Symbolic modeling and dynamic simulation of robotic manipulators with compliant links and joints

The explicit, non-recursive symbolic form of the dynamic model of robotic manipulators with compliant links and joints are developed based on a Lagrangian-assumed mode of formulation. This form of dynamic model is suitable for controller synthesis, as well as accurate simulations of robotic applications. The final form of the equations is organized in a form similar to rigid manipulator equations. This allows one to identify the differences between rigid and flexible manipulator dynamics explixitly. Therefore, current knowledge on control of rigid manipulators is likely to be utilized in a maximum way in developing new control algorithms for flexible manipulators.

Computer automated symbolic expansion of the dynamic model equations for any desired manipulator is accomplished with programs written based on commercial symbolic manipulation programs (SMP, MACSYMA, REDUCE). A two-link manipulator is used as an example. Computational complexity involved in real-time control, using the explicit, non-recursive form of equations, is studied on single CPU and multi-CPU parallel computation processors.     

Singularities in motion and displacement functions for a 7 degree-of-freedom manipulator

The authors propose a method for the determination of singularities in motion and displacement functions for a seven degree-of-freedom manipulator. The manipulator is considered, hereby, as a set of six degree-of-freedom manipulators. It is proven that two types of singularities in motion can occur at link positions that are independent and dependent with respect to the trajectory to be executed. The relations between the structure of singularity equations and displacement equations are discussed. The derivation of displacement equations for a manipulator with singularities of the second type is based on the idea of modeling of a manipulator by two open kinematic chains and invariants that may be found for these chains. The inverse kinematic equations and the equations of singularities in motion have been derived using a symbolic computer program which can handle manipulators of general structure (with five, six, and seven degrees-of-freedom). This program is written in the Symbolic Computation Language REDUCE.     

轮式移动机械臂的建模与仿真研究

移动机械臂系统一般由移动平台和机器臂组成,它既具有机器臂的操作灵活性,又具有移动机器人的可移动性,因此其应用范围要比单个系统宽得多。这篇文章主要研究了由非完整移动平台和完整机械臂组成的轮式移动机械臂系统的建模、跟踪控制及仿真问题。首先。利用拉格朗日动力学方程和非完整动力学罗兹方程建立了移动机械臂系统的精确数学模型;然后。利用非线性反馈将系统解耦。采用类PD控制器进行控制。在考虑了非完整约束及移动平台和机械臂的动态交互影响情况下,该控制算法保证系统同时跟踪给定的终端执行器和平台轨迹;最后,使用Maflah6．5对系统进行了仿真研究,仿真结果表明了其数学模型及控制方法的正确有效性。     

Prediction of geometric errors of robot manipulators with Particle Swarm Optimisation method

This paper reports on the prediction of the expected positioning errors of robot manipulators due to the errors in their geometric parameters. A Swarm Intelligence (SI) based algorithm, which is known as Particle Swarm Optimization (PSO), has been used to generate error estimation functions. The experimental system used is a Motoman SK120 manipulator. The error estimation functions are based on the robot position data provided by a high precision laser measurement system. The functions have been verified for three test trajectories, which contain various configurations of the manipulator. The experimental results demonstrate that the positioning errors of robot manipulators can be effectively predicted using some constant coefficient polynomials whose coefficients are determined by employing the PSO algorithm. It must be emphasized that once the estimation functions are obtained, there may be no need of any further experimental data in order to determine the expected positioning errors for a subsequent use in the error correction process.     

Modeling of tracked mobile manipulators with consideration of track–terrain and vehicle–manipulator interactions

This paper presents a systematic method to establish the kinematics model for a tracked mobile manipulator on firm grounds, with consideration of the interactive motions between the tracks and the terrain, as well as those between the tracked vehicle and the onboard manipulator. Kinematics analysis is essential for real-time pose estimation and online autonomous navigation of tracked mobile manipulators. Furthermore, to improve the effectiveness of motion planning, and to simulate or control tracked mobile manipulators, a reliable kinematics model is required. However, kinematics modeling for a tracked mobile manipulator is complicated by the fact that there are infinite number of contact points between the tracks and the terrain, which makes slippage unavoidable. The track–terrain and vehicle–manipulator interactions make the problem even more complicated as the motion of the onboard manipulator and the centrifugal forces during moderate or high speed motion give rise to transfer of the load distribution, which will affect the longitudinal and lateral tractive forces and the resistance. Also, the motion of the mobile platform contributes to the inertial forces of the manipulator, and the track–terrain interactive forces help balance the gravity as well as the manipulation forces. The developed kinematics modeling approach is presented on the basis of a tracked mobile manipulator in our laboratory, but the forward kinematics analysis method, and the track–terrain and vehicle–manipulator interaction analysis algorithm are general, and can be used for any tracked mobile manipulators with little modification. This work lays a solid foundation for autonomous control, online slippage estimation, real-time traction optimization as well as tip-over prediction and prevention of tracked mobile manipulators.     

Explicit dynamics of space free-flyers with multiple manipulators via SPACEMAPLE

This paper focuses on the dynamics of a multiple manipulator space free-flying robot (SFFR) with rigid links and issues relevant to the development of appropriate control algorithms. To develop an explicit dynamics model of such complex systems, the Lagrangian formulation is applied. First, the system kinetic energy is derived based on a developed kinematics approach. Then, through vigorous mathematical analyses, three formats are obtained which describe the contribution of each term of kinetic energy to the equations of motion. Next, explicit derivations of a system's mass matrix, and of the vectors of non-linear velocity terms and generalized forces are introduced for the first time. The obtained dynamics model is very useful for dynamics analyses, design and development of control algorithms for such complex systems. The explicit SFFR dynamics can be implemented either numerically or symbolically. Following the latter approach, the developed symbolic code for dynamics modeling, i.e. SPACEMAPLE, and its verification procedure are described, and issues relevant to the development and computation of dynamics models in control algorithms are briefly discussed. Specific dynamic characteristics of SFFRs compared to fixed-base manipulators are pointed out.     

Task-Space Modular Dynamics for Dual-Arms Expressed through a Relative Jacobian

This paper presents modular dynamics for dual-arms, expressed in terms of the kinematics and dynamics of each of the stand-alone manipulators. The two arms are controlled as a single manipulator in the task space that is relative to the two end-effectors of the dual-arm robot. A modular relative Jacobian, derived from a previous work, is used which is expressed in terms of the stand-alone manipulator Jacobians. The task space inertia is expressed in terms of the Jacobians and dynamics of each of the stand-alone manipulators. When manipulators are combined and controlled as a single manipulator, as in the case of dual-arms, our proposed approach will not require an entirely new dynamics model for the resulting combined manipulator. But one will use the existing Jacobians and dynamics model for each of the stand-alone manipulators to come up with the dynamics model of the combined manipulator. A dual-arm KUKA is used in the experimental implementation.     

Model of Mobile Manipulator Performance Measurement using SysML

Test methods for measuring safety and performance of mobile manipulators have yet to be developed. Therefore, potential mobile manipulator users cannot compare one system to another. Systems Modeling Language (SysML) is a general-purpose modeling language for systems engineering applications that supports the specification, analysis, design, verification, and validation of simple through complex systems, such as mobile manipulators. As test methods are developed to allow performance comparison of the varied mobile manipulators, so to should be the case of allowing comparison of most any mobile manipulator configuration and control strategy during performance measurements. Additionally, mobile manipulator manufacturers and users can then compare these systems to tasks using various methods. This paper uses SysML to describe two measurement methods (optical tracking and artifacts) and the performance measurement of mobile manipulators performing assembly tasks. The SysML models are verified through systems review, referenced experimentation and summarize with uncertainty propagation models of the mobile manipulator.     

Robust Fuzzy Control of Electrical Manipulators

Stability analysis for fuzzy control of robot manipulators has been a serious challenging problem in literature. The theoretical difficulties are highly increased due to the complexity of both manipulator dynamics and fuzzy controller structure. This paper develops a novel robust fuzzy control approach for electrical robot manipulators using the direct method of Lyapunov. We pass analytical difficulties by the use of voltage control strategy in replace of torque control strategy. Then, a normalized and decentralized Takagi–Sugeno fuzzy controller is presented in a simple structure. A simple Lyapunov candidate is proposed to apply stability analysis without knowing the explicit dynamics of system. Consequently, fuzzy control is analyzed and designed as a robust nonlinear control. Roles of scaling factors, gains in consequent parts, and membership functions in condition parts are considered in the control design. The proposed control approach is applied on a Puma560 robot arm.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

微重力环境下空间机械手的动力学建模新方法

未来空间作业将需要机械手在微重力的环境下完成各种复杂的任务．由于机械手与其本体的动态耦合，给机械手带来了许多运动学、动力学及控制方面的问题．本文提出了一种空间机械手动力学的建模新方法，对空间机械手的正、逆动力学进行了分析．应用该方法，建立了一种基于解出加速度的空间机械手的控制策略．本文所提出的方法不仅适合于单机械手系统，而且适合于多机械手的系统．     

Classification of kinematic singularities in planar robot manipulators

In [13, 14] we have proclaimed a singularity theory based programme of investigations of kinematic singularities in robot manipulators. The main achievement of the programme consists in providing local candidate models of kinematic singularities. However, due to the specific form of the manipulator kinematics, fitting the candidate models into the prescribed robot kinematics is a fairly open problem. The problem is easily solvable only around non-singular configurations of manipulators, where locally the kinematics can be modelled by linear injections or projections. In this paper we are concerned with planar manipulator kinematics, and prove that, under a mild geometric condition, such kinematics can be transformed around singular configurations to simple quadratic models of the Morse type. The models provide a complete local classification of generic planar kinematics of robot manipulators.     

Neural network based dynamic modeling of flexible‐link manipulators with application to the SSRMS

This paper presents an approach for dynamic modeling of flexible‐link manipulators using artificial neural networks. A state‐space representation is considered for a neural identifier. A recurrent network configuration is obtained by a combination of feedforward network architectures with dynamical elements in the form of stable filters. To guarantee the boundedness of the states, a joint PD control is introduced in the system. The method can be considered both as an online identifier that can be used as a basis for designing neural network controllers as well as an offline learning scheme to compute deflections due to link flexibility for evaluating forward dynamics. Unlike many other methods, the proposed approach does not assume knowledge of the nonlinearities of the system nor that the nonlinear system is linear in parameters. The performance of the proposed neural identifier is evaluated by identifying the dynamics of different flexible‐link manipulators. To demonstrate the effectiveness of the algorithm, simulation results for a single‐link manipulator, a two‐link planar manipulator, and the Space Station Remote Manipulator System (SSRMS) are presented. ©2000 John Wiley & Sons, Inc.     

Adaptive control for robot manipulators using multiple parameter models

In this paper, we propose multiple parameter models based adaptive switching control system for robot manipulators. We first uniformly distribute the parameter set into a finite number of smaller compact subsets. Then, distributed candidate controllers are designed for each of these smaller compact subsets. Using Lyapunov inequality, a candidate controller is identified from the finite set of distributed candidate controllers that best estimates the plant at each instant of time. The design reduced the observer-controller gains by reducing modeling errors and uncertainties via identifying an appropriate control/model via choosing largest guaranteed decrease in the value of the Lyapunov function energy function. Compared with CE based CAC design, the proposed design requires smaller observer-controller gains to ensure stability and tracking performance in the presence of large-scale modeling errors and disturbance uncertainties. In contrast with existing adaptive method, multiple model based distributed hybrid design can be used to reduce the energy consumption of the industrial robotic manipulator for large scale industrial automation by reducing actuator input energy. Finally, the proposed hybrid adaptive control design is experimentally tested on a 3-DOF Phantom^TM robot manipulator to demonstrate the theoretical development for real-time applications.

     

A new repetitive controller for mechanical manipulators

A new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks is developed. This controller does not require exact knowledge of the manipulator dynamic structure or its parameters, and is computationally efficient. In addition, no actual joint accelerations or any matrix inversions are needed in the control law. The global asymptotic stability of the ideal and the robust stability of the nonideal control system is proven, taking into account the full nonlinear dynamics of the manipulator. Simulation results of this algorithm applied to a realistic Scara type manipulator, which includes dry friction, pay-load inertia variations, actuator/sensor noise, and unmodelled dynamics are also presented.     

Modelling and simulation of an underwater manipulator

Recently, applications of articulated manipulators have increased to include extreme environments such as underwater and space. Simulation systems to support the design and control of industrial robots have been developed in many laboratories, and some high-speed calculation methods for inverse dynamics analysis of manipulators with series connections have been proposed. This paper deals with the dynamic simulation and modelling of underwater articulated manipulators. The dynamics of the above manipulators are formulated to evaluate the influence of the added mass tensor, the added inertia tensor, and fluid drag, and the lift on each arm according to classical Newton-Euler mechanics. Moreover, by generalizing this model, we can discuss the dynamics of a manipulator with dual arms and simulate some constrained motion of an end-effector. As an example of inverse dynamics analysis, the force and moment of a nine degrees of freedom (d.o.f.) manipulator with dual arms are analysed. As an example of direct dynamics analysis, hybrid control of both the force and the position of a 6 d.o.f. manipulator is simulated.     

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

Fuzzy-Basis-Function-Network-Based $H_infty$ Tracking Control for Robotic Manipulators Using Only Position Feedback

This paper presents an H _infin fuzzy output-feedback tracking-control scheme for robotic manipulators without measuring joint velocities. The developed controller and observer are based on a fuzzy basis function network (FBFN), which is employed to approximate nonlinear functions in the dynamics of controller and observer. The FBFN-based observer that estimates joint velocities can remove the needs of full-state measurements. According to the inevitable approximation errors and external disturbances, an H _infin auxiliary control signal is used to suppress the effects of the uncertainties. Moreover, all parameters of the fuzzy basis functions (FBFs) and FBF-to-output weights can be tuned online. The proposed controller requires no prior knowledge about the dynamics of the robot manipulator and no offline learning phase. Finally, comparative simulations on a three-link robot manipulator are provided to illustrate the tracking performance of the H _infin FBFN-based output-feedback control approach.     

Symbolic modeling in robotics: Genesis,applicaton, and future prospects

This survey article gives an overview of software packages for generating numerically efficient manipulator models in symbolic form, i.e. as computer programs written in a high-level language such as C or FORTRAN. We chronicle the history of computational robot dynamics and, to some extent, multibody systems dynamics. We survey several mechanical computer-aided engineering software packages because they have charted the course for symbolic robot modeling software. The attractive features of various programs regarding areas of application (vehicles, robots, satellites, etc.) and design possibilities (kinematic and dynamic analysis, modal analysis, optimization of mechanical design, numerical efficiency of generated symbolic models, etc.) are emphasized. Finally, as an example, we present the SYM program package in more detail and point out the new strategic area of robotics which has emerged during the last two years: computer-aided generation of control laws.     

Vibration analysis of cable-driven parallel manipulators

A cable-driven parallel manipulator is a manipulator whose end-effector is driven by a number of parallel cables instead of rigid links. Since cables always have more flexibility than rigid links, a cable manipulator bears a concern of possible vibration. Thus, investigation of vibration of cable manipulators caused by cable flexibility is important for applications requiring high system stiffness or bandwidth. This paper provides a vibration analysis of general 6-DOF cable-driven parallel manipulators. Based on the analysis of the natural frequencies of the multibody system, the study demonstrates that a cable manipulator can be designed stiff enough for special applications like the cable-manipulator based hardware-in-the-loop simulation of contact dynamics. Moreover, under an excitation, a cable may vibrate not only in its axial direction, but also in its transversal direction. The paper also analyzes the vibration of cable manipulators caused by cable flexibilities in both axial and transversal directions. It is shown that the vibration of a cable manipulator due to the transversal vibration of cables can be ignored comparing to that due to the axial flexibility of cables.