Polyhedral Finite Elements Using Harmonic Basis Functions

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.     

Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements

We provide a comprehensive study of arbitrarily high-order finite elements defined on pyramids. We propose a new family of high-order nodal pyramidal finite element which can be used in hybrid meshes which include hexahedra, tetrahedra, wedges and pyramids. Finite elements matrices can be evaluated through approximate integration, and we show that the order of convergence of the method is conserved. Numerical results demonstrate the efficiency of hybrid meshes compared to pure tetrahedral meshes or hexahedral meshes obtained by splitting tetrahedra into hexahedra.     

Multi-Level Shape Representation Using Global Deformations and Locally Adaptive Finite Elements

We present a model-based method for the multi-level shape, pose estimation and abstraction of an object's surface from range data. The surface shape is estimated based on the parameters of a superquadric that is subjected to global deformations (tapering and bending) and a varying number of levels of local deformations. Local deformations are implemented using locally adaptive finite elements whose shape functions are piecewise cubic functions with C ¹ continuity. The surface pose is estimated based on the model's translational and rotational degrees of freedom. The algorithm first does a coarse fit, solving for a first approximation to the translation, rotation and global deformation parameters and then does several passes of mesh refinement, by locally subdividing triangles based on the distance between the given datapoints and the model. The adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties of conformity, non-degeneracy and smoothness are maintained. Each pass of the algorithm uses physics-based modeling techniques to iteratively adjust the global and local parameters of the model in response to forces that are computed from approximation errors between the model and the data. We present results demonstrating the multi-level shape representation for both sparse and dense range data.     

Vision-Based Robotic Motion Control for Non-autonomous Environment

A visual servo control system with SOPC structure is implemented on a retrofitted Mitsubishi Movemaster RV-M2 robotic system. The hardware circuit has the functions of quadrature encoder decoding, limit switch detecting, pulse width modulation (PWM) generating and CMOS image signal capturing. The software embedded in Nios II micro processor has the functions of using UART to communicate with PC, robotic inverse kinematics calculation, robotic motion control schemes, digital image processing and gobang game AI algorithms. The digital hardware circuits are designed by using Verilog language, and programs in Nios II micro processor are coded with C language. An Altera Statrix II EP2S60F672C5Es FPGA chip is adopted as the main CPU of the development board. A CMOS color image sensor with 356 ×292 pixels resolution is selected to catch the environment time-varying change for robotic vision-based servo control. The system performance is evaluated by experimental tests. A gobang game is planned to reveal the visual servo robotic motion control objective in non-autonomous environment. Here, a model-free intelligent self-organizing fuzzy control strategy is employed to design the robotic joint controller. A vision based trajectory planning algorithm is designed to calculate the desired angular positions or trajectory on-line of each robotic joint. The experimental results show that this visual servo control robot has reliable control actions.     

A Collocation Solution For Burgers Equation Using Quadratic B-Spline Finite Elements

This paper discusses solving one of the important equations in Fluid Dynamics; which is the one-dimensional Burgers equation. For that purpose, we use quadratic B-spline finite elements within a Collocation method. It is shown that this method is capable of solving Burgers equation accurately for values of viscosity from small to large. Numerical results are obtained for test problems to show the behavior of the solutions of time dependent problems. Computed results are compared with other numerical results.     

Coordinated Motion and Force Control of Multi-Limbed Robotic Systems

This analytic and experimental study proposes a control algorithm for coordinated position and force control for autonomous multi-limbed mobile robotic systems. The technique is called Coordinated Jacobian Transpose Control (CJTC). Such position/force control algorithms will be required if future robotic systems are to operate effectively in unstructured environments. Generalized Control Variables (GCVs), express in a consistent and coordinated manner the desired behavior of the forces exerted by the multi-limbed robot on the environment and a system's motions. The effectiveness of this algorithm is demonstrated in simulation and laboratory experiments on a climbing system.     

Rolling Contact Motion Generation and Control of Robotic Fingers

Dexterity in human hand is connected with the fingertip rolling ability. In this work we consider rolling motion of spherical robotic fingertips as one of the control objectives together with the set point position control and force trajectory tracking. The generation of a rolling motion trajectory is proposed and a control solution is designed which achieves prescribed transient and steady state tracking behavior. The proposed control law is structurally and computationally simple and does not utilize the dynamics of the robot model or its approximation. A simulation of a five degrees of freedom robot show excellent contact rolling performance even at cases of adverse friction conditions while alternative controllers lead to contact sliding. Experiments with a KUKA LWR4 + are performed to validate the proposed method.     

Optimal Motion Planning of Robotic Manipulators Removing Mobile Objects Grasped in Motion

The following study deals with motion optimization of robot arms having to transfer mobile objects grasped when moving. This approach is aimed at performing repetitive transfer tasks at a rapid rate without interrupting the dynamics of both the manipulator and the moving object. The junction location of the robot gripper with the object, together with grasp conditions, are partly defined by a set of local constraints. Thus, optimizing the robot motion in the approach phase of the transfer task leads to the statement of an optimal junction problem between the robot and the moving object. This optimal control problem is characterized by constrained final state and unknown traveling time. In such a case, Pontryagin"s maximum principle is a powerful mathematical tool for solving this optimization problem. Three simulated results of removing a mobile object on a conveyor belt are presented; the object is grasped in motion by a planar three-link manipulator.     

Modeling of a Smart Nano Force Sensor Using Finite Elements and Neural Networks

Machine Intelligence Research - The aim of this work is to model and analyze the behavior of a new smart nano force sensor. To do so, the carbon nanotube has been used as a suspended gate of a...     

Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes

Realistic behavior of deformable objects is essential for many applications such as simulation for surgical training. Existing techniques of deformable modeling for real time simulation have either used approximate methods that are not physically accurate or linear methods that do not produce reasonable global behavior. Nonlinear finite element methods (FEM) are globally accurate, but conventional FEM is not real time. In this paper, we apply nonlinear FEM using mass lumping to produce a diagonal mass matrix that allows real time computation. Adaptive meshing is necessary to provide sufficient detail where required while minimizing unnecessary computation. We propose a scheme for mesh adaptation based on an extension of the progressive mesh concept, which we call dynamic progressive meshes.     

High Resolution Tracking of Non-Rigid Motion of Densely Sampled 3D Data Using Harmonic Maps

We present a novel automatic method for high resolution, non-rigid dense 3D point tracking. High quality dense point clouds of non-rigid geometry moving at video speeds are acquired using a phase-shifting structured light ranging technique. To use such data for the temporal study of subtle motions such as those seen in facial expressions, an efficient non-rigid 3D motion tracking algorithm is needed to establish inter-frame correspondences. The novelty of this paper is the development of an algorithmic framework for 3D tracking that unifies tracking of intensity and geometric features, using harmonic maps with added feature correspondence constraints. While the previous uses of harmonic maps provided only global alignment, the proposed introduction of interior feature constraints allows to track non-rigid deformations accurately as well. The harmonic map between two topological disks is a diffeomorphism with minimal stretching energy and bounded angle distortion. The map is stable, insensitive to resolution changes and is robust to noise. Due to the strong implicit and explicit smoothness constraints imposed by the algorithm and the high-resolution data, the resulting registration/deformation field is smooth, continuous and gives dense one-to-one inter-frame correspondences. Our method is validated through a series of experiments demonstrating its accuracy and efficiency.     

Distributed Motion Constraints for Algebraic Connectivity of Robotic Networks

This paper studies connectivity maintenance of robotic networks that communicate at discrete times and move in continuous space. We propose a distributed coordination algorithm that allows the robots to decide whether a desired collective motion breaks connectivity. We build on this procedure to design a second coordination algorithm that allows the robots to modify a desired collective motion to guarantee that connectivity is preserved. These algorithms work under imperfect information caused by delays in communication and the robots’ mobility. Under very outdated information, the proposed algorithms might prevent some or all of the robots from moving. We analyze the correctness of our algorithms by formulating them as games against a hypothetical adversary who chooses system states consistent with observed information. The technical approach combines tools from algebraic graph theory, linear algebra, and nonsmooth analysis.     

Emotion Editing using Finite Elements

This paper describes the prototype of a facial expression editor. In contrast to existing systems the presented editor takes advantage of both medical data for the simulation and the consideration of facial anatomy during the definition of muscle groups. The C^l-continuous geometry and the high degree of abstraction for the expression editing sets this system apart from others. Using finite elements we achieve a better precision in comparison to particle systems. Furthermore, a precomputing of facial action units enables us to compose facial expressions by a superposition of facial action geometries in real-time. The presented model is based on a generic facial model using a thin plate and membrane approach for the surface and elastic springs for facial tissue modeling. It has been used successfully for performing facial surgery simulation. We illustrate features of our system with examples from the Visible Human Dataset.™     

Three-Dimensional Robotic Vision Using Ultrasonic Sensors

This article describes a three-dimensional artificial vision system for robotic applications using an ultrasonic sensor array. The array is placed on the robot grip so that it is possible to detect the presence of an object, to direct the robot tool towards it, and to locate the object position. It will provide visual information about the object's surface by means of superficial scanning and it permits the object shape reconstruction. The developed system uses an approximation of the ultrasonic radiation and reception beam shape for calculating the first contact points with the object's surface. On the other hand, the position of the array's sensors has been selected in order to provide the sensorial head with other useful capabilities, such as edge detection and edge tracking. Furthermore, the article shows the structure of the sensorial head for avoiding successive rebounds between the head and the object surface, and for eliminating the mechanical vibrations among sensors.     

Planning 3-D Collision-Free Dynamic Robotic Motion Through Iterative Reshaping

We propose a general and practical planning framework for generating 3-D collision-free motions that take complex robot dynamics into account. The framework consists of two stages that are applied iteratively. In the first stage, a collision-free path is obtained through efficient geometric and kinematic sampling-based motion planning. In the second stage, the path is transformed into dynamically executable robot trajectories by dedicated dynamic motion generators. In the proposed iterative method, those dynamic trajectories are sent back again to the first stage to check for collisions. Depending on the application, temporal or spatial reshaping methods are used to treat detected collisions. Temporal reshaping adjusts the velocity, whereas spatial reshaping deforms the path itself. We demonstrate the effectiveness of the proposed method through examples of a space manipulator with highly nonlinear dynamics and a humanoid robot executing dynamic manipulation and locomotion at the same time.      

Obstacle Avoidance for Spatial Hyper‐Redundant Manipulators Using Harmonic Potential Functions and the Mode Shape Technique

This paper deals with the obstacle avoidance problem for spatial hyper‐redundant manipulators in known environments. The manipulator is divided into two sections, a proximal section that has not entered the space among the obstacles and a distal section among the obstacles. Harmonic potential functions are employed to achieve obstacle avoidance for the distal section in three‐dimensional space in order to avoid local minima in cluttered environments. A modified panel method is used to generate the potential of any arbitrary shaped obstacle in three‐dimensional space. An alternative backbone curve concept and an efficient fitting method are introduced to control the trajectory of proximal links. The fitting method is recursive and avoids the complications involved with solving large systems of nonlinear algebraic equations. The combination of a three‐dimensional safe path derived from the harmonic potential field and the backbone curve concept leads to an elegant kinematic control strategy that guarantees obstacle avoidance. © 2003 Wiley Periodicals, Inc.