Constraint Surface Research Articles

Accurate Estimation of ICA Weight Matrix by Implicit Constraint Imposition Using Lie Group

This paper presents a new stochastic algorithm to optimize the independence criterion-mutual information-among multivariate data using local, global, and hybrid optimizers, in conjunction with techniques involving a Lie group and its corresponding Lie algebra, for implicit imposition of the orthonormality constraint among the estimated sources. The major advantage of the proposed algorithm is the increased accuracy with which the weight matrix in the independent component analysis (ICA) model is estimated, compared to conventional schemes. When the local optimizer with Lie group techniques and the fast fixed-point (fastICA) algorithm were experimented by inputting the same set of random vectors, the former method superseded the conventional one by producing accurate weight matrix estimates in a majority of the test cases. Importantly, in our approach, the use of a Lie group to "lock" the weight matrix estimates onto the constraint surface enabled easy realization of the hybrid optimizers to yield near-global-optimum solutions consistently in most of the test cases, compared to well-known global optimizers. The inherent computational overhead in the hybrid optimizers was lowered by preprocessing the input data and periodically integrating the local optimizers with the global one. The proposed algorithms were applied to six-dimensional multispectral satellite image data to emphasize their usefulness in terms of accurate ICA weight matrix estimation.

Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

Hybrid Adaptive Vision—Force Control for Robot Manipulators Interacting with Unknown Surfaces

A hybrid control scheme based on adaptive visual servoing and direct force control is proposed for robot manipulators to perform interaction tasks on smooth surfaces. The camera parameters, as well as the constraint surface, are considered to be uncertain. A fixed camera with optical axis non-perpendicular to the robot workspace is used for position control, while a force sensor mounted on the robot wrist is used for force regulation. In order to solve the interaction problem on unknown surfaces, a method is developed to estimate the constraint geometry and keep the end-effector orthogonal to the surface at the contact point, during the task execution. Experimental results are presented to illustrate the performance and feasibility of the proposed scheme.

Collision-free construction of animated feathers using implicit constraint surfaces

We present a scheme for constructing complex feather geometry suitable for feature animation. The key points of our approach include the use of a potential field derived from guide geometry and an implicit constraint surface to create nonpenetrating feather geometry. Our method is frame independent and produces visually smooth animation that is free from popping and other visual artifacts. We provide details of the implementation and examples of the technique applied to an animated character with several thousand feathers.

ロボット手先・拘束面間のクーロン摩擦による拘束力干渉問題とその解決法(機械力学,計測,自動制御)

ロボット手先・拘束面間のクーロン摩擦による拘束力干渉問題とその解決法(機械力学,計測,自動制御)

Vision-based neural network control for constrained robots with constraint uncertainty

Research on hybrid position and force control of robot manipulators has assumed that the structure of constraint surface is known exactly. However, in many force control applications of robot, the exact model of the constraint surface cannot be obtained. In the presence of the constraint uncertainty, it is difficult to analyse the stability of the force control system. A vision-based neural network controller is proposed for robots with uncertain kinematics, dynamics and constraint surface. The proposed adaptive neural network controller does not require the exact model and structure of the constraint surface as assumed in the literature. It is shown that stability can be achieved with the uncertainties. Simulation results are presented to illustrate the performance of the proposed controller.

Covariance and time regained in canonical general relativity

Canonical vacuum gravity is expressed in generally covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance and ideas developed within history phase-space formalisms in [I. Kouletsis and K. V. Kuchar, Phys. Rev. D 65, 125026 (2002)], [K. Savvidou, Classical Quantum Gravity 18, 3611 (2001)], [K. Savvidou, Classical Quantum Gravity 21, 615 (2004)], [K. Savvidou, Classical Quantum Gravity 21, 631 (2004)], the time mapping T: M{yields}R and the space mapping X: M{yields}{sigma} that define the Dirac-Arnowitt-Deser-Misner (ADM) foliation are incorporated into the framework of the Hilbert variational principle. The resulting canonical action encompasses all individual Dirac-ADM actions, corresponding to different choices of foliating vacuum spacetimes by spacelike hypersurfaces. The equal-time phase space P=(g{sub ij},p{sup ij},Y{sup {alpha}},P{sub {alpha}}) includes the embeddings Y{sup {alpha}}: {sigma}{yields}M and their conjugate momenta P{sub {alpha}}. It is constrained by eight first-class constraints. The constraint surface C is determined by the super-Hamiltonian and supermomentum constraints of vacuum gravity and the vanishing of the embedding momenta. Deformations of the time and space mappings, {delta}T and {delta}X, and spacetime diffeomorphisms, V(set-membership sign)LDiffM, induce symplectic diffeomorphisms of P. While the generator D{sub ({delta}T,{delta}X)} of deformations depends on allmore » eight constraints, the generator D{sub V} of spacetime diffeomorphisms depends only on the embedding momentum constraints. As a result, spacetime observables, namely, dynamical variables F on P that are invariant under spacetime diffeomorphisms, (F,D{sub V})|{sub C}=0, are not necessarily invariant under the deformations of the mappings, (F,D{sub ({delta}T,{delta}X)})|{sub C}{ne}0, nor are they constants of the motion, (F,{integral}d{sup 3}xH)|{sub C}{ne}0. Dirac observables form only a subset of spacetime observables that are invariant under the transformations of T and X and do not evolve in time. In this generally covariant framework, the conventional interpretation of the canonical theory, due to Bergmann and Dirac, amounts to postulating that the transformations of the reference system (T,X) have no measurable consequences; i.e., that all first-class constraints generate gauge transformations. If this postulate is not deemed necessary, canonical gravity admits no classical problem of time.« less

Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators

Most studies on the coordination of multiple mobile manipulators system assume exact knowledge of system kinematics and dynamics, and deal only with motion tracking control. However, actual applications may involve tasks in which multiple coordinated mobile manipulators system is required to keep contact on the contour of the constraint surface in tasks. In this paper, we consider multiple mobile manipulators grasping a rigid object in contact with deformable working surfaces, whose geometric and physical model is unknown. The contact forces are nonlinear and unknown. Adaptive neuro-fuzzy (NF) control for coordinated mobile manipulators is proposed for robust force/motion tracking on the constraint surface while it is in motion. The control law is decoupled in three subspaces and adaptive tuning mechanism is developed to deal with the uncertain environmental constraints, disturbances, and unknown robotic dynamics. The proposed adaptive NF hybrid force/motion controller guarantees robust tracking of the desired motion and force trajectories. Simulation examples are presented to illustrate the results.

On the arc-length and other quadratic control methods: Established, less known and new implementation procedures

The use of control methods to compute geometrically nonlinear equilibrium paths is now well established. This paper reviews the arc-length method and other quadratic control methods, discussing implementation issues like (i) the root selection at the predictor and corrector stages, (ii) the use of partial corrections and the conjugation of arc-length and line search procedures, (iii) switching from spherical predictions to cylindric corrections, (iv) adopting constraint surfaces not centred at the last computed equilibrium point, (v) aligning elipsoidal constraint surfaces with the equilibrium path and (vi) the use of contractions from a plane surface to the quadratic surface. While most of these issues are not new, it seems useful to revisit some valuable techniques that a large number of researchers are unaware of – thus, they are presented in an unified way and geometric interpretations are provided whenever possible. Some original contributions are also made, mainly concerning the elipsoidal constraint surfaces. The paper concludes with the presentation of a few numerical tests to assess and compare the efficiency of the various implementations addressed.

Robust scheme of global parallel force/position regulators for robot manipulators under environment uncertainty

A simple robust scheme of parallel force/position control is proposed in this paper to deal with two problems for non-planar constraint surface and nonlinear mechanical feature of environment: i) uncertainties in environment that are usually not available or difficult to be determined in most practical situations; ii) stability problem or/and integrator windup due to the integration of force error in the force dominance rule in parallel force/position control. It shows that this robust scheme is a good alternative for anti-windup. In the presence of environment uncertainties, global asymptotic stability of the resulting closed-loop system is guaranteed; it also shows robustness of the proposed controller to uncertain environment with complex characteristics. Finally, numerical simulation verifies results via contact task of a two rigid-links robot manipulator.

幾何学的拘束を受けるマニピュレータの学習適応制御

When an endpoint of a manipulator is moving in touch with a rigid smooth surface, the manipulator should be controlled to achieve both a desired position trajectory of the endpoint and a desired contact force at the contact point. In this paper, we deal with a hybrid controller of repetitive learning control and model-based adaptive control for geometrically constrained robot manipulator. The convergence of joint angular errors and contact force errors is proved under an appropriate initial condition and the smoothness of the constraint surface. Furthermore, by the simulation experiment, we show that the proposed hybrid controller makes 2-link constrained manipulator track a desired position and a desired constraint force trajectory

Power Efficiency of the Rotational-to-Linear Infinitely Variable Cobotic Transmission

Abstract Cobots are a class of robots that use infinitely variable transmissions to develop high fidelity programmable constraint surfaces. Cobots consume very little electrical power even when resisting high forces, and their transmissions are highly power efficient across a broad range of transmission ratios. We have recently introduced the Cobotic Hand Controller, a haptic display that illustrates the high dynamic range and low-power consumption achievable by cobots. In this paper, we present models of the rotational-to-linear rolling contact transmissions utilized in the Cobotic Hand Controller. We compare their efficiency to fixed-ratio gear trains. We also compare the overall power efficiency of the cobotic architecture to the power efficiency of a conventional electromechanical actuation scheme, for both constant and dynamic power flows. The cobotic architecture is shown to be more efficient at frequencies and power levels characteristic of voluntary human motions.

Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace

This paper deals with an optimal dimensional synthesis method of the DELTA parallel robot for a prescribed workspace. The objective function is based on the mathematical concept of the power of a point with respect to bounding constraint surfaces. A genetic algorithm based method was used to solve this problem. The proposed method is simple and was shown to be effective in finding the dimensions of the DELTA robot having the smallest workspace containing a prespecified region in space. These dimensions were also determined in the case where the user defines a safety region, to avoid points in the prescribed workspace being on the boundary of the DELTA robot’s actual workspace.

Oblique impact of inflated balls at large deflections

A planar theory for oblique impact of thin-walled spherical balls against a rough rigid surface has been developed on the basis of an assumed deformation field—an initially spherical ball is assumed to flatten against the constraint surface while the remainder of the ball remains undeformed. For inflated thin-walled balls, which are represented by these assumptions (basketballs, soccer balls, volleyballs, etc) the normal reaction force acting on the flattened contact patch is predominately due to the internal gas pressure—the reaction due to shell bending is insignificant in comparison with this gas force. During impact of a thin-walled ball there also is a non-conservative momentum flux reaction that is caused by the flow of momentum into and out-of the flattened contact patch. If the ball is translating as well as rotating about an axis perpendicular to the plane of motion, the distribution of the normal component of velocity for material entering and exiting the flattened contact patch results in a distribution of momentum flux force intensity around the periphery of the contact patch and consequently, a momentum flux torque acting on the flattened sphere. The effect of these reaction forces and torque on oblique impact of thin-walled spherical balls is calculated as a function of the ball deflection (or normal component of impact velocity). In comparison with rigid body calculations for oblique impact of a spinning ball against a rough surface at angles<45° from normal, the effect of maximum deflections as large as half the initial radius is to slightly accentuate the effect of friction on angle of rebound and moderately decrease the angular velocity of the ball. However, for angles >45° from normal, the final angular velocity can be as small as 40% of that predicted by rigid body theory. The most significant changes in rebound angle are for cases with initial backspin—a technique commonly used in many ball sports.

Visual servoing for constrained planar robots subject to complex friction

The theoretical framework and the experimental validation of a new image-based position-force control for planar robots are presented in this paper. This scheme produces simultaneous convergence of the constrained visual position and the contact force between the end effector and the constraint surface. Camera, robot, and the visual jacobian parameters are considered unknown. This approach is based on a new formulation of the orthogonalization principle used in the robot force control, termed the visual orthogonalization principle. This allows, under the framework of passivity, to yield a synergetic closed-loop system that fuses accordingly camera, encoder, and the force sensor signals. Furthermore, due to the technological limitations, it can be noticed that the visual servoing contact tasks are characterized by slow motion, typically with frequent velocity reversals along the constraint surface, thus, important friction problems arise at the joints and the contact points. Therefore, visual compensation of the complex dynamic joint friction and the viscous contact friction are also studied. A Linux real-time operating-system-based experimental system is implemented to visually drive a constrained direct-drive planar robot manipulator, equipped with six-axes JR3 force sensor and a digital fixed camera, thus proving the effectiveness of the proposed scheme

Design and implementation of a robust switching control scheme for a class of constrained robot tasks

The focus of the paper is on the design and real-time control implementation issues of a switching control scheme for a robot interacting with a constraint surface. One key aspect that is investigated is the effect of uncertainty in the location of the constraint surface. A switching controller that is robust to uncertainty in the location of the constraint surface is given; overall stability of the controller for a typical constrained robot task is shown. A strategy for real-time trajectory modification, which is required to compensate for the discrepancy in the a priori known location and the actual location of the constraint, is given. An experimental platform consisting of a planar robot manipulator equipped with a force sensor and a robotic surface finishing tool is described; typical experimental results for the manipulator following straight and circular surfaces are given for the proposed real-time implementation scheme. The proposed research can find applications in robotic surface finishing operations such as polishing, chamfering and deburring, etc.

A new approach to solve key issues in multi-step inverse finite-element method in sheet metal stamping

Multi-step inverse finite-element method (FEM) has been introduced to improve the accuracy of simulation in the sheet metal stamping. Moreover, it has also been used to try to obtain the strain distribution and shape of the blank in the intermediate steps. But there are two key problems which are essential for the realization of multi-step inverse FEM: the first one is the determination of initial solutions on the intermediate three-dimensional (3-D) configurations and the other is how to control the movement of nodes only on sliding constraint surfaces during Newton–Raphson iterations. In the study, the two questions above have been solved with our proposed methods: the former is obtained by mapping the arc-length of the final part onto intermediate sliding constraint surfaces with modified arc-length search method, and the latter is conducted by introducing an approach which is similar to that of contact search. The present inverse multi-step FEM has been realized and applied to a two-step deep drawing product. The obtained numerical results have been used to compare with that of incremental FEM to evaluate the effectiveness of the procedures proposed. Comparisons between multi-step inverse FEM and one-step inverse FEM have also been conducted to verify the effect of multi-step.

Methods of analytical mechanics for dynamics of the Kirchhoff elastic rod

A cross section of the rod is taken as object of investigation. The freedom of the section in free or constraint case is analyzed and the definition of virtual displacement of the section is given, which can be expressed by a variational operation. Assuming the variational and partial differential operations has commutativity, based on the hypothesis about surface constraint subjected to the rod, the freedom of the section on constraint surface is discussed and the equations satisfied by virtual displacements of the section are given. Combining D'Alembert principle and the principle of virtual work, D'Alembert-Lagrange principle is established. When constitutive equation of material of the rod is linear, the principle can be transformed to Euler-Lagrange form. From the principle, a dynamical equation in various forms such as Kirchhoff, Lagrange, Nielsen and Appell equation can be derived. For the case when a rod is subjected to a surface or a nonholonomic constraint, Lagrange equation with undetermined multipliers is obtained. Integral variational principle of dynamics of a super-thin elastic rod is also established, from which Hamilton principle formulation is obtained when the material of the rod is linear. Finally, canonical variables to describe the state of the section and Hamilton function are defined, and Hamilton canonical equation is derived. The analytical methods of dynamical modeling of a super-thin elastic rod have been constructed, which can serve as a theoretical framework of analytical dynamics of a super-thin elastic rod with two independent variables.

2P2-B18 速度指令形運動制御による3リンクアームの力制御

We propose that a manipulator using a spring that is a simple force-controlled end effector can perform operations, which need a static pressing force. This paper describes simulations and experiments of the hybrid position/force control of a horizontal three-link manipulator with a spring end effector. Tip position of the manipulator is controlled to follow the desired position trajectory along with the wall constraint surface and tip reaction force that is perpendicular to the wall is simultaneously controlled. Force control is performed by joint velocity control method using virtual desired trajectory corresponding to desired force.

Projector quantization method of systems with linearly dependent constraints

The local free coordinates on the constraint surface are obtained within symplectic projector method when the constraints are linearly dependent. One example is investigated in details.