A velocity observer design for tracking task-based motions of unicycle type mobile robots

The paper presents a design of a nonlinear velocity observer and its application within a model-based tracking control strategy for tracking task-based motions of unicycle type mobile robots. The strategy is the model reference tracking control strategy for programmed motion and it enables switching between controllers employed in it to improve a tracking precision as well as switching between coordinates used for modeling based on a type of a nonholonomic system. The strategy benefits by adding the velocity observer to its architecture due to the reduction of a number of measurements needed for feedback tracking.     

Modelling of closed-chain manipulators on an excavator vehicle

The main focus of this paper is to develop a physics-based model for a closed-chain manipulator in an excavator vehicle. The derivation of closed-chain manipulator dynamic equations with a structure similar to open-chain manipulator equations is an important research problem, particularly with reference to controller design. In this paper, an approach for deriving closed-chain manipulator equations with an open-chain structure, based on trigonometric t-formulae, is presented. Holonomic loop closure constraints are employed in order to derive the closed-chain mechanism dynamics from the reduced system dynamics. The closed-chain equations, with a structure similar to serial link equations, are presented. The model incorporates the dynamic properties of the manipulator and bucket. The dynamic model for the excavation system is validated against measured data obtained from a full-scale closed-chain excavator vehicle. A dynamic model is important for the design of control strategies for trajectory tracking, a key requirement for automating the excavation task. It is noted that even though the results presented in this paper are focused on a particular excavator vehicle, the research is generic and can be adapted to any closed-chain manipulator.     

Relationship between the Udwadia–Kalaba equations and the generalized Lagrange and Maggi equations

In their paper “A New Perspective on Constrained Motion,” F. E. Udwadia and R. E. Kalaba propose a new form of matrix equations of motion for nonholonomic systems subject to linear nonholonomic second-order constraints. These equations contain all of the generalized coordinates of the mechanical system in question and, at the same time, they do not involve the forces of constraint. The equations under study have been shown to follow naturally from the generalized Lagrange and Maggi equations; they can be also obtained using the contravariant form of the motion equations of a mechanical system subjected to nonholonomic linear constraints of second order. It has been noted that a similar method of eliminating the forces of constraint from differential equations is usually useful for practical purposes in the study of motion of mechanical systems subjected to holonomic or classical nonholonomic constraints of first order. As a result, one obtains motion equations that involve only generalized coordinates of a mechanical system, which corresponds to the equations in the Udwadia–Kalaba form.     

基于尖点突变的知识应用过程中溢出效应研究

本文引入“知识浓度”和“知识应用速度”两个概念,利用知识稀释效应的系统动力方程解释知识溢出机理。从突变视角分析了知识溢出的突变特性,借鉴尖点突变理论对系统动力方程进行换元变换,建立了知识溢出状态的尖点突变模型,讨论了知识稀释系统控制因子的变化与知识溢出状态间的判定规则,说明了知识应用过程中知识溢出特性如突跳、滞后效应等特性及知识溢出态和接受态之间转化的尖点突变机理。最后,利用我国31个省级行政区面板数据进行实证研究,揭示以省级行政区为对象的知识溢出状态、变化情况及发展趋势,为我国区域经济发展和知识战略提供理论指导。     

Stabilization of the motions of mechanical systems in prescribed phase-space manifolds

A method for constructing a mathematical model of the dynamics of a mechanical system is proposed. An algorithm is constructed for determining the expressions for the control forces and the components of the constraint reactions. A modification is made to the dynamic equations which enables one to solve the problem of stabilizing the constraints and which ensures the required accuracy in the numerical solution of the corresponding system of differential-algebraic equations describing the constraints imposed on the system, its kinematics and dynamics. By virtue of well-known dynamic analogies, the proposed method can be used to investigate the dynamics of different physical systems. The problem of modelling the dynamics of an adaptive optical system with two degrees of freedom is considered.     

A numerical method for the servo constraint problem of underactuated mechanical systems

Servo constraints are used in inverse dynamics simulations of discrete mechanical systems, especially for trajectory tracking control problems [1], whose desired outputs are represented by state variables and treated as servo constraints [2]. Servo constraint problems can be classified into fully actuated and underactuated multibody systems, and the equations of motion take the form of differential algebraic equations (DAEs) including holonomic and servo constraints. For fully actuated systems, control inputs can be solved from the equations by model inversion, as the input distribution matrix is nonsingular and invertible. However, underactuated systems have more degrees of freedom than control inputs. The input distribution matrix is not invertible, and in contrast to passive constraints, the realization of servo constraints with the use of control forces can range from orthogonal to tangential [3]. Therefore, it is challenging for the determination of control inputs which force the underactuated system to realize the partly specified motion. For differentially flat underactuated systems, the differentiation index of DAEs may exceed three. Hence we need to apply specific index reduction techniques, such as the projection approach applied in [3], [4], and [6]. The present work applies index reduction by minimal extension [5] to differentially flat underactuated crane systems and shows that the index can be reduced from five to three and even to one. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tracking within a time interval on the basis of data supplied by finite observers

We solve the tracking control problem, in which one should bring a trajectory of a system of linear ordinary differential equations into a neighborhood of a trajectory of another system within a given time interval. After getting into this neighborhood, one should keep the trajectory of the first subsystem in it for a time interval of given duration. For the control synthesis, we use incomplete and imprecise information on the online deviation of one trajectory from the other, which is obtained in real time from linear equations of observation. We consider distinct structures of observers, which substantially affect the solution of control problems for such systems. The equations of dynamics and admissible measurements contain uncertainty for which one knows only some hard pointwise constraints. To solve the main problem, we use an approach that can be reduced to the construction of auxiliary information sets and weakly invariant sets with a subsequent “aiming” of one set at a tube. We suggest an efficient method for an approximate solution on the basis of ellipsoidal calculus techniques. The results of the algorithm operation are illustrated by an example of the solution of a tracking control problem for two fourth-order subsystems.     

Design an interactive virtual physics environment with uncertainties control to support motion tracking

The development of robot or character motion tracking algorithms is inherently a challenging task. This is more than ever true when the latest trends in motion tracking are considered. Some researchers can deal with kinematic and dynamic constraints induced by the mechanical structure. Another class of researchers fulfills various types of optimality conditions, yet others include means of dealing with uncertainties about the robot or character and its environment. In order to deal with the complexity of developing motion tracking algorithms, it is proposed in this paper to design an interactive virtual physics environment with uncertainties for motion tracking based on sliding mode control. The advantages of doing so are outlined and a virtual environment presented which is well suited to support motion tracking development. The environment makes full use of multi-body system dynamics and a robust sliding mode controller independent of model as simulation kernel. So the environment is capable of simulating setups which fulfill the requirements posed by state-of-the-art motion tracking algorithm development. The demonstration results verified the validity of the environment.     

Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

In this paper, the developed model of an N-flexible-link mobile manipulator with revolute-prismatic joints is presented for the cooperative flexible multi mobile manipulator. In this model, the deformation of flexible links is calculated by using the assumed modes method. In additions, non-holonomic constraints of the robots’ mobile platforms that bound its locomotion are considered. This limitation is alleviated through the concurrent motion of revolute and prismatic joints, although it results in computational complexity and changes the final motion equations to time-varying form. Not only is the proposed dynamic model implemented for the multi-mobile manipulators with arms having independent motion, but also for multi-mobile manipulators in cooperation after defining gripper's kinematic constraints. These constraints are imported to the dynamic equations by defining Lagrange multipliers. The recursive Gibbs–Appell formulation is preferred over other similar approaches owing to the capability of solving the equations without the need to use Lagrange multipliers for eliminating non-holonomic constraints in addition to the novel optimized process of obtaining system equations. Hence, cumbersome simultaneous computations for eliminating the constraints of platform and arms are circumvented. Therefore, this formulation is improved for the first time by importing Lagrange multipliers for solving kinematic constrained systems. In the simulation section, the results of forward dynamics solution for two flexible single-arm manipulators with revolute-prismatic joints while carrying a rigid object are presented. Inverse dynamics equations of the system are also presented to obtain the maximum dynamic load-carrying capacity of the two-rigid-link mobile manipulators on a predefined path. Two constraints, namely the capacity of joint motors torque and robot motion stability are considered as the limitation criteria. The concluded motion equations are used to accurately control the movement of sensitive bodies, which is not achievable through the use of one platform.     

An index tracking model with stratified sampling and optimal allocation

This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out‐of‐sample performance. A mixed‐integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out‐of‐sample time period. As mixed‐integer program is a well‐known NP‐hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental results show that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.     

Model Predictive Control for Nonlinear Parabolic Differential Equations Based on a Linear Quadratic Gaussian Design

We consider optimal control problems for semilinear parabolic partial differential equations where process and measurement noise can occur. If we apply a Model Predictive Control (MPC) scheme we obtain optimal control problems on small time intervals. The resulting “smaller problems” can be linearized around a reference and solved by using a Linear Quadratic Gaussian (LQG) design. We present some theoretical background of the strategy above as well as results of a numerical implementation for a 3D problem. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Testing regularity of functional equations with computer

One of the standard methods of solving functional equations is reducing the equations to a form which is easily handled by the methods of analysis, for example differential equations, partial differential equations, integral equations, etc. For the reduction we must know some “strong” regularity properties of the unknown functions, which regularity follows from the “week” properties of the known functions. Our long-term plan is to create a method not only for specialists in research but for professionals in other areas using functional equations—for example engineers, economists. As a first attempt we worked out a program for some particular, but fairly general type of equations in the Computer Algebra System Maple^?, which enables an easy detection of the applicability of known regularity theorems.     

Straight chains of interconnected mass points under the action of non-symmetric dry friction

The motion of a chain of interconnected equal material points placed on a rough straight line and connected by equal kinematical constraints is considered. It is supposed that the system experiences a small non-symmetric Coulomb dry frictional force acting from the line side upon each mass point and opposite to the direction of motion. The magnitude of this force depends on the direction of motion. To the equation of motion the procedure of averaging is applied. The expression for the stationary “on the average” velocity of the motion of the system as a single whole is found. The obtained theoretical results can be used for the design of worm-like vibration robots. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computer system for kinematic and dynamic analysis synthesis of rigid and flexible multibody systems

In the paper an overview of a general numerical algorithm and program system library for deriving the kinematic constraint equations and dynamic equations of motion, as well as, computation of their first and second order partial derivatives with respect to kinematic parameters of motion, design parameters and mass and inertia characteristics for rigid and flexible multibody systems is presented. These are the main basic computational modules for implementation of kinematic and dynamic synthesis, optimization and design. The main theoretical basis consists in matrix methods for deriving the kinematic constraints and dynamic equations, as well as, the generalized Newton – Euler dynamic equations for rigid and flexible bodies, and finite element discretization in relative coordinates. Block–scheme of the computational procedures and problem oriented program compilation is presented. An example of kinematic synthesis of six–link path generating mechanism with singular points is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于区间二型梯形模糊集的应急物资储备动态协同决策模型

重大灾害下应急物资储备决策是阻止突发灾难蔓延的有效手段之一。针对救灾信息具备不确定性与复杂性特点,构建基于区间二型梯形模糊集的应急物资储备动态协同决策模型,并给出应急物资储备策略。利用区间二型模糊集理论的决策方案并结合比例分析法(COPRAS),构建常态环境下应急物资供应商选择的群决策模型,解决不相容群决策属性之间的冲突问题;进而,充分考虑“救灾阶段性动态时间因素”对储备决策的影响,构建动态救灾环境下应急物资储备结构模糊优化模型,实现常态决策与非常态应急决策之间的动态协同;最后,以2012年云南丽江“6.14”突发特大山洪灾害为实例进行数值分析,验证该动态协同决策模型的合理性与可行性,能有效解决动态救灾环境下应急物资储备结构优化问题。     

On Vector Form of Differential Variational Principles of Mechanics

We introduce variation of a vector δx which can be interpreted either as a virtual displacement of a system, or as variation of the velocity of a system, or as variation of the acceleration of a system. This vector is used to obtain a unified form of differential variational principles of mechanics from the scalar representative equations of motion. Conversely, this notation implies the original equations of motion, which enables one to consider the obtained scalar products as principles of mechanics. Using the same logical scheme, one constructs a differential principle on the basis of the vector equation of constrained motion of a mechanical system. In this form of notation, it is proposed to conserve the zero scalar products of reactions of ideal constraints and the vector δx. This enables one to obtain also the equations involving generalized constrained forces from this form of notation.     

Infinite-horizon boundary control of distributed systems

For a boundary controlled dynamic system, algorithms for solving the problem of tracking reference motion and the problem of tracking reference control are described. The algorithms are robust to information noise and computational errors. The solution method is based on the extremal shift method from the theory of positional differential games.     

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations leads to large sparse saddle point systems in two levels. In this paper, we consider distributed optimal control for the Stokes system and test the particular case when the arising linear system can be compressed after eliminating the control function. In that case, a system arises in a form which enables the application of an efficient block matrix preconditioner that previously has been applied to solve complex-valued systems in real arithmetic. Under certain conditions, the condition number of the so preconditioned matrix is bounded by 2. The numerical and computational efficiency of the method in terms of number of iterations and execution time is favorably compared with other published methods.