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To design a robust attitude control system for the ascent flight phase of satellite launch vehicles (SLVs).

The autopilot is based on generalized dynamic inversion (GDI). Dynamic constraints are prescribed in the form of differential equations that encapsulate the control objectives, and are generalized inverted using the Moore-Penrose Generalized Inverse (MPGI) based Greville formula to obtain the control law. The MPGI is modified via a dynamic scaling factor for assuring generalized inversion singularity-robust tracking control. An additional sliding mode control (SMC) loop is augmented to robustify the GDI closed-loop system against model uncertainties and external disturbances.

The robust GDI control law allows for two cooperating controllers that act on two orthogonally complement control spaces: one is the particular controller that realizes the dynamic constraints, and the other is the auxiliary controller that is affined in the null control vector, and is used to enforce global closed-loop stability.

Orthogonality of the particular and the auxiliary control subspaces ensures noninterference of the two control actions, and thus, it ensures that both actions work toward a unified goal. The robust control loop increases practicality of the GDI control design.

The first successful implementation of GDI to the SLV control problem.

Stiffness control of redundant robot arm, aimed at using extra degrees of freedom (DoF) to shape the robot tool center point (TCP) elastomechanical behavior to be consistent with the essential requirements needed for a successful part mating process, i.e., to mimic part supporting mechanism with selective quasi-isotropic compliance (Remote Center of Compliance – RCC), with additional properties of inherent flexibility.

Theoretical analysis and synthesis of the complementary projector for null-space stiffness control of kinematically redundant robot arm. Practical feasibility of the proposed approach was proven by extensive computer simulations and physical experiments, based on commercially available 7 DoF SIA 10 F Yaskawa articulated robot arm, equipped with the open-architecture control system, system for generating excitation force, dedicated sensory system for displacement measurement and a system for real-time acquisition of sensory data.

Simulation experiments demonstrated convergence and stability of the proposed complementary projector. Physical experiments demonstrated that the proposed complementary projector can be implemented on the commercially available anthropomorphic redundant arm upgraded with open-architecture control system and that this projector has the capacity to efficiently affect the task-space TCP stiffness of the robot arm, with a satisfactory degree of consistency with the behavior obtained in the simulation experiments.

A novel complementary projector was synthesized based on the adopted objective function. Practical verification was conducted using computer simulations and physical experiments. For the needs of physical experiments, an adequate open-architecture control system was developed and upgraded through the implementation of the proposed complementary projector and an adequate system for generating excitation and measuring displacement of the robot TCP. Experiments demonstrated that the proposed complementary projector for null-space stiffness control is capable of producing the task-space TCP stiffness, which can satisfy the essential requirements needed for a successful part-mating process, thus allowing the redundant robot arm to mimic the RCC supporting mechanism behavior in a programmable manner.

This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

The purpose of this paper is to propose an adaptive control for a redundant robot manipulator interacting physically with the environment, especially with the existence of humans, on its body.

The redundant properties of the robot manipulator are used and a reference velocity variable is introduced to unify the operation-space tracking control and the null-space impedance control under one common framework. Neural networks are constructed to deal with unstructured and unmodeled dynamic nonlinearities. Lyapunov function is used during the course of control design and simulation studies are carried out to further illustrate the effectiveness of the proposed strategies.

Satisfying tracking performance in the operation-space and compliance behavior in the null-space of the redundant robot manipulator are ensured simultaneously.

The design procedure of redundant robot manipulators control can be greatly simplified, and the framework of multi-priority control can be transformed into a joint-space velocity tracking problem via the introducing of a reference velocity variable.

This paper aims to use redundant manipulators to solve the challenge of collision avoidance in construction operations such as welding and painting.

In this paper, a null-space-based task-priority adjustment approach is developed to avoid collisions. The method establishes the relative position of the obstacle and the robot arm by defining the “link space,” and then the priority of the collision avoidance task and the end-effector task is adjusted according to the relative position by introducing the null space task conversion factors.

Numerical simulations demonstrate that the proposed method can realize collision-free maneuvers for redundant manipulators and guarantee the tracking precision of the end-effector task. The experimental results show that the method can avoid dynamic obstacles in redundant manipulator welding tasks.

A new formula for task priority adjustment for collision avoidance of redundant manipulators is proposed, and the original task tracking accuracy is guaranteed under the premise of safety.

This paper seeks to present an efficient algorithm for the formation of null basis for finite element model discretized as rectangular bending elements. The bases obtained by this algorithm correspond to highly sparse and narrowly banded flexibility matrices and such bases can be considered as an efficient tool for optimal analysis of structures.

In the present method, two graphs are associated with finite element mesh consisting of an “interface graph” and an “associate digraph”. The underlying subgraphs of the self‐equilibrating systems (SESs) (null vectors) are obtained by graph theoretical approaches forming a null basis. Application of unit loads (moments) at the end of the generator of each subgraph results in the corresponding null vector.

In the present hybrid method, graph theory is used for the formation of null vectors as far as it is possible and then algebraic method is utilized to find the complementary part of the null basis.

This hybrid approach makes the use of pure force method in the finite element analysis feasible. Here, a simplified version of the algorithm is also presented where the SESs for weighted graphs are obtained using an analytical approach. Thus, the formation of null bases is achieved using the least amount of algebraic operations, resulting in substantial saving in computational time and storage.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The efficiency of the finite element analysis via force method depends on the overall flexibility matrix of the structure, while this matrix is directly affected from null bases vectors. As the null bases for an indeterminate structure are not unique, for an optimal analysis, the selected null bases should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrix. This paper aims to present an efficient method for the formation of optimal flexibility matrix of finite element models comprising tetrahedron elements via mathematical optimization technique.

For this purpose, a linear mixed integer programming model is presented for finding sparse solution of underdetermined linear system, which is correspond to sparse null vector. The charged system search algorithm is improved and used to find the best generator for formation of null bases.

The efficiency of the present method is illustrated through some examples. The proposed method leads to highly sparse, banded and accurate null basis matrices. It makes an efficient force method feasible for the analysis of finite element model comprising tetrahedron elements.

The force method, in which the member forces are used as unknowns, can be appealing to engineers. The main problem in the application of the force method is the formation of a self-stress matrix corresponding to a sparse flexibility matrix. In this paper, the highly sparse, banded and accurate null basis matrices gains by using mathematical optimization technique.

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.