Stability problem formulation of structurally compliant robot manipulators during contact task execution: A singular perturbation approach

Aspects of modelling, stability and control of robotic manipulators with structurally compliant links and joints during contact with a stiff work environment are presented in this paper. System models of n joint robotic manipulators are cast into multiple time-scale formulations. Several different models are developed, based on the relative differences in magnitude of the scaling parameters associated with the manipulator link, joint and environment stiffnesses. These stiffnesses, if greatly different, lead to a four time-scale system with virtually no interaction between these subsystems. In these models, as various subsystem stiffness coefficients become approximately equal, strong interaction among the subsystems is seen. Utilizing the theory of singularly perturbed dynamic systems, aspects of overall system stability are touched on, and possible use of a high speed stabilizing control is considered. It is seen from the analysis presented, that depending on the relative structural stiffness of the link, joint and work environment, is is not always possible to apply a corrective control for certain structural compliance effects. An example serves to illustrate some of the concepts discussed in the paper.

It is noted that this paper does not provide general stability conclusions, but rather forms a framework for stability investigation.     

Kinematics and dynamic modeling for holonomic constrained multiple robot systems through principle of workspace orthogonalization

This paper deals with an efficient mathematical modeling for multiple robot manipulators (or multifingered robot hands) holding and transporting a rigid common object on the constraint surfaces, subject to a set of holonomic (integrable) constraints. First, the kinematics and dynamics of the multiple robot systems are formulated. After a series of model transformations, a combined dynamic model is derived from a unified viewpoint. Then the system dynamics can be decomposed into two orthogonal subsystems the (reduced-order) motion subsystem and the force subsystem. From a practical point of view, the new dynamic model presented in this paper is suitable form for dynamic analysis and hybrid (position/force) control synthesis.     

A mathematical study on a unified variational principle with two constrained parameters

In this paper, a parameterized variational principle based on a mixed functional obtained by a linear combination of the total potential energy functional, the modified Hellinger-Reissner functional, and the Hu-Washizu functional with two constrained parameters is proposed, and the mathematical characteristics of the variational equation of the principle are investigated for the analysis of boundary value problems in linear elasticity. It is first proved that the Euler-Lagrange equations of the variational equation is identical to the governing equations for the given problem. Then existence of the unique solution of the variational equation is systematically proved by showing that the energy bilinear form is weakly-coercive. As an application, the stress/strain smoothing can be obtained as a form of mixed FEM based on the variational equation.     

Analysis of kinematic systems: a generalized approach

The goal of the designer of kinematic systems is a deterministic and stable design. An analysis method must, therefore, be able to quantify both aspects. The generalized approach to the analysis of kinematic systems presented herein reduces the analysis of kinematic systems to simple matrix analysis. The system matrix containing the geometry of the system is introduced as the key to the analysis of kinematic systems. The procedure calculates the magnitudes of the contact forces from the external forces. Then Hertz's theory is used to estimate the deflections at the contact points, from which global error motions are computed. The method has been developed for two-body systems with an arbitrary number of unconstrained degrees of freedom. From these elementary building blocks, more complex systems can be assembled. We show how friction can be included in the model, based on simplifying assumptions. The quality/performance of the design can be checked at various points throughout the analysis. We show that the stability of kinematic systems is closely linked to the eigen values of the system matrix. The general formulation naturally includes previous work on such special cases as couplings and linear motion systems.     

Statistical formulation of friction systems

If the lubricant film fails to separate completely the parts of a friction system then the stability of the system is controlled by the population of contacts, over a large range of strain energy levels. Such a population may be treated as a canonical ensemble possessing some time-invariant macroscopic features, so that the techniques of statistical mechanics can be applied.Following the same steps as for the study of entropy, it is possible to obtain expressions for the partition function of the friction system and for the probability of contacts at a particular energy level. These expressions can be further used to deduce wear rates and to evaluate a set of thermodynamic-like terms on the basis of which new techniques of analysis may be developed.     

Crawler robot kinematics modeling by using a two-wheeled approach

The aim of this paper is to analyze the kinematics of a small crawler robot. A mathematical model of kinematics based on a two-wheeled approach is proposed. This model is experimentally verified using vision-based motion measurements of a crawler vehicle equipped with encoders and a remote control system. It is assumed that the vehicle moves along a few curves with different angular speeds of its wheels. Based on the model of motion and the values of these speeds, numerical simulations are investigated. The results obtained from numerical and experimental validation are presented and discussed. The comparison delivered some important conclusions.

     

Closed-loop control of constrained discrete event systems: application to a networked automation system

In this paper, we are interested in the design of closed-loop control laws to satisfy a set of temporal constraints in discrete event systems modeled by timed event graphs (TEGs). The dynamic behavior of the TEG is represented by a system of linear equations in Max-Plus algebra. Temporal constraints are imposed on some paths of the TEG and are expressed by a set of Max-Plus linear inequalities. The proposed approach is applied to the control of a networked automation producer/consumer system under a temporal constraint. The temporal constraint to be satisfied is imposed on the response time of the considered networked automation system (NAS). The calculated control laws are causal feedbacks and can be represented by monitor places connected to the NAS model.     

Digital controller design for absolute value function constrained nonlinear systems via scalar sign function approach

In this paper, a scalar sign function-based digital design methodology is developed for modeling and control of a class of analog nonlinear systems that are restricted by the absolute value function constraints. As is found to be not uncommon, many real systems are subject to the constraints which are described by the non-smooth functions such as absolute value function. The non-smooth and nonlinear nature poses significant challenges to the modeling and control work. To overcome these difficulties, a novel idea proposed in this work is to use a scalar sign function approach to effectively transform the original nonlinear and non-smooth model into a smooth nonlinear rational function model. Upon the resulting smooth model, a systematic digital controller design procedure is established, in which an optimal linearization method, LQR design and digital implementation through an advanced digital redesign technique are sequentially applied. The example of tracking control of a piezoelectric actuator system is utilized throughout the paper for illustrating the proposed methodology.     

CLFs-based optimization control for a class of constrained visual servoing systems

In this paper, we use the control Lyapunov function (CLF) technique to present an optimized visual servo control method for constrained eye-in-hand robot visual servoing systems. With the knowledge of camera intrinsic parameters and depth of target changes, visual servo control laws (i.e. translation speed) with adjustable parameters are derived by image point features and some known CLF of the visual servoing system. The Fibonacci method is employed to online compute the optimal value of those adjustable parameters, which yields an optimized control law to satisfy constraints of the visual servoing system. The Lyapunov's theorem and the properties of CLF are used to establish stability of the constrained visual servoing system in the closed-loop with the optimized control law. One merit of the presented method is that there is no requirement of online calculating the pseudo-inverse of the image Jacobian's matrix and the homography matrix. Simulation and experimental results illustrated the effectiveness of the method proposed here.     

Finite-time sliding surface constrained control for a robot manipulator with an unknown deadzone and disturbance

This paper presents finite-time sliding mode control (FSMC) with predefined constraints for the tracking error and sliding surface in order to obtain robust positioning of a robot manipulator with input nonlinearity due to an unknown deadzone and external disturbance. An assumed model feedforward FSMC was designed to avoid tedious identification procedures for the manipulator parameters and to obtain a fast response time. Two constraint switching control functions based on the tracking error and finite-time sliding surface were added to the FSMC to guarantee the predefined tracking performance despite the presence of an unknown deadzone and disturbance. The tracking error due to the deadzone and disturbance can be suppressed within the predefined error boundary simply by tuning the gain value of the constraint switching function and without the addition of an extra compensator. Therefore, the designed constraint controller has a simpler structure than conventional transformed error constraint methods and the sliding surface constraint scheme can also indirectly guarantee the tracking error constraint while being more stable than the tracking error constraint control. A simulation and experiment were performed on an articulated robot manipulator to validate the proposed control schemes.     

Fixed structure compensator design using a constrained hybrid evolutionary optimization approach

This paper presents an efficient technique for designing a fixed order compensator for compensating current mode control architecture of DC−DC converters. The compensator design is formulated as an optimization problem, which seeks to attain a set of frequency domain specifications. The highly nonlinear nature of the optimization problem demands the use of an initial parameterization independent global search technique. In this regard, the optimization problem is solved using a hybrid evolutionary optimization approach, because of its simple structure, faster execution time and greater probability in achieving the global solution. The proposed algorithm involves the combination of a population search based optimization approach i.e. Particle Swarm Optimization (PSO) and local search based method. The op-amp dynamics have been incorporated during the design process. Considering the limitations of fixed structure compensator in achieving loop bandwidth higher than a certain threshold, the proposed approach also determines the op-amp bandwidth, which would be able to achieve the same. The effectiveness of the proposed approach in meeting the desired frequency domain specifications is experimentally tested on a peak current mode control dc−dc buck converter.     

A unified modeling of Kanban systems using petri nets

The success of some Just In Time (JIT) systems has led to a growing interest in Kanban systems, which provide a way to implement a JIT control policy. Much work has recently been devoted to this problem, and especially many models have been developed to evaluate the performance of such systems. In this article, we focus our attention of these existing models. Each author uses his/her own representation, which is not formal in most cases, and so it is often difficult to understand the proposed model and to compare it with others. In this article, we show that Petri nets are well suited to provide a unified modeling of Kanban systems. We first propose a basic model, then show that most models encountered in the literature can easily be represented by a Petri net model. Once such a formal model is obtained, it can then be used to analyze the behavior of the system, both qualitatively and quantitatively. Some preliminary results pertaining to the quantitative analysis are presented at the end of the article.     

Trajectory planning and tracking control of a ground mobile robot:A reconstruction approach towards space vehicle

With the development of the similarity calculation method, the orbital motion of space vehicle can be translated into a sequence of waypoints that reflect position and velocity on the ground. In this paper, a motion control system is proposed to make the mobile robot pass through the desired waypoints for reconstructing the orbital motion. First, the parameterized trajectory optimization method is applied to generate a curvature-continuous trajectory from the waypoints, the position and velocity demands are presented as the equality constraints. Virtual positions are introduced to reduce the oscillation, and the total execution time of the whole trajectory is selected as the optimization parameter to reduce the computational burden. Then, an equivalence transformation is provided to translate the error system into an affine form, which is beneficial for the feedback controller design. Based on this, a nonlinear trajectory tracking controller is proposed, which includes a feedforward controller and an error feedback controller, and its exponential stability is proved using Persistency of Excitation Lemma. In addition, a shunting neural dynamics model is employed to avoid sharp velocity jumps. Finally, the performed experiments verify the effectiveness of the proposed method.     

A connector-based approach to the modular formulation problem for a mechanical product

To respond to marketing competition, companies strive to provide a large variety of products to meet consumers requirements. With more choices in products, such variety brings the company closer to the consumers. However, manufacturers are facing a new challenge. The assembly and partitioning of components and subassembly are becoming increasingly more complicated, which cause not only a proliferation of subassemblies but also increases the difficulty in manufacturing. To solve this problem, modular design is a key issue.This study presents a methodology for the formulation of modules on the basis of the connector concept. Based on the information entry in the assembly network sequence proposed by Tseng and Li [12], a modular partition based on the connector concept is explored. Moreover, the problem of assigning components after partitioning and the evaluation of the partitioning results are discussed.In this study, the definition and representation of connectors are described first. Then, the algorithm for the formulation of modules is discussed. Finally, a case study with a detailed analysis is provided to illustrate the application of the proposed methodology.     

支持复杂物理系统设计的多领域统一建模平台

针对复杂物理系统工程设计中多领域之间耦合并需要统一建模的问题,研究了基于Modelica语言多领域统一建模平台所涉及的文本建模、可视化建模、文本关联和模型解析等关键技术,并开发了相应的平台.开发了支持关键字高亮技术的文本编辑器,实现了文本建模;提出了模型库的序列化加载策略以提高模型库的加载速度;采用文本关联修改技术,保证了可视化建模中的模型与Modelica描述文本的一致性;通过词法分析、语法分析和语义检查等解析机制对文本建模或可视化建模所建立的Modelica模型进行合法性检查.最后给出了建模实例.     

Mobile robot trajectory tracking using noisy RSS measurements: An RFID approach

Most RF beacons-based mobile robot navigation techniques rely on approximating line-of-sight (LOS) distances between the beacons and the robot. This is mostly performed using the robot's received signal strength (RSS) measurements from the beacons. However, accurate mapping between the RSS measurements and the LOS distance is almost impossible to achieve in reverberant environments. This paper presents a partially-observed feedback controller for a wheeled mobile robot where the feedback signal is in the form of noisy RSS measurements emitted from radio frequency identification (RFID) tags. The proposed controller requires neither an accurate mapping between the LOS distance and the RSS measurements, nor the linearization of the robot model. The controller performance is demonstrated through numerical simulations and real-time experiments.     

A preview approach to force control of robot manipulators

Automated assembly operations that utilize robots tend to constrain the robot's motion due to the task geometry. This constrained motion is termed compliant motion. Complaint motion can be actively controlled using a method of force feedback based upon servo-loop compensation, or it can be passively controlled by mechanical devices integrated into the robot structure. The “preview approach” to force control presented in this paper is a scheme based on predictive calculation of the contact forces that develop at the interface between mating parts. The preview approach utilizes predicted, present and past information to execute motion control. Contact forces are calculated using a mathematical model of the assembly process and are then used to control the compliant motion through suitable compensation torques. The control algorithm used here is more efficient than the standard methods that rely on data from force sensors and use no preview.     

Fuzzy force control of constrained robot manipulators based on impedance model in an unknown environment

To precisely implement the force control of robot manipulators in an unknown environment, a control strategy based on fuzzy prediction of the reference trajectory in the impedance model is developed. The force tracking experiments are executed in an open-architecture control system with different tracking velocities, different desired forces, different contact stiffnesses and different surface figurations. The corresponding force control results are compared and analyzed. The influences of unknown parameters of the environment on the contact force are analyzed based on experimental data, and the tunings of predictive scale factors are illustrated. The experimental results show that the desired trajectory in the impedance model is predicted exactly and rapidly in the cases that the contact surface is unknown, the contact stiffness changes, and the fuzzy force control algorithm has high adaptability to the unknown environment. Translated from Journal of Northeastern University (Natural Science), 2005, 26(8): 766–769 [译自: 东北大学学报 (自然科学版)]     

水下机器人关节电机驱动系统研究

针对水下机器人关节电机驱动系统体积和功耗大的问题,根据对其系统原理和结构的分析,提出了一种采用高集成度器件、小型封装、多层印制电路板、低功耗器件、电能管理等方法来减小其体积和功耗的方法。研制了一套水下无刷直流电机驱动系统,该系统包括驱动电路、控制算法与控制界面,测量了驱动电路的面积和功耗值,并进行了速度伺服实验。研究结果表明:驱动电路的面积减小到仅为8.2 cm2,可以将其直接装入电机中;驱动系统的静态功耗和动态功耗分别为0.24 W和0.5 W,满足水下作业时的低功耗需求;电机装入操作臂时,给定120 r/min参考转速,电机能够在1 s内稳定,并准确地跟踪给定转速,完成水下作业任务。