A Neural Network Approach to the Frictionless Grasping Problem

This article presents a heuristic technique used for solving linear complementarity problems(LCP). Determination of minimum forces needed to firmly grasp an object by a multifingered robot gripper for different external force and finger positions is our proposed application. The contact type is assumed to be frictionless. The interaction in the gripper–object system is formulated as an LCP. A numerical algorithm (Lemke) is used to solve the problem [3]. Lemke is a direct deterministic method that finds exact solutions under some constraints. Our proposed neural network technique finds almost exact solutions in solvable positions, and very good solutions for positions that Lemke fails to find solutions. A new adaptive technique is used for training the neural network and it is compared with the standard technique. Mathematical analysis for the convergence of the proposed technique is presented.     

Numerical solution of large deformation problems involving stability and unilateral constraints

The present study is concerned with the numerical treatment of large deformation beam problems where stability as well as post-buckling behaviour is coupled with frictional contact constraints. The flexible beams are described according to a nonlinear rod-type theory which accounts for both finite rotations and large deformations. The contact conditions are introduced via a penalty function method. From these conditions we obtain a linear complementary problem (LCP) resulting from the variational inequality formulation. For the examination of the post-buckling behaviour the displacement control method is applied. Particular attention is paid to the development of the linear complementary problem combining with the computational strategy for tracing limit points. Finally, the modification algorithms of the linear complementary problem, in which the penalty factors have been eliminated, are proposed. The numerical techniques not only allow some limit points to be passed, but also guarantee the computational stability characteristics during the Newton-Raphson's iterative process. Numerical examples are presented that illustrate the performances of the proposed algorithms.     

An augmented Lagrangian optimization method for contact analysis problems, 2: numerical evaluation

The ALM2 solution procedure is evaluated by solving two simple contact analysis problems for different friction conditions. These example problems are devised to have closed form solutions. This way there is no uncertainty about the target solution for evaluation of the proposed algorithm as well as existing algorithms. The numerical results with ALM2 are compared with the analytical solutions as well as with the penalty, Lagrange multiplier and existing augmented Lagrangian methods. All the algorithms are analysed for stick and slip friction conditions. The example problems are used to show clearly the dependence of the existing solution methods on the number of load steps and penalty values. It is concluded that convergence of incremental solution schemes employed in these methods does not guarantee accuracy of the contact solution even with the use of solution enhancement schemes such as automatic load stepping and contact load prediction. The example problems are also used to demonstrate solution independence of the proposed ALM2 procedure from penalty values, and from the number of load steps. The proposed formulation for calculation of frictional forces and the ALM solution algorithm have worked quite well for the example problems. However, the algorithm needs to be developed and evaluated for more complex contact analysis problems.     

A gap element for three-dimensional elasto-plastic contact problems

A simple yet efficient contact algorithm with gap elements is developed to solve three-dimensional elasto-plastic contact problems without friction. A special gap element is presented, together with a stress invariance principle, to model the contact process. The solution is achieved through an iterative procedure which adjusts the modulus of the gap elements. The elasto-plastic solid element with variable nodes and nonconforming modes is employed for the effective and economic three-dimensional finite element analysis. The validity and performance of the proposed contact algorithm with gap elements are demonstrated through various numerical tests.     

Computation of force-closure grasps: an iterative algorithm

Computation of grasps with form/force closure is one of the fundamental problems in the study of multifingered grasping and dextrous manipulation. Based on the geometric condition of the closure property, this paper presents a numerical test to quantify how far a grasp is from losing form/force closure. With the polyhedral approximation of the friction cone, the proposed numerical test can be formulated as a single linear program. An iterative algorithm for computing optimal force-closure grasps, which is implemented by minimizing the proposed numerical test in the grasp configuration space, is also developed. The algorithm is computationally efficient and generally applicable. It can be used for computing form/force-closure grasps on 3-D objects with curved surfaces, and with any number of contact points. Simulation examples are given to show the effectiveness and computational efficiency of the proposed algorithm.     

American option pricing problem transformed on finite interval

We study the American option pricing linear complementarity problem (LCP), transformed on finite interval as it is initially defined on semi-infinite real axis. We aim to validate this transformation, investigating the well-posedness of the resulting problem in weighted Sobolev spaces. The monotonic penalty method reformulates the LCP as a semi-linear partial differential equation (PDE) and our analysis of the penalized problem results in uniform convergence estimates. The resulting PDE is further discretized by a fitted finite volume method since the transformed partial differential operator degenerates on the boundary. We show solvability of the semi-discrete and fully discrete problems. The Brennan–Schwarz algorithm is also presented for comparison of the numerical experiments, given in support to our theoretical considerations.     

A simple algorithm for three-dimensional finite element analysis of contact problems

This paper addresses the numerical solution of three-dimensional frictionless contact problems by a finite element method. The two-body contact problem is considered in the context of fully non-linear kinematics. The impenetrability constraint is satisfied via a classical penalty formulation. The contacting surfaces are discretized by means of projections of the interacting element faces onto suitably chosen flat surfaces. Attention is focused on the efficiency of the overall algorithm. Numerical simulations are conducted for a series of test problems to assess the performance of the proposed methodology.     

Parallel solution of contact shape optimization problems based on Total FETI domain decomposition method

An application of a variant of the parallel domain decomposition method that we call Total FETI or TFETI (Total Finite Element Tearing and Interconnecting) for the solution of contact problems of elasticity to the parallel solution of contact shape optimization problems is described. A unique feature of the TFETI algorithm is its capability to solve large contact problems with optimal, i.e., asymptotically linear complexity. We show that the algorithm is even more efficient for the solution of the contact shape optimization problems as it can exploit effectively a specific structure of the auxiliary problems arising in the semi-analytic sensitivity analysis. Thus the triangular factorizations of the stiffness matrices of the subdomains are carried out in parallel only once for each design step, the evaluation of the components of the gradient of the cost function can be carried out in parallel, and even the evaluation of each component of the gradient itself can be further parallelized using the standard TFETI scheme. Theoretical results which prove asymptotically linear complexity of the solution are reported and documented by numerical experiments. The results of numerical solution of a 3D contact shape optimization problem confirm the high degree of parallelism of the algorithm.     

Pose estimation-based path planning for a tracked mobile robot traversing uneven terrains

A novel path-planning algorithm is proposed for a tracked mobile robot to traverse uneven terrains, which can efficiently search for stability sub-optimal paths. This algorithm consists of combining two RRT-like algorithms (the Transition-based RRT (T-RRT) and the Dynamic-Domain RRT (DD-RRT) algorithms) bidirectionally and of representing the robot–terrain interaction with the robot’s quasi-static tip-over stability measure (assuming that the robot traverses uneven terrains at low speed for safety). The robot’s stability is computed by first estimating the robot’s pose, which in turn is interpreted as a contact problem, formulated as a linear complementarity problem (LCP), and solved using the Lemke’s method (which guarantees a fast convergence). The present work compares the performance of the proposed algorithm to other RRT-like algorithms (in terms of planning time, rate of success in finding solutions and the associated cost values) over various uneven terrains and shows that the proposed algorithm can be advantageous over its counterparts in various aspects of the planning performance.     

基于边权约束法实现接触问题多约束图剖分

为提高接触问题并行计算的效率,分析内力计算和接触计算过程的并行性,提出基于边权约束法构造接触多约束图的方法,对比和分析多约束图剖分算法和双重区域剖分算法的负载平衡和通信性能.数值实验表明,在典型二维模型中多约束图剖分算法的负载平衡性能略低于双重区域剖分算法,但仍可将负载不平衡度控制在较好的范围内,简化并行计算的通信过程,减少总通信量并降低动态通信量比例.     

评价ANSYS分析方法求解楔类接触问题的效果

采用什么样的数值分析方法才能高效、高精度和高可靠性地求解楔类接触是工程界非常关注的问题.剖析了ANSYS有限元中点面接触和面面接触算法的基本设置及注意事项.运用这两种算法求解了平面刚性和弹性楔类接触问题.然后与理论解进行对比分析,指出了这两种算法求解楔类接触问题的精度、可靠性、效率及适用范围.研究结果表明：点面接触算法的求解精度和可靠性比面面接触算法高,点面接触算法在应力集中的区域能得到较精确的结果;但是,点面接触算法的求解效率比面面接触算法低.虽然上述讨论基于平面问题,实际上这两种算法也可以应用于求解三维楔类接触、塑性和超弹性材料的楔类接触等问题.     

Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications

Summary In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional contact formulation is fully developed on the continuum setting and then a spatial (Galerkin projection) and temporal (time-stepping algorithm) discretization is applied. A contact pressure and temperature dependent thermal contact model has been used. A fractional step method arising from an operator split of the governing equations has been used to solve the coupled nonlinear system of equations, leading to a staggered solution algorithm. The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of coupled thermomechanical frictional contact problems.     

Quadratic programming method in numerical simulation of metal forming process

In this paper, a quadratic programming (QP) model based on a parametric variational principle is proposed for elastic–plastic (EP) finite element analysis of metal forming processes. The contact problem with friction between blank and tools is treated in the same way as in plastic analysis. The penalty factors, which are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of metal forming, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. The algorithms for contact analysis and plastic analysis are established in one frame and consistent with each other. Compared with the conventional EP FEM, the newly developed method requires no tedious iterative procedures, and has no convergence problems. To apply this method easily to simulation of metal forming, detailed forms of some key matrices or vectors for 2D FEM and 3D FEM are presented, and a parametric loading algorithm for the QP model is developed, which is suitable for QP problem with free variables, and can decrease memory cost by avoiding the introduction of additional slack variables and improve the solution efficiency to some extent. Finally the proposed QP model is validated by two examples, analysis of V-notched tension test and analysis of the drawing of a square box––one of the benchmarks proposed at NUMISHEET93. It can be seen that the accuracy of solution of the new EP FEM based on QP is better than that of the conventional EP FEM based on iteration. To make the new EP FEM more applicable to metal forming industries, It is necessary to develop a more efficient QP algorithm that is suitable for large-scale problems.     

Surface Smoothing Procedures in Computational Contact Mechanics

This work addresses the problems arising in the finite element simulation of contact problems undergoing large deformation. The frictional contact problem is formulated in the continuum framework, introducing the interface laws for the normal and tangential stress components in the contact area. The variational formulation is presented, considering different methods to enforce the contact constraints. The spatial discretization within the finite element method is applied, as well as the temporal discretization required to solve the three sources of nonlinearities: geometric, material and frictional contact. The discretization of contact surfaces is discussed in detail, including different surface smoothing procedures. This numerical strategy allows to solve the difficulties associated with the discontinuities in the contact surface geometry introduced by finite element discretization, which leads to nonphysical oscillations of the contact force for large sliding problems. The geometrical accuracy of different interpolation methods is evaluated, paying particular attention to the Nagata patch interpolation recently proposed. In this framework, the Node-to-Nagata contact elements are developed using the augmented Lagrangian method to regularize the variational frictional contact problem. The techniques used to search for contact in case of large deformations are discussed, including self-contact phenomena. Several numerical examples are presented, comprising both the contact between deformable and rigid obstacles and the contact between deformable bodies. The results show that the accuracy and robustness of the numerical simulations is improved when the contact surface is smoothed with Nagata patches.     

Accurate contact angle boundary conditions for the Cahn–Hilliard equations

The contact angle dynamics between a two-phase interface and a solid surface is important in physical interpretations, mathematical modeling, and numerical treatments. We present a novel formulation based on a characteristic interpolation for the contact angle boundary conditions for the Cahn–Hilliard equation. The new scheme inherits characteristic properties, such as the mass conservation, the total energy decrease, and the unconditionally gradient stability. We demonstrate the accuracy and robustness of the proposed contact angle boundary formulation with various numerical experiments. The numerical results indicate a potential usefulness of the proposed method for accurately calculating contact angle problems.     

Linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization

Non-blind motion deblurring problems are highly ill-posed and so it is quite difficult to find the original sharp and clean image. To handle ill-posedness of the motion deblurring problem, we use nonlocal total variation (abbreviated as TV) regularization approaches. Nonlocal TV can restore periodic textures and local geometric information better than local TV. But, since nonlocal TV requires weighted difference between pixels in the whole image, it demands much more computational resources than local TV. By using the linearization of the fidelity term and the proximal function, our proposed algorithm does not require any inversion of blurring operator and nonlocal operator. Therefore, the proposed algorithm is very efficient for motion deblurring problems. We compare the numerical performance of our proposed algorithm with that of several state-of-the-art algorithms for deblurring problems. Our numerical results show that the proposed method is faster and more robust than state-of-the-art algorithms on motion deblurring problems.     

A decomposition algorithm for nonlinear inseparable hierarchical optimization problems

In this paper a decomposition algorithm is proposed to solve nonlinear inseparable hierarchical optimization problems. It can be seen as an improved version of Kronsjö's algorithm which is suitable only for separable problems. Two considerably complicated numerical examples are computed. The results show that the algorithm given here is satisfactory. Through recursive application of the algorithm multi-level problems can also be solved.     

Numerical treatment of the sea bed-long underwater cable dynamic interaction problem by an upper bounding algorithm

The numerical treatment of the dynamic response of an underwater cable, constrained by a frictionless rigid sea profile, by the use of an upper bounding algorithm is considered. By applying an appropriate discretization scheme with respect to time and space, the arising unilateral contact/impact problem is formulated as a sequence of variational inequality problems or as a sequence of quadratic programming problems that are equivalent to linear complementarity problems. The latter are numerically treated by applying an easy-to-use upper bounding Mangasarian algorithm leading to the solution of a linear programming problem which permits the treatment of large-scale problems.     

Contact problems with friction: models and simulations

This article deals with the modeling and the numerical simulation of contact and friction problems. Some friction formulations are proposed and numerical methods of resolution by finite elements are presented. Two methods are more particularly developed. The first one is based on a formulation using displacements and the second one is based on a mixed formulation using displacements and contact forces. Then, some improvements of these two methods as well as a comparison of their respective performances are presented.     

非线性互补问题的粒子群算法

针对非线性互补问题求解的困难,利用粒子群算法并结合极大熵函数法给出了该类问题的一种新的有效算法。该算法首先利用极大熵函数将非线性互补问题转化为一个无约束最优化问题,将该函数作为粒子群算法的适应值函数;然后应用粒子群算法来优化该问题。数值结果表明,该算法收敛快、数值稳定性较好,是求解非线性互补问题的一种有效算法。