A globally stable state feedback controller for flexible joint robots

The paper addresses the problem of controlling the joints of a flexible joint robot with a state feedback controller and proposes a gradual way of extending such a controller towards the complete decoupling of the robot dynamics. The global asymptotic stability for the state feedback controller with gravity compensation is proven, followed by some theoretical remarks on its passivity properties. By proper parameterization, the proposed controller structure can implement a position, a stiffness or a torque controller. Experimental results on the DLR lightweight robots validate the method.     

基于关节力矩传感器的灵巧手指的阻抗控制

基于位置的阻抗控制以位置控制为基础,将它作为整个控制器的内环,附加的外环是阻抗力控制器,其控制效果的好坏取决于位置控制器的精确程度。将轨迹跟踪控制算法构建的位置控制器作为控制内环,同样阻抗参数下,增加了控制的稳定性和柔顺性,减小了超调和跟踪阶段的误差。并给出了基于H IT/DLR灵巧手手指基关节力矩传感器的阻抗控制的实验效果。     

On the Passivity-Based Impedance Control of Flexible Joint Robots

In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.     

Control of constrained robots including effects of joint flexibility and actuator dynamics

We consider mathematical representations of constrained robot systems in which the effects of joint flexibility and actuator dynamics are significant. The objective is to design a feedback control law so that the position output variables and the force output variables of the robot follows the desired position and the desired force trajectories respectively despite the presence of joint flexibility and actuator dynamics. A systematic procedure is developed for designing a feedback control law which ensures that the position variables track the desired position trajectories exponentially, and the force variables track the desired force trajectories exponentially. The development of the control law is based on the model of a constrained robot system which includes the effects of actuator dynamics and joint flexibility. Thus using the force/position control law developed in this paper one can achieve better tracking performance in cases where such effects are significant.     

基于关节力矩的柔性关节机器人的控制策略

由于关节柔性降低了系统的带宽并影响系统的鲁棒稳定性,因此,采用基于关节力矩负反馈的控制策略。通过减小电机端有效惯量的方法可以大大提高系统带宽并增强鲁棒稳定性;在机器人的控制上,采用一种基于全状态反馈的复合控制结构,证明了系统的稳定性,并在现有的机械臂上实现了位置和阻抗控制实验,验证了该控制策略的有效性和可行性。     

基于连杆力矩传感器动态补偿的机器人灵巧手笛卡儿阻抗控制

为了对连杆空间力矩传感器进行动态补偿,提出了适用于求取串联机器人任意连杆中任意一点处所受的内力和内力矩的算法.该算法采用连杆假想截断原理利用牛顿-欧拉方程推导而出.推导过程综合考虑了串联机器人是否处于静态以及末端是否受外力作用的情况,以及串联机器人的关节是否是回转关节的情况.然后利用该算法计算动态补偿值,构建了基于连杆力矩传感器动态补偿的笛卡儿阻抗控制器.最后在HIT/DLR Hand II五指灵巧手上进行了实验验证.实验结果一方面验证了该算法的有效性,另一方面也验证了本文所构建的笛卡儿阻抗控制器的有效性.     

Overview of the Lucy Project: Dynamic Stabilization of a Biped Powered by Pneumatic Artificial Muscles

This paper gives an overview of the Lucy project. What is special is that the biped is not actuated with the classical electrical drives, but with pleated pneumatic artificial muscles. In an antagonistic setup of such muscles both the torque and the compliance are controllable. From human walking there is evidence that joint compliance plays an important role in energy-efficient walking and running. To be able to walk at different walking speeds and step lengths, a trajectory generator and joint trajectory tracking controller are combined. The first generates dynamically stable trajectories based on the objective locomotion parameters which can be changed from step to step. The joint trajectory tracking unit controls the pressure inside the muscles so the desired motion is followed. It is based on a computed torque model and takes the torque–angle relation of the antagonistic muscle setup into account. With this strategy the robot is able to walk at a speed up to 0.15 m/s. A compliance controller is developed to reduce the energy consumption by combining active trajectory control with the exploitation of the natural dynamics. A mathematical formulation was developed to find an optimal compliance setting depending on the desired trajectory and physical properties of the system. This strategy is experimentally evaluated on a single pendulum structure and not implemented on the real robot because the walking speed of the robot is currently too slow. At the end a discussion is given about the pros and cons of building a pneumatic biped, and the control architecture used.     

Dynamic Load Carrying Capacity of Flexible Cable Suspended Robot: Robust Feedback Linearization Control Approach

In this paper dynamic load carrying capacity (DLCC) of a cable robot equipped with a closed loop control system based on feedback linearization, is calculated for both rigid and flexible joint systems. This parameter is the most important character of a cable robot since the main application of this kind of robots is their high load carrying capacity. First of all the dynamic equations required for control approach are represented and then the formulation of control approach is driven based on feedback linearization method which is the most suitable control algorithm for nonlinear dynamic systems like robots. This method provides a perfect accuracy and also satisfies the Lyapunov stability since any desired pole placement can be achieved by using suitable gain for controller. Flexible joint cable robot is also analyzed in this paper and its stability is ensured by implementing robust control for the designed control system. DLCC of the robot is calculated considering motor torque constrain and accuracy constrain. Finally a simulation study is done for two samples of rigid cable robot, a planar complete constrained sample with three cables and 2 degrees of freedom and a spatial unconstrained case with six cables and 6 degrees of freedom. Simulation studies continue with the same spatial robot but flexible joint characteristics. Not only the DLCC of the mentioned robots are calculated but also required motors torque and desired angular velocity of the motors are calculated in the closed loop condition for a predefined trajectory. The effectiveness of the designed controller is shown by the aid of simulation results as well as comparison between rigid and flexible systems.     

无轴承同步磁阻电机逆系统解耦控制仿真研究

研究无轴承同步磁阻电机稳定性控制问题,由于无轴承同步磁阻电机是一个强耦合的非线性系统,为实现负载条件下的稳定悬浮运行,需解除电机转矩和径向悬浮力等多变量之间的耦合关系。针对前馈补偿解耦的缺陷,给出了无轴承同步磁阻电机包含转矩控制和悬浮力控制的统一数学模型,证明电机逆系统存在,设计了一种通过非线性状态反馈的逆系统解耦控制方案,将复杂的无轴承同步磁阻电机系统解耦成两个转子径向位置二阶积分子系统和一个转速一阶积分子系统,并用PI和PID调节器分别对转子位置与转速进行综合设计。运用MATLAB软件对电机控制系统进行仿真。仿真结果证明,解耦控制方案的有效性,为电机系统优化设计提供了保证。     

The control of robot manipulators with bounded input

The problem of tracking a desired trajectory in the state space of ann-link robotic manipulator with bounds on the allowable input torque is considered. Using a so-called optimal decision strategy (ODS), a pointwise optimal control law is derived which, at each timet, minimizes the deviation between the vector of joint accelerations and a desired joint acceleration vector, subject to the input constraints. The design of the optimal control law is reduced to the solution of a quadratic programming problem which is solved using the primal-dual method. The solution gives an on-line feedback control scheme for trajectory following in the presence of input constraints. In addition, we extend the above optimal decision strategy to the case where the controller design is based on a simplified model or where the plant itself is imprecisely known. The resulting torque optimization scheme may be incorporated into any existing control scheme to account for input bounds. This has important implications for the problem of deriving robust control schemes that take into account parameter uncertainty and model simplification. Simulations are presented for the case of a three-link manipulator with bounded torque, and our results are compared to the computed torque method. Our simulations show that by optimally adjusting the input torque to each joint when one or more of them saturates, significant improvement in tracking performance can result.     

Force-guided motions of a 6-d.o.f. industrial robot with a joint space approach

This article deals with the interaction between humans and industrial robots, more specifically with the new design and implementation of an algorithm for force-guided motions of a 6-d.o.f. robot. It may be used to comfortably teach positions without using any teaching pendant or for some assistance tasks. For this purpose, from readings of the force/torque sensor mounted in the robot wrist, the gravity forces and torques first have to be eliminated. To control the robot in joint space, it is then convenient to transform the external force and torque values from Cartesian space into joint space using the manipulator transposed Jacobian. This is why with the present approach the Jacobian matrix of the robot used was calculated. Now, from the computed joint torques, suitable position commands of the robot arm can be generated to obtain the desired behavior. A suggestion for this desired behavior is also included in this article. It is based on the impedance control approach in joint space. The proposed algorithm was implemented with the standard Stäubli RX90B industrial robot.     

Two adaptive control structures of robot manipulators

This paper proposes two simple adaptive control schemes of robot manipulators. The first one is the state feedback control which consists of feedforward from the desired position trajectory, PD feedback from the actual trajectory, and an auxiliary input. The second one is the feedforward/feedback control which consists of a feedforward term from the desired position, velocity, and acceleration trajectory based on the inverse of robot dynamics. The feedforward, feedback, and auxiliary gains are adapted using simple equations derived from the decentralized adaptive control theory based on Lyapunov's direct method, and using only the local information of the corresponding joint. The proposed control schemes are computationally fast and do not require a priori knowledge of the detail parameters of the manipulator or the payload. Simulation results are presented in support of the proposed schemes. The results demonstrate that both controllers perform well with bounded adaptive gains.     

A predictive controller based on dynamic matrix control for a non-minimum phase robot manipulator

In this paper a hybrid control strategy is presented based on Dynamic Matrix Control (DMC) and feedback linearization methods for designing a predictive controller of five bar linkage manipulator as a MIMO system (two inputs and two outputs). Analyzing the internal dynamic of robot shows the open loop system is unstable and non-minimum phase, so in order to apply the predictive controller, special modifications are needed. These modifications on non-minimum phase behavior are performed using feedback linearization procedure based on state space realization. The design objective is to track a desirable set point as well as time varying trajectories as a command references with globally asymptotical stabilization. The proposed controller is applied to nonlinear fully coupled model of the typical five bar linkage manipulator with non-minimum phase behavior. Simulation results show that the proposed controller has good efficiency. The step responses of system with and without feedback linearization process illustrated that the mentioned modification for stabilizing is performed properly. After applying the proposed predictive controller, the joint angle of robot tracks the reference input while another input acts as the disturbance and vice versa.     

A PASSIVITY PLUS FLATNESS CONTROLLER FOR THE PERMANENT MAGNET STEPPER MOTOR

A passivity based controller, in suitable combination with the flatness property of the system, is proposed for the effective feedback equilibrium to equilibrium regulation, via planned trajectory tracking, of the angular position in a permanent magnet (PM) stepper motor. The control scheme is shown to be easily modifiable as to include traditional proportional‐integral‐derivative (PID) feedback control actions which efficiently account for unmodeled load torque perturbations.     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

Manipulator motion control in operational space using joint velocity inner loops

This paper addresses the operational space motion control—trajectory tracking—of robot manipulators endowed with joint velocity feedback inner loops. A general structure for model-based joint velocity controllers is proposed for the inner loop. The required joint velocity reference is provided by an outer loop inspired from the robot kinematic control approach. It is shown that above two-loops control schemes lead to a nice cascade structure for the corresponding closed-loop systems. A stability result adapted for analysis of this particular kind of systems is developed in the paper; sufficient conditions for global exponential stability of this class of cascade systems are obtained. The effectiveness of the proposed control approach is evaluated on a direct-drive mechanical arm, and compared with a typical control strategy based on inverse kinematics resolution for computation of the desired motion in joint space, and the use of the computed-torque technique. The experimental evidences show better performance of the proposed two-loops controller.     

基于免疫优化的平面Acrobot线性自抗扰鲁棒镇定

针对受不确定性影响的平面Acrobot机器人,提出一种基于免疫优化的线性自抗扰鲁棒控制设计方法,实现机器人末端点从任意初始位置到达并镇定在目标位置.首先,借助驱动关节与被动关节角度之间的状态约束获取机器人末端点位置与驱动关节角度的对应关系,使末端点的位置控制转换为驱动关节的角度控制;其次,为缩短运动路径加入最小角度位移限制条件,设计免疫算法求解目标位置所对应的驱动关节角度的最小期望值;再次,引入线性自抗扰控制技术,把机器人的模型不确定性、未知干扰等因素视为一个新的扩张状态变量,设计线性扩张状态观测器和基于状态误差的反馈控制器,在仅驱动关节角度可测的情况下实现Acrobot的鲁棒镇定;最后,通过仿真实验验证所提出方法具有更好的鲁棒控制性能.     

Adaptive output feedback tracking control of robot manipulators using position measurements only

In this paper, a new adaptive neuro controller for trajectory tracking is developed for robot manipulators without velocity measurements, taking into account the actuator constraints. The controller is based on structural knowledge of the dynamics of the robot and measurements of joint positions only. The system uncertainty, which may include payload variation, unknown nonlinearities and torque disturbances is estimated by a Chebyshev neural network (CNN). The adaptive controller represents an amalgamation of a filtering technique to generate pseudo filtered tracking error signals (for the elimination of velocity measurements) and the theory of function approximation using CNN. The proposed controller ensures the local asymptotic stability and the convergence of the position error to zero. The proposed controller is robust not only to structured uncertainty such as payload variation but also to unstructured one such as disturbances. Moreover the computational complexity of the proposed controller is reduced as compared to the multilayered neural network controller. The validity of the control scheme is shown by simulation results of a two-link robot manipulator. Simulation results are also provided to compare the proposed controller with a controller where velocity is estimated by finite difference methods using position measurements only.     

机器人关节用高精度交流伺服系统研究与实现

机器人关节驱动要求满足响应速度快﹑运行稳定及精度高等性能指标,其关键是通过转矩控制及位置调节器设计来满足要求;首先针对非理想反电势的永磁交流伺服机,对转矩构成进行了推导,分析了转矩和反电动势、占空比的关系,提出了一种基于离线反电势测量实现了抑制转矩脉动的控制方法;其次,位置伺服采用了模糊自适应PID控制器实现位置的快速跟踪控制,采用此法能够克服单纯使用PID控制存在的超调和振荡,使系统输出超调明显减小,定位精度得到提高。在实验系统中,采用以英飞凌公司的XC167CI控制系统和功率MOSFET逆变器组成的伺服系统,实现了速度阶跃响应时间<20ms,速度稳定精度±2%,转矩精度±1%。整个过程速度响应迅速又运动平稳,位置能也迅速跟踪给定信号,且位置响应无超调;证明所提出的方法对于提高系统的性能是有效的,最后将其成功应用于自行研制的高压输电线巡检机器人控制系统中,获得了满意的效果。     

Dynamic visual servo control of a 4-axis joint tool to track image trajectories during machining complex shapes

A large part of the new generation of computer numerical control systems has adopted an architecture based on robotic systems. This architecture improves the implementation of many manufacturing processes in terms of flexibility, efficiency, accuracy and velocity. This paper presents a 4-axis robot tool based on a joint structure whose primary use is to perform complex machining shapes in some non-contact processes. A new dynamic visual controller is proposed in order to control the 4-axis joint structure, where image information is used in the control loop to guide the robot tool in the machining task. In addition, this controller eliminates the chaotic joint behavior which appears during tracking of the quasi-repetitive trajectories required in machining processes. Moreover, this robot tool can be coupled to a manipulator robot in order to form a multi-robot platform for complex manufacturing tasks. Therefore, the robot tool could perform a machining task using a piece grasped from the workspace by a manipulator robot. This manipulator robot could be guided by using visual information given by the robot tool, thereby obtaining an intelligent multi-robot platform controlled by only one camera.