Adaptive control of free-floating space robots in Cartesian coordinates

An adaptive control scheme is proposed for the end-effector trajectory tracking control of free-floating space robots. In order to cope with the nonlinear parameterization problem of the dynamic model of the free-floating space robot system, the system is modeled as an extended robot which is composed of a pseudo-arm representing the base motions and a real robot arm. An on-line estimation of the unknown parameters along with a computed-torque controller is used to track the desired trajectory. The proposed control scheme does not require measurement of the accelerations of the base and the real robot arm. A two-link planar space robot system is simulated to illustrate the validity and effectiveness of the proposed control scheme.     

Finite-difference method for solving gas dynamics equations using adaptive artificial viscosity

A finite-difference method is proposed for solving gas dynamics equations, i.e., a homogeneous, monotonous finite-difference scheme of the second- order time approximation and space variables outside the areas of discontinuities and compression waves. A new way to introduce adaptive artificial viscosity (AAV) in a difference scheme is considered. The stability of the proposed difference scheme is numerically studied. Test calculations are presented for the motion of contact discontinuities, blast waves, and disintegration of discontinuities.     

Finite-difference method for computation of 3-D gas dynamics equations with artificial viscosity

A new numerical method for the solution of gas dynamics problems for three-dimensional (3D) systems in Eulerian variables is presented in the paper. The proposed method uses the approximation O(τ² + h _x ² + h _y ² + h _z ²) in the areas of the solution’s smoothness and beyond the compression waves; τ is the time step; and h _x , h _y , and h _z are space variable steps. In the proposed difference scheme, in addition to Lax-Wendroff corrections, artificial viscosity μ that monotonizes the scheme is introduced. The viscosity is obtained from the conditions of the maximum principle. The results of the computation of the 3D test problem for the Euler equation are presented.     

Method of adaptive artificial viscosity for gas dynamics equations on triangular and tetrahedral grids

In studies [1–7] a method of adaptive artificial viscosity (AAV) was proposed for the solution of gas dynamics equations. In this paper, this method is extended to the case of triangular grids for two-dimensional (2D) equations in the variables x, y, and r, z, and of tetrahedral grids for equations in Cartesian variables x, y, and z. The calculation results for the test problems are presented.     

Quasi-acoustic scheme for gas dynamics Euler equations in the two-dimensional case

The new algorithm for numerically solving the gas dynamic Euler equations is presented. The algorithm is based on the linear reconstruction and quasi-acoustic presentation solution within a computational mesh. The proposed method is adapted for the three-dimensional (3D) case. Application problem is solved on the interaction of gas jets emitted from an aircraft engine interact with a reflecting screen.     

A multi-dimensional HLL-Riemann solver for Euler equations of gas dynamics

This article presents a numerical model that enables to solve on unstructured triangular meshes and with a high-order of accuracy, a multi-dimensional Riemann problem that appears when solving hyperbolic problems.For this purpose, we use a MUSCL-like procedure in a “cell-vertex” finite-volume framework.In the first part of this procedure, we devise a four-state bi-dimensional HLL solver (HLL-2D). This solver is based upon the Riemann problem generated at the centre of gravity of a triangular cell, from surrounding cell-averages. A new three-wave model makes it possible to solve this problem, approximately. A first-order version of the bi-dimensional Riemann solver is then generated for discretizing the full compressible Euler equations.In the second part of the MUSCL procedure, we develop a polynomial reconstruction that uses all the surrounding numerical data of a given point, to give at best third-order accuracy. The resulting over determined system is solved by using a least-square methodology. To enforce monotonicity conditions into the polynomial interpolation, we develop a simplified central WENO (CWENO) procedure.Numerical tests and comparisons with competing numerical methods enable to identify the salient features of the whole model.     

Adaptive multiresolution for finite volume solutions of gas dynamics

Multiresolution analysis is used to improve the CPU and memory performance of a finite volume scheme. Departing from Harten's original scheme we present a fully adaptive scheme in the sense that at a given time, the solution is represented in a compressed form by a set of significant wavelet coefficients. Numerical benchmarks for Euler's system of compressible gas dynamics are performed on triangular meshes.     

Approximate factorization of the discrete Navier-Stokes equations in Cartesian and cylindrical coordinates

A new pseudospectral technique for integrating incompressible Navier-Stokes equations with one nonperiodic boundary in Cartesian or cylindrical coordinate system is presented. Algorithm constructed makes use of Chebyshev collocation technique in nonperiodic direction. Special attention is paid to the approximate factorization of the discrete Navier-Stokes equations in cylindrical geometry leading to highly fast and robust numerical procedure providing spectral accuracy. New approach is an efficient tool for further investigation of turbulent shear flows, for physical hypotheses and alternative algorithms testing. Classical problems of incompressible fluid flows in an infinite plane channel and annuli at transitional Reynolds numbers are taken as model ones.     

Adaptive memory search for multidemand multidimensional knapsack problems

We describe a simple adaptive memory search method for the 0/1 Multidemand Multidimensional Knapsack Problem (0/1 MDMKP). The search balances the level of infeasibility against the quality of the solution, and uses a simple dynamic tabu search mechanism. A weighting scheme to balance out the differences in the tightness of the constraints is also implemented. Computational results on a portfolio of test problems taken from the literature are reported, showing very favorable results, both in terms of solution quality and the ability of the search to find feasible solutions.     

Adaptive controller designs for robot manipulator systems yielding reduced Cartesian error

A set of nonlinear coupled differential equations that represents a mathematical model of a robot manipulator whose coefficients are unknown due to the effects of payload, friction and/or backlash, etc., is considered in this note. It is shown that by proper compensation of the input torque, the norm of the state error becomes less than that which resulted from the conventional design. A Jacobian relation is introduced and is used in the design methodology of the Lyapunov direct method to reduce the Cartesian error.     

Performance analysis in soccer: a Cartesian coordinates based approach using RoboCup data

In soccer, like in business, results are often the best indicator of a team’s performance in a certain competition but insufficient to a coach to asses his team performance. As a consequence, measurement tools play an important role in this particular field. In this research work, a performance tool for soccer, based only in Cartesian coordinates is presented. Capable of calculating final game statistics, suisber of shots, the calculus methodology analyzes the game in a sequential manner, starting with the identification of the kick event (the basis for detecting all events), which is related with a positive variation in the ball’s velocity vector. The achieved results were quite satisfactory, mainly due to the number of successfully detected events in the validation process (based on manual annotation). For the majority of the statistics, these values are above 92% and only in the case of shots do these values drop to numbers between 74 and 85%. In the future, this methodology could be improved, especially regarding the shot statistics, integrated with a real-time localization system, or expanded for other collective sports games, such as hockey or basketball.     

Convergence of a two-layer scheme for equations of gas dynamics in Eulerian variables with geo-physical applications

This paper deals with the convergence of a completely conservative, two-layer difference scheme for equations of gas dynamics in Eulerian variables. The convergence of the difference solution to the smooth solution of the original periodic Cauchy problem of order τ²+h ² at layer-by-layer norm L ₂ is proved, provided that the mesh step sizes are sufficiently small and that τ=h ^1+? (?=constant>0). Several modifications of the proposed method were used for the numerical solution of a one-dimensional mathematical model (on the basis of the shallow water theory), which describes crash events produced by dam collapse.     

Adaptive filtering and limiting in compact high order methods for multiscale gas dynamics and MHD systems

The adaptive multistep linear and nonlinear filters for multiscale shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows of the authors are extended to include compact high order central differencing as the spatial base scheme. The adaptive mechanism makes used of multiresolution wavelet decomposition of the computed flow data as sensors for numerical dissipative control. The objective is to expand the work initiated in [Yee HC, Sjögreen B. Nonlinear filtering in compact high order schemes. In: Proceedings of the 19th ICNSP and 7th APPTC conference; 2005; J Plasma Phys 2006;72:833–36] and compare the performance of adaptive multistep filtering in compact high order schemes with adaptive filtering in standard central (non-compact) schemes for multiscale problems containing shock waves.     

A method for solving the molecular Schrödinger equation in Cartesian coordinates via angular momentum projection operators

A method for solving the Schrödinger equation of N-atom molecules in 3N−3 Cartesian coordinates usually defined by Jacobi vectors is presented. The separation and conservation of the total angular momentum are obtained not by transforming the Hamiltonian in internal curvilinear coordinates but instead, by keeping the Cartesian formulation of the Hamiltonian operator and projecting the initial wavefunction onto the proper irreducible representation angular momentum subspace. The increased number of degrees of freedom from 3N−6 to 3N−3, compared to previous methods for solving the Schrödinger equation, is compensated by the simplicity of the kinetic energy operator and its finite difference representations which result in sparse Hamiltonian matrices. A parallel code in Fortran 95 has been developed and tested for model potentials of harmonic oscillators. Moreover, we compare data obtained for the three-dimensional hydrogen molecule and the six-dimensional water molecule with results from the literature. The availability of large clusters of computers with hundreds of CPUs and GBytes of memory, as well as the rapid development of distributed (Grid) computing, make the proposed method, which is unequivocally highly demanding in memory and computer time, attractive for studying Quantum Molecular Dynamics.     

Adaptive wave variables for bilateral teleoperation using neural networks

Stability and transparency determine the performance of bilateral teleoperation systems. Previous studies on passivity-based control focused on stability such that the results of the study are robust in terms of the time delay issue. But there are not sufficient studies on performance analysis based on environmental elements related to transparency. This paper suggests an adaptive wave transformation system where stability is secured by controlling characteristic impedance in the existing wave variables system adaptively according to time delay and environmental elements and simultaneously ensuring a proper dynamic performance depending on external force. Neural network was utilized to design the system that enables controlling the characteristic impedance depending on external factors such as time delay and comparison with the existing wave variables.     

Application of artificial viscosity for suppressing the carbuncle phenomenon in Godunov-type schemes

A new approach for solving the carbuncle phenomenon that occurs in Godunov-type schemes when applied to hypersonic flow simulations is proposed. The approach suppresses carbuncle-instability by additional dissipative terms in the form of the right-hand side of Navier-Stokes equations, but with artificial instead of molecular viscosity. The efficiency of the proposed approach is demonstrated on several test problems.     

A superelement model based on Lagrangian coordinates for multibody system dynamics

This paper presents a general-purpose superelement model for computer-aided analysis of multibody systems subject to kinematic constraints. The superelement concept is defined and a method based on Lagrangian coordinates is developed to obtain superelement parameters. Differential equations of motion of a system consisting of superelements and other elements is developed. Constraints internal to the superelements do not appear in the resulting differential equations. This leads to a set of differential and algebraic equations that has fewer dimensions and that requires less CPU time than the existing general-purpose schemes. Two examples are presented to demonstrate the feasibility and efficiency of the model.     

Adaptive heuristic search algorithm for discrete variables based multi-objective optimization

Although metamodel technique has been successfully used to enhance the efficiency of the multi-objective optimization (MOO) with black-box objective functions, the metamodel could become less accurate or even unavailable when the design variables are discrete. In order to overcome the bottleneck, this work proposes a novel random search algorithm for discrete variables based multi-objective optimization with black-box functions, named as k-mean cluster based heuristic sampling with Utopia-Pareto directing adaptive strategy (KCHS-UPDA). This method constructs a few adaptive sampling sets in the solution space and draws samples according to a heuristic probability model. Several benchmark problems are supplied to test the performance of KCHS-UPDA including closeness, diversity, efficiency and robustness. It is verified that KCHS-UPDA can generally converge to the Pareto frontier with a small quantity of number of function evaluations. Finally, a vehicle frontal member crashworthiness optimization is successfully solved by KCHS-UPDA.     

Kinematics and dynamics of a rigid body in nonholonomic coordinates

In this paper we consider dynamic equations of nonholomic systes in terms of pseudo-coordinates which appear in the general theory of rigid body. Especially, the rotator kinematics and dynamics in nonholonomic coordinates is presented. Besides, using the appropriate methods of the differential geometry and theory of Lie groups and Lie algebras a simplification of motion equations in the tangent space is obtained.     

On Cartesian stiffness matrices in rigid body dynamics: an energetic perspective

Several Cartesian stiffness matrices for a single rigid body subject to a conservative force field are developed in this paper. The treatment is based on energetic arguments and an Euler angle parameterization of the rotation of the rigid body is employed. Several new representations for the stiffness matrix are obtained and the relation to other works on Cartesian stiffness matrices and Hessians is illuminated. Additional details are presented with respect to determining the Cartesian stiffness matrix for a pair of rigid bodies, as well as for a system of rigid bodies constrained to a plane.