Constrained motion control of flexible robot manipulators based on recurrent neural networks

In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force everted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control, scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.     

Hybrid control: A constrained motion perspective

Control of manipulators during execution of tasks that require the end-effector to come into contact with objects in its work environment represents an important class of control problem. Hybrid control, a concept which defines the architecture of a class of control laws has been proposed as a method with which to solve this control problem. One interpretation of the hybrid control method is within the framework of constrained motion control. Constrained motion occurs during contact by the manipulator end-effector with rigid objects in the workplace, hence the motion of the manipulator is kinematically constrained. Papers have appeared in the robotics control literature addressing hybrid control within the constrained motion context which do not explicitly use the constrained dynamic formulation that correctly describes the dynamic behaviour of the manipulator. This article serves to link results from constrained motion control and the existing literature on the hybrid control method. In this article a formulation of the constrained manipulator dynamics is presented in which the hybrid control design is most naturally carried out. This formulation of the manipulator dynamics, previously proposed in the robotics literature, is such that the generalized force and position coordinates to be controlled are mutually orthogonal. Hence, the hybrid selection matrices, a key element of the hybrid control design philosophy, are implicit in this coordinate representation. A hybrid control design methodology is then formulated based on this development. Two hybrid control laws are proposed. For each hybrid control law, the global asymptotic stability is readily established due to the natural coordinate representation. One of these hybrid control laws, a constrained motion control law already proposed in the literature, is given to illustrate the equivalence of the hybrid control design and certain existing constrained motion control methods. Finally, a concrete example of a three-degree-of-freedom robotic manipulator illustrates the hybrid design methodology proposed.     

接触作业型飞行机械臂系统的力/位置混合控制

针对飞行机械臂系统移动接触作业问题,使用了一个力/位置混合控制框架,用以控制飞行器系统持续可靠地接触外部环境同时保持一定大小的接触力,并实现在接触过程中的期望轨迹跟踪.首先将作业空间分成2个子空间--约束空间和自由空间,并分别进行力控制和位置控制.对于力控制问题,证明闭环无人机系统是一个类弹簧-质量-阻尼系统,然后在约束子空间中设计逆动力学控制器来实现接触力控制.自由飞行空间中的运动控制依靠轨迹规划和位置控制器来实现.最后,开发了基于六旋翼飞行机器人的单自由度飞行机械臂系统,在飞行状态下进行接触墙面并跟踪倾斜直线轨迹的实验.结果显示本文所使用方法能够保证在平稳移动的同时控制期望的接触力.     

Position/Force Control of an Underwater Mobile Manipulator

This paper proposes a new control method applied to an underwater vehicle equipped with a robot manipulator. This control method is based on force control to stabilize the platform when the manipulator works in free or constrained space. The torque produced by the arm on the platform is estimated with a force sensor installed between the base of the manipulator and the vehicle. This allows correcting the position errors of the platform using an external force control loop. This paper presents this control law and shows some simulation results. © 2003 Wiley Periodicals, Inc.     

Stability of hybrid position and force control for robotic manipulator with kinematics and dynamics uncertainties

Most research so far on hybrid position and force control laws of robotic manipulator has assumed that knowledge of kinematics is known exactly. In the presence of modeling errors, it is unknown whether the stability of the constrained robot system can still be ensured. In this paper, stability and setpoint control problems of constrained robot with kinematics and dynamics uncertainties are formulated and solved. We shall show that the manipulator end-effector's motion is asymptotically stable even in the presence of such uncertainties.     

Continuous shape-grinding experiment based on model-independent force/position hybrid control method with on-line spline approximation

Based on the analysis of interaction between manipulator’s hand and working object, a model representing the constrained dynamics of robot is first discussed. The constraint forces are expressed by algebraic function of states, input generalized forces, and constraint condition, and then a decoupling control method of force and position of manipulator’s hand tip is proposed. In order to give the grinding system the ability to adapt to any object shape being changed by the grinding, estimating function of the constraint condition in real time for the adaptive force/position control was added, which is indispensable for the proposed method without using force sensor. This paper explores whether the performance of the proposed controller is independent of alloy work-piece models or not. The experimental result is shown to verify the feature of the decoupling control of force and position of the tip.     

Impedance control of industrial robots

Manipulation fundamentally requires the manipulator to be mechanically coupled to the object being manipulated. A consideration of the physical constraints imposed by dynamic interaction shows that control of a vector quantity such as position or force is inadequate and that control of the manipulator impedance is necessary. Techniques for planning and control of manipulator behavior are presented which result in a unified approach to target acquisition, obstable avoidance, kinematically constrained motion, and dynamic interaction. A feedback control algorithm for implementing a cartesian end-point impedance on a nonlinear manipulator is presented. The modulation of end-point impedance independent of feedback is also considered. A method for choosing the impedance appropriate to a task using optimization theory is discussed.     

一种受限机械手的自适应力/位置控制方法*

对于受限机械臂,本文提出了一种自适应的力/位置控制方法。其实现是基于给出的新的降阶动力学模型,在反馈信号中引入力的累积误差信号,利用降阶模型的本身特性从而达到自适应力/位置控制的目的。给出的自适应律是通过跟踪误差信号来调节的。仿真结果证实了本方法的正确性。     

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.     

Adaptive force and position control of manipulators

The article presents simple methods for the design of adaptive force and position controllers for robot manipulators within the hybrid control architecture. The force controller is composed of an adaptive PID feedback controller, an auxiliary signal, and a force feedforward term, and achieves tracking of desired force setpoints in the constraint directions. The position controller consists of adaptive feedback and feedforward controllers as well as an auxiliary signal, and accomplishes tracking of desired position trajectories in the free directions. The controllers are capable of compensating for dynamic cross-couplings that exist between the position and force control loops in the hybrid control architecture. The adaptive controllers do not require knowledge of the complex dynamic model or parameter values of the manipulator or the environment. The proposed control schemes are computationally fast and suitable for implementation in online control with high sampling rates. The methods are applied to a two-link manipulator for simultaneous force and position control. Simulation results confirm that the adaptive controllers perform remarkably well under different conditions.     

Independent Hybrid Force/Motion Control of Constrained Six-Degrees-of-Freedom Manipulators

Controlling the dynamics of a constrained manipulator includesposition tracking as well as stabilization of the contact wrench.In this paper we derive a control scheme, that makes it possible to treat position and force control independently.The approach is based on a mass-orthogonal splitting of the space of joint torques, allowing independent actuation and therefore independent specification of control laws. An appropriate definition of the reference wrenchmakes it possible to achieve independent stability of the position and force loop.     

On the decoupling of position and force controllers in constrained robotic tasks

In hybrid control of robot manipulators separate controllers are designed for force and position errors control. Controllers are designed either in task or joint space and their outputs combine to provide input torque to the manipulator. Position and force controllers performance in a constrained robotic task is affected by their interaction to a degree dependent on the controller's ability to reject disturbances. Ideally, decoupling of the two control loops is desired to achieve the best performance in position and force directions. In this article, analysis of control loop interactions is performed for contact and noncontact phases, and controller design requirements are developed to achieve maximum decoupling. Design requirements involve output subspace of each controller leading to control discontinuities for contact and noncontact phases. In the noncontact phase, satisfaction of design requirements leads to a fully linearized and decoupled system. When in contact with the constraining surface, design requirements eliminate disturbances in the force loop, but minimize disturbances in the position loop to an extent dependent on force loop performance. Known hybrid control schemes analysis is performed to reveal existence of control loop interactions in these schemes. Confirmation of theoretical analysis is done through simulation of a three revolute planar manipulator. © 1998 John Wiley & Sons, Inc.     

机器人位置/力控制系统的稳定性

本文通过一个简单的两自由度机器人,分析了 Raibert 和 Craig 提出的位置/力混合控制器的不稳定性问题,提出了力微分反馈控制和在力控制方向引入位置反馈这两种克服不稳定性的方法;在此基础上,对一般机器人提出了一种有效的位置/力控制结构。大量的仿真研究显示了该控制结构的有效性,并给出了关于力控制器设计的一些重要结论.     

失重环境下可控柔性臂的模态特性

在非重力场中,考虑控制器动态反馈的影响,对存在控制器定位约束的柔性臂系统进行动力分析,研 究其在相对平衡位置的模态特性．以具有柔性关节和弹性臂杆的可控柔性臂为研究对象,分析了控制器作用下的反 馈约束特性,将控制器位置和速度增益引入力边界条件,得到了耦合控制器参量的模态特征方程,证明了反馈约束 的存在使得系统特征频率为复频率,且模态主振型是复变函数．通过数值仿真,明确了可控柔性臂的模态特性与控 制器增益之间的关系,得到了不同于经典振动理论的结论．设计了可控柔性臂的仿失重实验平台,试验模态结果证 明了理论分析的有效性．     

Stability and control aspects of flexible link robot manipulators during constrained motion tasks

The effect of robotic manipulator structural compliance on system stability and trajectory tracking performance and the compensation of this structural compliance has been the subject of a number of publications for the case of robotic manipulator noncontact task execution. The subject of this article is the examination of dynamics and stability issues of a robotic manipulator modeled with link structural flexibility during execution of a task that requires the robot tip to contact fixed rigid objects in the work environment. The dynamic behavior of a general n degree of freedom flexible link manipulator is investigated with a previously proposed nonlinear computed torque constrained motion control applied, computed based on the rigid link equations of motion. Through the use of techniques from the theory of singular perturbations, the analysis of the system stability is investigated by examining the stability of the “slow” and “fast” subsystem dynamics. The conditions under which the fast subsystem dynamics exhibit a stable response are examined. It is shown that if certain conditions are satisfied a control based on only the rigid link equations of motion will lead to asymptotic trajectory tracking of the desired generalized position and force trajectories during constrained motion. Experiments reported here have been carried out to investigate the performance of the nonlinear computed torque control law during constrained motion of the manipulator. While based only on the rigid link equations of motion, experimental results confirm that high-frequency structural link modes, exhibited in the response of the robot, are asymptotically stable and do not destabilize the slow subsystem dynamics, leading to asymptotic trajectory tracking of the overall system. © 1992 John Wiley & Sons, Inc.     

Sliding mode force,motion control,and stabilization of elastic manipulator in the presence of uncertainties

This article considers the question of position and force control of three-link elastic robotic systems on a constraint surface in the presence of robot parameter and environmental constraint geometry uncertainties. The approach of this article is applicable to any multi-link elastic robot. A sliding mode control law is derived for the position and force trajectory control of manipulator. Unlike the rigid robots, sliding mode control of an end point gives rise to unstable zero dynamics. Instability of the zero dynamics is avoided by Controlling a point that lies in the neighborhood of the actual end point position. The sliding mode controller accomplishes tracking of the end-effector and force trajectories on the constrained surface; however, the maneuver of the arm causes elastic mode excitation. For point-to-point control on the constraint surface, a stabilizer is designed for the final capture of the terminal state and vibration suppression. Numerical results are presented to show that in the closed-loop system position and force control is accomplished in spite of payload and constraint surface geometry uncertainty. © 1995 John Wiley & Sons, Inc.     

面向位控机器人的力/位混合控制

本文提出了一种面向位控机器人的力/位混合控制策略．通过力反馈信息对未知约 束进行估计获得位控和力控方向,根据位控和力控方向对机器人终端的运动轨迹进行规划, 并采用阻抗力控制规律以使机器人获得较好的柔顺性．仿真试验表明,该策略具有较高的力 控制精度和表面跟踪能力．     

平面双连杆受限柔性机器人臂的动力学建模*

对一类平面双连杆受限柔性机器人臂的动力学建模问题进行研究，利用Ｄ’Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理得到了一组描述该机器人系统运动性态的动力学方程。与已有的动力学模型相比，本文所建立的运动方程和振动方程具有模型准确、结构简单等特点，且具有与传统无约束刚性机器人类似的模型形式，因而有可能直接或间接利用现有的关于刚性机器人运动控制等方面的成果来研究复杂的受限柔性机器人的控制问题。     

Intelligent compliant motion control

The role of a compliant motion scheme is to control a robot manipulator in contact with its environment. By accommodating with the interaction force, the manipulator can be used to accomplish tasks that involve constrained motions. This paper presents a new work on the compliant motion control for position-controlled manipulator. A new method for achieving efficient interaction between the manipulator and its environment is developed. The interaction force is reduced using a quadratic cost function. In this method, the compliance is formulated as function of the interaction force. An adaptive element is used to update the compliance. The stability of the system is investigated using the Lyapunov approach. Experiments are conducted in our laboratory to demonstrate the use of such scheme.