Showing papers on "Configuration space published in 2006"

An integrated approach to inverse kinematics and path planning for redundant manipulators

Abstract: We propose a novel solution to the problem of inverse kinematics for redundant robotic manipulators for the purposes of goal selection for path planning. We unify the calculation of the goal configuration with searching for a path in order to avoid the uncertainties inherent to selecting goal configurations which may be unreachable because they currently lie in components of the free configuration space disconnected from the initial configuration. We adopt workspace heuristic functions that implicitly define goal regions of the configuration space and guide the extension of rapidly-exploring random trees (RRTs), which are used to search for these regions. The algorithm has successfully been used to efficiently plan reaching and grasping motions for a humanoid robot equipped with redundant manipulator arms

Almost-global tracking of simple mechanical systems on a general class of Lie Groups

Abstract: We present a general intrinsic tracking controller design for fully-actuated simple mechanical systems, when the configuration space is one of a general class of Lie groups. We first express a state-feedback controller in terms of a function-the "error function"-satisfying certain regularity conditions. If an error function can be found, then a general smooth and bounded reference trajectory may be tracked asymptotically from almost every initial condition, with locally exponential convergence. Asymptotic convergence from almost every initial condition is referred to as "almost-global" asymptotic stability. Error functions may be shown to exist on any compact Lie group, or any Lie group diffeomorphic to the product of a compact Lie group and R/sup n/. This covers many cases of practical interest, such as SO(n), SE(n), their subgroups, and direct products. We show here that for compact Lie groups the dynamic configuration-feedback controller obtained by composing the full state-feedback law with an exponentially convergent velocity observer is also almost-globally asymptotically stable with respect to the tracking error. We emphasize that no invariance is needed for these results. However, for the special case where the kinetic energy is left-invariant, we show that the explicit expression of these controllers does not require coordinates on the Lie group. The controller constructions are demonstrated on SO(3), and simulated for the axi-symmetric top. Results show excellent performance.

SPOCK.CI: a multireference spin-orbit configuration interaction method for large molecules.

Abstract: We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.

Practical kinematics for real-time implementation of continuum robots

Abstract: This paper introduces new analyses and algorithms which are essential for the practical implementation of continuous backbone continuum robots. Actuator length limits strongly shape the configuration or joint space of continuum manipulators, introducing couplings which are not reflected in previously published kinematic models. These unmodeled effects significantly restrict the practical application of previously established kinematic models on continuum robot hardware. This paper presents a new analysis of the effects of actuator limits on continuum robots. Based on the new understanding of the configuration space uncovered, we derive for the first time the configuration space of continuum robots when constrained by actuator length limits. These contributions are essential for effective use of a wide range of continuum robots and have been implemented and tested on two different types of continuum robots. Results and insight gained from this implementation are presented

Safe Path Planning in an Uncertain-Configuration Space using RRT

Abstract: This paper addresses the problem of safe path planning in an uncertain-configuration space. We consider the case of a car-like robot moving in an indoor environment (three-dimensional space). The Extended Kalman Filter (EKF) is a popular way to localize such a robot and to estimate its configuration uncertainty during navigation. Consequently, we supply an EKF with simulated measurements in order to compute realistic uncertainties (in a four-dimensional space) during path planning. We show that our Safe-RRT algorithm, based upon Rapidly-exploring Random Trees (RRT), is an efficient way to find a path in the resulting seven-dimensional uncertain-configuration space.

On contact processes in continuum

Abstract: We introduce a continuous version of the contact model which is well known and widely studied in the lattice case. Under certain general assumptions on the infection spreading characteristics, we construct the contact process as a Markov process in the configuration space of the system.

Manifolds and Metrics in the Relative Spacecraft Motion Problem

Abstract: This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing the Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and noncommensurable mean motions. A number of analytic solutions as well as useful examples are provided, illustrating the calculated bounds. A few particular cases that yield simple solutions are given. Nomenclature a = semimajor axis E = eccentric anomaly E = follower orbit e = eccentricity F = follower perifocal frame f = true anomaly I = inertial frame i = inclination Jk = Bessel function L = leader-fixed frame M = mean anomaly n = mean motion n0 = fundamental frequency R = leader position vector R = relative motion invariant manifold r = follower position vector W = distance function α = normalized semimajor axis μ = gravitational constant ρ = relative position vector � = right ascension of the ascending node ω = argument of periapsis ω = angular velocity vector |·| = vector norm �·� = signal norm Superscripts � = leader ∗ = relative orbital element

Stability conditions and the braid group

Abstract: We find stability conditions [6, 3] on some derived categories of differential graded modules over a graded algebra studied in [12, 10]. This category arises in both derived Fukaya categories and derived categories of coherent sheaves. This gives the first examples of stability conditions on the A-model side of mirror symmetry, where the triangulated category is not naturally the derived category of an abelian category. The existence of stability conditions, however, gives many such abelian categories, as predicted by mirror symmetry. In our examples in 2 dimensions, we completely describe a connected component of the space of stability conditions. It is the universal cover of the configuration space C k+1 of k + 1 points in C with centre of mass zero, with deck transformations the braid group action of [10, 15]. This gives a geometric origin for these braid group actions and their faithfulness, and axiomatises the proposal for stability of Lagrangians in [18] and the example proved by mean curvature flow in [19].

On the metrical properties of the configuration space

Abstract: We study some topological and metrical properties of configuration spaces. In particular, we introduce a family of metrics on the configuration space Γ, which makes it a Polish space. Compact functions on Γ are also considered. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Generalized penetration depth computation

Abstract: Penetration depth (PD) is a distance metric that is used to describe the extent of overlap between two intersecting objects. Most of the prior work in PD computation has been restricted to translational PD, which is defined as the minimal translational motion that one of the overlapping objects must undergo in order to make the two objects disjoint. In this paper, we extend the notion of PD to take into account both translational and rotational motion to separate the intersecting objects, namely generalized PD. When an object undergoes rigid transformation, some point on the object traces the longest trajectory. The generalized PD between two overlapping objects is defined as the minimum of the longest trajectories of one object under all possible rigid transformations to separate the overlapping objects.We present three new results to compute generalized PD between polyhedral models. First, we show that for two overlapping convex polytopes, the generalized PD is same as the translational PD. Second, when the complement of one of the objects is convex, we pose the generalized PD computation as a variant of the convex containment problem and compute an upper bound using optimization techniques. Finally, when both the objects are non-convex, we treat them as a combination of the above two cases, and present an algorithm that computes a lower and an upper bound on generalized PD. We highlight the performance of our algorithms on different models that undergo rigid motion in the 6-dimensional configuration space. Moreover, we utilize our algorithm for complete motion planning of polygonal robots undergoing translational and rotational motion in a plane. In particular, we use generalized PD computation for checking path non-existence.

Nonpositive Curvature and Pareto Optimal Coordination of Robots

Abstract: Given a collection of robots sharing a common environment, assume that each possesses a graph (a one-dimensional complex also known as a roadmap) approximating its configuration space and, furthermore, that each robot wishes to travel to a goal while optimizing elapsed time. We consider vector-valued (or Pareto) optima for collision-free coordination on the product of these roadmaps with collision-type obstacles. Such optima are by no means unique: in fact, continua of Pareto optimal coordinations are possible. We prove a finite bound on the number of optimal coordinations in the physically relevant case where all obstacles are cylindrical (i.e., defined by pairwise collisions). The proofs rely crucially on perspectives from geometric group theory and CAT(0) geometry. In particular, the finiteness bound depends on the fact that the associated coordination space is devoid of positive curvature. We also demonstrate that the finiteness bound holds for systems with moving obstacles following known trajectories.

Nonequilibrium Glauber-type dynamics in continuum

Abstract: We construct the nonequilibrium Glauber dynamics as a Markov process in configuration space for an infinite particle system in continuum with a general class of initial distributions. This class we define in terms of correlation functions bounds and it is preserved during the Markov evolution we constructed.

D matrix analysis of the Renner-Teller effect: An accurate three-state diabatization for NH2

Abstract: Some time ago we published our first article on the Renner-Teller (RT) model to treat the electronic interaction for a triatomic molecule [J. Chem. Phys. 124, 081106 (2006)]. The main purpose of that Communication was to suggest considering the RT phenomenon as a topological effect, just like the Jahn-Teller phenomenon. However, whereas in the first publication we just summarized a few basic features to support that idea, here in the present article, we extend the topological approach and show that all the expected features that characterize a three (multi) state RT-type'3 system of a triatomic molecule can be studied and analyzed within the framework of that approach. This, among other things, enables us to employ the topological D matrix [Phys. Rev. A 62, 032506 (2000)] to determine, a priori, under what conditions a three-state system can be diabatized. The theoretical presentation is accompanied by a detailed numerical study as carried out for the HNH system. The D-matrix analysis shows that the two original electronic states 2A1 and 2B1 (evolving from the collinear degenerate Pi doublet), frequently used to study this Renner-Teller-type system, are insufficient for diabatization. This is true, in particular, for the stable ground-state configurations of the HNH molecule. However, by including just one additional electronic state--a B state (originating from a collinear Sigma state)--it is found that a rigorous, meaningful three-state diabatization can be carried out for large regions of configuration space, particularly for those, near the stable configuration of NH2. This opens the way for an accurate study of this important molecule even where the electronic angular momentum deviates significantly from an integer value.

Abstracting Vehicle Shape and Kinematic Constraints from Obstacle Avoidance Methods

Abstract: Most obstacle avoidance techniques do not take into account vehicle shape and kinematic constraints. They assume a punctual and omnidirectional vehicle and thus they are doomed to rely on approximations when used on real vehicles. Our main contribution is a framework to consider shape and kinematics together in an exact manner in the obstacle avoidance process, by abstracting these constraints from the avoidance method usage. Our approach can be applied to many non-holonomic vehicles with arbitrary shape. For these vehicles, the configuration space is three-dimensional, while the control space is two-dimensional. The main idea is to construct (centred on the robot at any time) the two-dimensional manifold of the configuration space that is defined by elementary circular paths. This manifold contains all the configurations that can be attained at each step of the obstacle avoidance and is thus general for all methods. Another important contribution of the paper is the exact calculus of the obstacle representation in this manifold for any robot shape (i.e. the configuration regions in collision). Finally, we propose a change of coordinates of this manifold so that the elementary paths become straight lines. Therefore, the three-dimensional obstacle avoidance problem with kinematic constraints is transformed into the simple obstacle avoidance problem for a point moving in a two-dimensional space without any kinematic restriction (the usual approximation in obstacle avoidance). Thus, existing avoidance techniques become applicable. The relevance of this proposal is to improve the domain of applicability of a wide range of obstacle avoidance methods. We validated the technique by integrating two avoidance methods in our framework and performing tests in the real robot.

Partitioning memory mapped device configuration space

Abstract: Embodiments of apparatuses, methods, and systems for partitioning memory mapped device configuration space are disclosed. In one embodiment, an apparatus includes a configuration space address storage location, an access map storage location, and addressing logic. The configuration space address storage location is to store a pointer to a memory region to which transactions to configure devices in a partition of a partitioned system are addressed. The access map storage location is to store an access map or a pointer to an access map. The addressing logic is to use the access map to determine whether a configuration transaction from a processor to one of the devices is to be allowed.

Combinatorial models for real configuration spaces and En-operads

Abstract: We define several partially ordered sets with the equivariant homotopy type of real configuration spaces F (Rn, p). The main tool is a general method for constructing En-suboperads of a given E∞-operad by appropriate cellular subdivision.

Dynamic Textures Synthesis as Nonlinear Manifold Learning and Traversing

Abstract: We formulate the problem of dynamic texture synthesis as a nonlinear manifold learning and traversing problem. We characterize dynamic textures as the temporal changes in spectral parameters of image sequences. For continuous changes of such parameters, it is commonly assumed that all these parameters lie on or close to a low-dimensional manifold embedded in the original configuration space. For complex dynamic data, the manifolds are usually nonlinear and we propose to use a mixture of linear subspaces to model a nonlinear manifold. These locally linear subspaces are further aligned within a global coordinate system. With the nonlinear manifold being globally parameterized, we overcome motion discontinuity problems encountered in switching linear models and dynamics. We present a nonparametric method to describe the complex dynamics of data sequences on the manifold. We also apply such approach to dynamic spatial parameters such as motion capture data. The experimental results suggest that our approach is able to synthesize smooth, complex dynamic textures and human motions, and has potential applications to other dynamic data synthesis problems.

Geodesics and Killing tensors in mechanics

Abstract: Killing tensors give polynomial constants of the geodesic motion. The trajectories of a conservative mechanical system correspond to geodesics when the kinetic energy metric is conformally scaled to the Jacobi metric. Alternatively, the trajectories may be related to geodesics of some higher-dimensional warped product manifold. These two different ways of relating mechanical trajectories to geodesics are reviewed and compared. It is shown how a relation between Killing tensors on configuration space and the potential gives rise to Killing tensors on both the Jacobi and warped product manifolds.

Dynamic Path Planning for a 7-DOF Robot Arm

Abstract: We present an on-line, robust, and efficient path planner for the redundant Mitsubishi PA-10 arm with 7 degrees of freedom (DOF) in non-stationary environments. Because of the specific kinematic model of the arm, path planning can be first reduced to a redundant 6-DOF problem in a 5D configuration space, which can be further decomposed into two problems: (i) 3D position planning in Cartesian space and (ii) planning in a 3D space composed of two orientation angles and an explicit parameterization of the arms redundancy. Position and orientation planning are interweaving and performed "on-the-fly" without explicit global knowledge of the environment using two instances of the dynamic wave expansion neural network (DWENN), an effective method for path generation in arbitrarily changing environments. The dynamic and explorative nature of the DWENN algorithm allows to treat stationary and dynamic obstacles in a unified manner. Through a number of simulative tests, we show that the planner is capable of reaching both a satisfactory robustness level and real-time performance, as required by many practical applications.

Relational particle models. II. Use as toy models for quantum geometrodynamics

Abstract: Relational particle models are employed as toy models for the study of the problem of time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape space of these models are close analogues from various perspectives of superspace and conformal superspace, respectively. The geometry of these spaces and quantization thereupon is presented. A quantity that is frozen in the scale-invariant relational particle model is demonstrated to be an internal time in a certain portion of the relational particle reformulation of Newtonian mechanics. The semiclassical approach for these models is studied as an emergent time resolution for these models, as are consistent records approaches.

Solidity of viscous liquids. IV. Density fluctuations.

Abstract: This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event a jump between two energy minima in configuration space are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k space of the form 0+ Dk 2 with D0a 2 where a is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian free energy may be taken to be ultralocal. As an illustration of the theory the case with the simplest nontrivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an 1/2 decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed.

Hybrid Routhian reduction of Lagrangian hybrid systems

Abstract: This paper extends Routhian reduction to a hybrid setting, i.e., to systems that display both continuous and discrete behavior. We begin by considering a Lagrangian together with a configuration space with unilateral constraints on the set of admissible configurations. This naturally yields the notion of a hybrid Lagrangian, from which we obtain a Lagrangian hybrid system in a way analogous to the association of a Lagrangian vector field to a Lagrangian. We first give general conditions on when it is possible to reduce a cyclic Lagrangian hybrid system, and explicitly compute the reduced Lagrangian hybrid system in the case when it is obtained from a cyclic hybrid Lagrangian.

Controlling the trajectory of an effector

Abstract: The invention refers to a method for controlling the effector trajectory from a current state to a target state First invariant control parameters of the trajectory are determined The effector trajectory is then represented in a task description being void of the invariant control parameters The effector trajectory is controlled on the basis of this task description The invention further refers to a method for controlling the effector trajectory wherein the effector trajectory is calculated by mapping increments from a control parameter space on a configuration space The dimensional difference between the configuration space and the control parameter space leaves redundant degrees of freedom of a Null space The degrees of freedom of the Null space are increased using a task description being void of invariant control parameters The invention further refers to a respective computer software program product, a manipulator, an actuated camera system, a robot comprising one or more manipulators and an automobile equipped with a driver support system

Topology preserving approximation of free configuration space

Abstract: We present a simple algorithm for approximating the free configuration space of robots with low degrees of freedom (DOFs). We represent the free space as an arrangement of contact surfaces. We approximate the free space using an adaptive volumetric grid that is computed by performing simple geometric tests on the contact surfaces. We use an isosurface extraction algorithm to compute a piecewise-linear approximation to the boundary of the free space. We prove that our approximation is topologically equivalent to the exact free space boundary. We also ensure that our approximation is geometrically close to the exact free space boundary by bounding its two-sided Hausdorff error. We have applied our algorithm to compute the free configuration space for the following instances: (1) a 2D polygonal robot with translational and rotational DOFs navigating among polygonal obstacles, and (2) a 3D polyhedral robot translating among polyhedral obstacles. In practice, our algorithm works well on robots with three DOFs