Multiple Disk-Shaped Robots with Independent Goals within Obstacle-Cluttered Environments

Abstract: In this work, we propose a hybrid control scheme to address the navigation problem for a team of disk-shaped robotic platforms operating within an obstacle-cluttered planar workspace. Given an initial and a desired configuration of the system, we devise a hierarchical cell decomposition methodology which is able to determine which regions of the configuration space need to be further subdivided at each iteration, thus avoiding redundant cell expansions. Furthermore, given a sequence of free configuration space cells with an arbitrary connectedness and shape, we employ harmonic transformations and harmonic potential fields to accomplish safe transitions between adjacent cells, thus ensuring almost-global convergence to the desired configuration. Finally, we present the comparative simulation results that demonstrate the efficacy of the proposed control scheme and its superiority in terms of complexity while yielding a satisfactory performance without incorporating optimization in the selection of the paths.

Incremental Path Planning Algorithm via Topological Mapping with Metric Gluing

Abstract: We present an incremental topology-based motion planner that, while planning paths in the configuration space, performs metric gluing on the constructed Vietoris-Rips simplicial complex of each sub-space (voxel). By incrementally capturing topological and geometric information in batches of voxel graphs, our algorithm avoids the time overhead of analyzing the properties of the entire configuration space. We theoretically prove in this paper that the simplices of all voxel graphs joined together are homotopy-equivalent to the union of the simplices in the configuration space. Experiments were carried out in seven different environments using various robots, including the articulated linkage robot, the Kuka YouBot, and the PR2 robot. In all environments, the results show that our algorithm achieves better convergence for path cost and computation time with a memory-efficient roadmap than state-of-the-art methods.

Coordinate-Free Jacobian Motion Planning: A 3-D Space Robot

Abstract: We address the motion planning problem for a robotic system whose configuration manifold contains a group of rotations. Our approach is applied to a free-floating space robot composed of a three-dimensional base (a spacecraft) and an anthropomorphic onboard manipulator. The robot is actuated by the torques exerted at the joints of the onboard manipulator. A coordinate-free representation of rotations is utilized. The Lagrangian formalism is employed in order to derive a dynamics model of the robot that takes the form of a control system defined on the group of rotations and the joint space of the onboard manipulator. Using the conservation of angular momentum of the robot, a Jacobian motion planning algorithm is designed relying on the Endogenous Configuration Space Approach. The performance of the algorithm is verified by computer simulations.

Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH3OH–Cu(111)

Abstract: A method for computing anharmonic thermophysical properties for adsorbates on metal surfaces has been extended to include libration, or frustrated rotation. Classical phase space integration is used with Monte Carlo sampling of the configuration space to obtain the partition function of CO on Pt(111) and CH3OH on Cu(111). A minima-preserving neural network potential energy surrogate is used within the integration routines. Direct state counting using discrete variable representation is used to benchmark the results. We find that the phase space integration approach is in excellent agreement with the direct state counting results. Comparison with standard models such as the harmonic oscillator indicates that anharmonicity contributes significantly to the thermodynamic properties of CH3OH on Cu(111). We find that there is also a considerable difference between the harmonic oscillator and phase space integration for CO on Pt(111), although the discrepancy can largely be attributed to the presence of multiple binding sites within the unit cell. We demonstrate that a multisite harmonic oscillator model might be sufficient for CO–Pt(111). A more thorough description of the potential energy surface, which can be achieved with phase space integration, is necessary for weakly bound adsorbates such as CH3OH. The thermophysical properties were used to calculate free energies of adsorption on the respective metals, and subsequently the equilibrium constants and Langmuir isotherms in relevant temperature ranges. The results show that the choice of model to obtain partition functions greatly affects the resulting surface coverages in kinetic models.

Solving the Schr\"odinger Equation in the Configuration Space with Generative Machine Learning

Abstract: The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schr\"odinger equation for realistic molecules and materials but is characterized by an unfavourable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wavefunction is a fundamental step towards practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.

Curriculum-based reinforcement learning for path tracking in an underactuated nonholonomic system

Abstract: Underactuated mechanical systems with nonholonomic constraints find applications in bioinspired robotics, such as snake-like robots and more recently in fish-like aquatic robots. Animal locomotion suggests that in such bioinspired robots, gaits or cyclic changes in kinematics or shape variables lead to efficient and agile motion. Path tracking in such nonholonomic systems that are not purely kinematic can be a challenging problem. In this paper we consider the problem of path tracking by a modified Chaplygin sleigh with a ‘tail’ which is a four degree of freedom nonholonomic system, possessing a single internal reaction wheel as an actuator. We develop a curriculum based deep Reinforcement Learning (RL) optimal control approach for simultaneous velocity and path tracking for this system. The curriculum based learning approach first leads to a policy for optimal tracking of limit cycles in a reduced velocity space and then in a next step to track a path. This curriculum approach allows an RL agent to learn the ’mechanics on invariant manifolds’ of the system and can be a useful approach in the motion control of high degree of freedom robots with increasing model complexity.

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.

Hierarchical Motion Planning for Autonomous Driving in Large-Scale Complex Scenarios

Abstract: Motion planning algorithms, an essential part of the autonomous driving system, have been extensively studied. However, in large-scale complex scenarios, how to develop an optimal path to comply with the requirements of smoothness and safety remains a vital issue. In this study, a hierarchical search spacial scales-based hybrid A* (termed as HHA*) motion planning method is proposed, capable of efficiently generating smooth and safe paths. The proposed HHA* method covers two stages. First, the search space is divided on a coarse scale to generate local goals. Subsequently, the novel heuristic function and exploration strategies are adopted in the fine-scale search space to generate paths like that with a human driver guided by the local goals. Moreover, with the usage of the clothoid, the smoothness of the generated path is improved to be G ² –continuous (i.e., curvature continuous), which fits the vehicle’s kinematic constraints without the need for later smoothing. Numerous experimental results from the simulation and on-road tests indicate that the proposed method can effectively perform motion planning that meets smoothness and safety in large-scale complex scenarios.

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.

From integrals to combinatorial formulas of finite type invariants -- a case study

Abstract: We obtain a localized version of the configuration space integral for the Casson knot invariant, where the standard symmetric Gauss form is replaced with a locally supported form. An interesting technical difference between the arguments presented here and the classical arguments is that the vanishing of integrals over hidden and anomalous faces does not require the well-known ``involution tricks''. Further, the integral formula easily yields the well-known arrow diagram expression for the invariant, first presented in the work of Polyak and Viro. We also take the next step of extending the arrow diagram expression to multicrossing knot diagrams and obtain a lower bound for the {\em {\"u}bercrossing number}. The primary motivation is to better understand a connection between the classical configuration space integrals and the arrow diagram expressions for finite type invariants.