In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as "hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.
We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.
Let $\Omega$ be a bounded open subset of $\mathbb{R}^{n}$, $n>2$. In $\Omega$ we deduce the global differentiability result \[u \in H^{2}(\Omega, \mathbb{R}^{N}) \] for the solutions $u \in H^{1}(\Omega, \mathbb{R}^{n})$ of the Dirichlet problem \[ u-g \in H^{1}_{0}(\Omega, \mathbb{R}^{N}), -\sum _{i}D_{i}a^{i}(x,u,Du)=B_{0}(x,u,Du) \] with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems.
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.
There are several ways that can be implemented in a vehicle tracking system such as recognizing a vehicle color, a shape or a vehicle plate itself. In this paper, we will concentrate ourselves on recognizing a vehicle on a highway through vehicle plate recognition. Generally, recognizing a vehicle plate for a toll-gate system or parking system is easier than recognizing a car plate for the highway system. There are many cameras installed on the highway to capture images and every camera has different angles of images. As a result, the images are captured under varied imaging conditions and not focusing on the vehicle itself. Therefore, we need a system that is able to recognize the object first. However, such a system consumes a large amount of time to complete the whole process. To overcome this drawback, we installed this process with grid computing as a solution. At the end of this paper, we will discuss our obtained result from an experiment.
The split graph $K_r+\overline {K_s}$ on $r+s$ vertices is denoted by $S_{r,s}$. A non-increasing sequence $\pi =(d_1,d_2,\ldots ,d_n)$ of nonnegative integers is said to be potentially $S_{r,s}$-graphic if there exists a realization of $\pi $ containing $S_{r,s}$ as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for $\pi $ to be potentially $S_{r,s}$-graphic. They are extensions of two theorems due to A. R. Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series 4 (1979), 251–267 and An Erdős-Gallai type result on the clique number of a realization of a degree sequence, unpublished).
Slurry transport in horizontal and vertical pipelines is one of the major means of transport of sands and gravels in the dredging industry. There exist 4 main flow regimes, the fixed or stationary bed regime, the sliding bed regime, the heterogeneous flow regime and the homogeneous flow regime. Of course the transitions between the regimes are not very sharp, depending on parameters like the particle size distribution. The focus in this paper is on the homogeneous regime. Often the so called equivalent liquid model (ELM) is applied, however many researchers found hydraulic gradients smaller than predicted with the ELM, but larger that the hydraulic gradient of liquid. Talmon (2011, 2013) derived a fundamental equation (method) proving that the hydraulic gradient can be smaller than predicted by the ELM, based on the assumption of a particle free viscous sub-layer. He used a 2D velocity distribution without a concentration distribution. In this paper 5 methods are described (and derived) to determine the hydraulic gradient in homogeneous flow, of which the last method is based on pipe flow with a concentration distribution. It appears that the use of von Driest (Schlichting, 1968) damping, if present, dominates the results, however applying a concentration distribution may neutralise this. The final equation contains both the damping and a concentration distribution giving the possibility to calibrate the constant in the equation with experimental data. The final equation is flexible and gives a good match with experimental results in vertical and horizontal pipelines for a value of ACv = 1.3. Data of horizontal experiments Dp = 0.05-0.30 m, d = 0.04 mm, vertical experiments Dp = 0.026 m, d = 0.125, 0.345, 0.560, and 0.750 mm.
This paper presents an observation on adaptation of Hopfield neural network dynamics configured as a relaxation-based search algorithm for static optimization. More specifically, two adaptation rules, one heuristically formulated and the second being gradient descent based, for updating constraint weighting coefficients of Hopfield neural network dynamics are discussed. Application of two adaptation rules for constraint weighting coefficients is shown to lead to an identical form for update equations. This finding suggests that the heuristically-formulated rule and the gradient descent based rule are analogues of each other. Accordingly, in the current context, common sense reasoning by a domain expert appears to possess a corresponding mathematical framework.