A New Method for Motion Planning of Rotating Bodies under Multiple Constraints

A new approach to time-optimal trajectory planning with torque and jerk limits for robot

A unified modeling approach for rotating flexible shaft-disk systems with general boundary and coupling conditions

During task execution by a space manipulator, many factors need to be considered, such as joint motion range, external environment interference, running speed and task time. Studying the motion planning strategy under multi-constraint conditions is important for optimizing the task flow of the manipulator and improving the planning autonomy. Aiming at this, this paper proposes a method based on a hierarchical task network which has the ability to connect non-adjacent nodes of topology when generating the best path; it also carries out the control simulation of traditional path planning of a manipulator for typical tasks and the latter two working conditions using an optimal task planning method. The results show that this method is effective for realizing the Cartesian spatial task planning of a manipulator under multiple constraints and has important on-orbit application significance for improving the continuous autonomy of task completion.

In the case that the total angular momentum conservation about the system center of mass, a torque-free spacecraft system with space manipulators becomes the nonholonomic control system. Due to the nonholonomic characteristic, the motion planning and control of a nonholonomic system is much more difficult than that of a conventional. In terms of the nonholonomic characteristic, the three-dimensional attitude control problem of the free floating space manipulators is investigated. The mathematical model of attitude control of rigid spacecraft with space manipulators is obtained. The control problem of the spacecraft attitude becomes a motion planning problem for a drift free control system. The control input rule is expressed by Fourier orthonormal basis and coefficient vector. Based on the optimal motion planning, the particle swarm optimization algorithm is proposed for free floating space manipulators. The results of numerical simulation indicate that this approach is effective for the motion planning problem of space manipulators.

SUMMARYA novel method to solve the minimum‐time anti‐swing motion planning problem for cranes based on the use of linear programming is proposed. It is shown that its solution can be obtained by solving a sequence of fixed‐time maximum‐range linear programming problems. A convergence proof is presented. A classical kinematical model for which the trolley acceleration is the control variable is used. The crane motion equations are discretized in time assuming that the control variable is piecewise constant. Inequality constraints on both trolley speed and acceleration are included to represent physical bounds associated to the electromechanical driving system. The load and the trolley are required to be at rest both at the initial and at the final times. The load cable length as a function of time is assumed given. The ease of both the formulation and the solution of the problem is in contrast with the traditional two‐point boundary value problem associated to the Pontryagin's minimum principle. Copyright © 2012 John Wiley & Sons, Ltd.

The most general admissible boundary conditions are derived for an idealized Aharonov–Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the Aharonov–Bohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the Aharonov–Bohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail.

A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.

Currently used methods for the analysis of contingency tables with log-linear models and their extensions are essentially a way to subject the parameters of the saturated model to a set of linear constraints. However, in many contexts, expecially when a subset of the variables are ordinal, it would be very useful to be able to consider also linear inequality constraints. In this paper we show how to extend previous models for contingency tables by considering simultaneously both equality constraints. We also give a self contained discussion of the problem of testing equality and inequality constraints in the context of contingency tables analysis.

The conventional no-slip boundary condition does not always hold in several fluid flow applications and must be replaced with appropriate slip conditions according to the wall and fluid properties. However, not only slip boundary conditions are still a subject of discussion among fluid dynamicists, but also their numerical treatment is far from being well-developed, particularly in the context of very high-order accurate methods. The complexity of these conditions significantly increases when the boundary is not aligned with the chosen coordinate system and, even more challenging, when the fluid slips along a curved boundary. The present work proposes a simple and efficient numerical treatment of general slip boundary conditions on arbitrary curved boundaries for three-dimensional fluid flow problems governed by the incompressible Navier–Stokes equations. In that regard, two critical challenges arise: (i) achieving very high-order of convergence with arbitrary curved boundaries for the classical no-slip boundary conditions and (ii) extending the developed numerical techniques to impose general slip boundary conditions. The conventional treatment of curved boundaries relies on generating curved meshes to eliminate the geometrical mismatch between the physical and computational boundaries and achieve high-order of convergence. However, such an approach requires sophisticated meshing algorithms, cumbersome quadrature rules on curved elements, and complex non-linear transformations. In contrast, the reconstruction for off-site data (ROD) method handles arbitrary curved boundaries approximated with linear piecewise elements while employing polynomial reconstructions with specific linear constraints to fulfil the prescribed boundary conditions. For that purpose, the general slip boundary conditions are reformulated on a local orthonormal basis to allow a straightforward application of the ROD method with scalar boundary conditions. The Navier–Stokes equations are discretised with a staggered finite volume method, and the numerical fluxes are computed solely on the polygonal mesh elements. Several benchmark test cases of fluid flow problems in non-trivial three-dimensional curved domains are addressed and confirm that the proposed method effectively achieves up to the eighth-order of convergence.

Nonlinear dynamics of straight fluid-conveying pipes with general boundary conditions and additional springs and masses

The three most commonly used boundary conditions for charged colloidal systems are constant charge (insulator), constant potential (conducting electrode) and charge regulation (ionizable groups at the surface). It is usually believed that the charge regulation is a generalized boundary condition that reduces in some specific limits to either constant-charge or constant-potential boundary conditions. By computing the disjoining pressure between two symmetric planes for these three boundary conditions, both numerically (for all inter-plate separations) and analytically (for small inter-plate separations), we show that this is not, in general, the case. In fact, the limit of charge regulation is a separate boundary condition, yielding a disjoining pressure with a different characteristic separation scaling. Our findings are supported by several examples demonstrating that the disjoining pressure at small separations for the charge regulation boundary condition depends on the details of the dissociation/association process.

Static and dynamic analysis of two-phase peridynamic one-dimensional systems is thoroughly investigated in this paper for various boundary conditions by exact and numerical approaches. Such a nonlocal study concerns the axial or torsional responses of two-phase peridynamic rods or the behavior of a two-phase peridynamic string. For a normalized exponential kernel, the integro-differential equation of the two-phase peridynamic problem can be converted as a linear higher-order differential equation with constant coefficients. Exact static solutions of fixed–fixed and fixed–free two-phase peridynamic axial rod (TPPAR) under uniform distributed loading and concentrated force are analytically derived. It is shown that the pure peridynamic rod problem can be ill-posed due to a conflict between the natural boundary condition and the peridynamic constitutive boundary condition. The two-phase peridynamic problem may be justified from physical arguments, and is also seen as a regularized peridynamic problem. The exact eigen-frequencies of the two-phase peridynamic rods are also analytically obtained for various boundary conditions, including fixed–free, fixed–fixed or free–free boundary conditions. These theoretical approaches are corroborated by numerical investigations based on Finite Difference Method (FDM), Finite Element Method (FEM), exact FEM and variational iterative methods. Two FDM schemes are presented for the statics and the vibration of two-phase peridynamic rods, with convergence orders of 1 and 2, respectively. Moreover, three different FE procedures are proposed as: (1) FEM for direct solving the integro-differential equations of two-phase peridynamic one-dimensional system, (2) FEM for discretizing the pure differential equations, and (3) Exact FEM to obtain both the exact stiffness matrix and exact dynamic stiffness matrix of two-phase peridynamic one-dimensional system, based on Eisenberger’s methodology. The order of convergence for the first and the second proposed FEM is equal to 2 and 4, according to the type of selected finite elements. Moreover, the third proposed FEM based on the exact shape function of the peridynamic problem gives the exact solution from one single FEM element. In addition, the variational iterative method of Stodola–Vianello is successfully applied to the two-phase peridynamic eigenvalue problems.

Efficient spectral-Galerkin methods for polar and cylindrical geometries

Systems of linear fuzzy constraints

This paper explores several approaches for articulated-pose estimation, assuming that video-rate depth information is available, from either stereo cameras or other sensors. We use these depth measurements in the traditional linear brightness constraint equation, as well as in a depth constraint equation. To capture the joint constraints, we combine the brightness and depth constraints with twist mathematics. We address several important issues in the formation of the constraint equations, including updating the body rotation matrix without using a first-order matrix approximation and removing the coupling between the rotation and translation updates. The resulting constraint equations are linear on a modified parameter set. After solving these linear constraints, there is a single closed-form non-linear transformation to return the updates to the original pose parameters. We show results for tracking body pose in oblique views of synthetic walking sequences and in moving-camera views of synthetic jumping-jack sequences. We also show results for tracking body pose in side views of a real walking sequence.