Global positioning of robot manipulators via PD control plus aclass of nonlinear integral actions

Deals with the position control of robot manipulators. Proposed is a simple class of robot regulators consisting of a linear proportional-derivative (PD) feedback plus an integral action of a nonlinear function of position errors. By using Lyapunov's direct method and LaSalle's invariance principle, the authors characterize a class of such nonlinear functions, and they provide explicit conditions on the regulator gains to ensure global asymptotic stability. These regulators offer an attractive alternative to global regulation compared with the well-known partially model-based PD control with gravity compensation and PD control with desired gravity compensation     

Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control

The output feedback control of the popular magnetic ball levitation system is addressed from a suitable combination of several complementary viewpoints. We use: first, recent developments on exact feedforward linearisation controllers for nonlinear flat systems to substantially reduce the linear feedback controller efforts through pre-compensation. Second, an on-line ball velocity estimation strategy is proposed by using a model-based integral reconstructor, which is a linear combination of iterated integrals of the input and the output of the system, thus avoiding the use of traditional observers or noisy derivative estimations. Finally, we use a generalised proportional integral (GPI) controller which compensates the errors in the integral reconstructor and further bestows the enhanced robustness on the closed-loop system via output tracking error iterated integration feedback. This methodology only requires the measurements of the position of the levitated ball and of the control input voltage. The proposed feedback regulation scheme is shown to locally guarantee an asymptotically exponentially stable behaviour of the controlled ball position and, definitely, allows for the possibilities of safely carrying out the rest-to-rest trajectory tracking tasks on the ball position. The proposed output feedback controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilisation and trajectory tracking tasks.     

An observer-based set-point controller for robot manipulators with flexible joints

We present a globally asymptotically stable controller for point-to-point regulation of robot manipulators with flexible joints that uses only position measurement on the motor side. Existing asymptotically stable schemes for the set point regulation problem without velocity measurement address only the rigid robot case. Furthermore, these solutions ensure only local stability provided some bounds on the dynamic part of the robot model are known. Also, they require the injection of high gains into the loop to enlarge the equilibrium domain of attraction. In contrast, our solution is global, applies for robots with flexible joints and assumes only that the gravity forces are known. The underlying rationale of the design is to ‘shape’ the potential energy of the closed loop system so that it has an absolute minimum at the desired equilibrium, and add the required dampingto achieve asymptotic stability. This is attained by adding a (linear) observer that converges to the position required to compensate the gravity forces and injects the damping, and a ‘spring-like’ effect between the observer and the robot that ‘pulls’ the robot to the desired target. This approach to observer-based controller design differs from the classical certainly equivalent approach and effectively exploits the dynamic properties of the physical system.     

Moving formation convergence of a group of mobile robots via decentralised information feedback

In this article, a decentralised information feedback mechanism is introduced to a group of mobile robots such that the robots asymptotically converge to a given moving formation. It is assumed that the robots can exchange only position information according to a pre-specified communication graph. Each node represents a robot. Two robots are neighbours of each other if there is an edge between the two nodes. A feedback controller is performed for each robot by only using its own velocity information and the position information from its neighbours. It is proven that if the graph is connected, then the convergence to the moving formation of the closed-loop system is guaranteed. Several numerical simulations are presented to illustrate the results.     

Velocity observer-based iterative learning control for robot manipulators

This article addresses the problem of designing an iterative learning control for trajectory tracking of rigid robot manipulators subject to external disturbances, and performing repetitive tasks, without using the velocity measurement. For solving this problem, a velocity observer having an iterative form is proposed to reconstruct the velocity signal in the control laws. Under assumptions that the disturbances are repetitive and the velocities are bounded, it has been shown that the whole control system (robot plus controller plus observer) is asymptotically stable and the observation error is globally asymptotically stable, over the whole finite time-interval when the iteration number tends to infinity. This proof is based upon the use of a Lyapunov-like positive definite sequence, which is shown to be monotonically decreasing under the proposed observer–controller schemes.     

轮式移动机器人的位置量测输出反馈轨迹跟踪控制

针对机器人的姿态角难以精确测量的困难,本文研究基于位置测量的轮式移动机器人的轨迹跟踪问题.首先提出一种利用机器人的位置信息估计其姿态角的降维状态观测器,当机器人的线速度严格大于零时,可保证姿态角观测误差的指数收敛.然后给出一种新的状态反馈轨迹跟踪控制律,当参考轨迹满足一定的激励条件时,可以保证机器人的线速度严格大于零且跟踪误差全局渐近收敛.进一步结合姿态角观测器和状态反馈控制律,得到一种输出反馈轨迹跟踪控制算法.理论分析表明,当参考轨迹满足一定的激励条件时,所提出的输出反馈控制算法可以保证跟踪误差的全局渐近收敛.最后对所提出的姿态角观测器、状态反馈和输出反馈轨迹跟踪控制算法进行了仿真验证,证实了算法的有效性,并且当存在位置测量误差时,所提出的输出反馈轨迹跟踪控制算法仍可以保证机器人对参考轨迹的实际跟踪.     

Linear learning control of robot motion

For the trajectory following problem of a robot manipulator, a new linear learning control law, consisting of the conventional proportional-integral-differential (PID) control law, with respect to position tracking error, and an iterative learning term is provided. The learning part is a linear feedback control of position, velocity, and acceleration errors (PDD²). It has been shown that, under the proposed learning control, the position, velocity, and acceleration tracking errors are asymptotically stable in the presence of highly nonlinear dynamics. The proposed control is robust in the sense that exact knowledge about nonlinear dynamics is not required except for the bounding functions on their magnitudes. Further, neither is linear approximation of nonlinear dynamics nor repeatability of robot motion required.     

A Class of Transpose Jacobian‐based NPID Regulators for Robot Manipulators with an Uncertain Kinematics

Transpose Jacobian‐based controllers present an attractive approach to robot set‐point control in Cartesian space that derive the end‐effector posture to a specified desired position and orientation with neither solving the inverse kinematics nor computing the inverse Jacobian. By a Lyapunov function with virtual artificial potential energy, a class of complete transpose Jacobian‐based Nonlinear proportional‐integral‐derivative regulators is proposed in this paper for robot manipulators with uncertain kinematics on the basis of the set of all continuous differentiable increasing functions. It shows globally asymptotic stability for the result closed‐loop system on the condition of suitable feedback gains and suitable parameter selection for the corresponding function set as well as artificial potential function, and only upper bound on Jacobian matrix error and Cartesian dynamics parameters are needed. The existing linear PID (LPID) regulators are the special cases of it. Nevertheless, in the case of LPID regulators, only locally asymptotic stability is guaranteed if the corresponding conditions are satisfied. Simulations demonstrate the result and robustness of transpose Jacobian‐based NPID regulators. © 2002 Wiley Periodicals, Inc.     

Semiglobal stability of saturated linear PID control for robot manipulators

This paper addresses the position regulation problem of robot manipulators under control input constraints. It is proven that the robot system under a saturated linear PID control is semiglobally asymptotically stable, if the torque bounds are larger than gravitational torques, and if the proportional gain is large enough and the integral gain is small enough.The stability analysis makes use of singular perturbation tools and the results are illustrated via numerical simulations.     

Robust adaptive decentralized control of robot manipulators

The authors proposes a robust adaptive decentralized control algorithm for trajectory tracking of robot manipulators. The controller is designed based on a Lyapunov method, which consists of a PD (proportional plus derivative) feedback part and a dynamic compensation part. It is shown that, without any prior knowledge of manipulator or payload parameters and possibly under deterioration of parameter variation with time or state-independent input disturbances, the tracking error is bound to converge to zero asymptotically. In particular, the algorithm does not require explicit system parameter estimation and therefore makes the controller structurally simple and computationally easy. Moreover, the controller is implemented in a decentralized manner, i.e. a subcontroller is independently and locally equipped at each joint servoloop. To illustrate the performance of the controller, a numerical simulation example is provided     

Linear state feedback regulator for rigid link manipulators

A new generic representation of the gravity vector in the rigid link robot dynamic model is proposed. We use this representation to design a linear state feedback regulator and show that the closed loop nonlinear system is globally asymptotically stable and exponentially stable in any closed ball. We exploit the fact that the gravity vector is the gradient of the potential function. We also consider robustness of the linear state feedback regulator to parameter uncertainty.     

PD control with on-line gravity compensation for robots with elastic joints: Theory and experiments

A proportional-derivative (PD) control with on-line gravity compensation is proposed for regulation tasks of robot manipulators with elastic joints. The work extends a previous PD control with constant gravity compensation at the desired configuration. The control law requires measuring only position and velocity on the motor side of the elastic joints, while the on-line gravity compensation torque uses a biased measure of the motor position. It is proved via a Lyapunov argument that the control law globally asymptotically stabilizes the desired robot configuration. A simulation study on a two-joint arm reveals the better performance that can be obtained with the new scheme as compared to the case of constant gravity compensation. Moreover, the proposed controller is experimentally tested on an eight-joint cable-driven robot manipulator, in combination with a point-to-point interpolating trajectory, showing the practical advantages of the on-line compensation.     

An Adaptive Regulator of Robotic Manipulators in the Task Space

This note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space. A computationally simple class of task space regulators consisting of a transpose adaptive Jacobian controller plus an adaptive term estimating generalized gravity forces is proposed. The Lyapunov stability theory is used to derive the control scheme. The conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations. The performance of the proposed control strategy is illustrated through computer simulations for a direct-drive arm of a SCARA type redundant manipulator with the three revolute kinematic pairs operating in a two-dimensional task space.     

Robust tracking control for wheeled mobile robot based on extended state observer

This paper presents a new control scheme on trajectory tracking of wheeled mobile robot with nonholonomic constraints. Extended state observer is introduced to estimate unknown disturbances and velocity information. A robust tracking controller is designed to implement the accurate trajectory tracking and disturbance compensation. By theoretical, position and velocity tracking errors of wheeled mobile robot are proven uniformly ultimately asymptotically stable. Simulation results are given to illustrate the effectiveness of the developed technique.     

A simple PID control for asymptotic visual regulation of robot manipulators

This paper addresses the asymptotic regulation problem of robot manipulators with a vision‐based feedback. A simple image‐based transpose Jacobian proportional‐integral‐derivative (PID) control is proposed. The closed‐loop system formed by the proposed PID control and robot system is shown to be asymptotically stable by using Lyapunov's direct method and LaSalle's invariance theorem. Advantages of the proposed control include the absence of dynamical model parameters in the control law formulation and the control gains are easily chosen according to simple inequalities including some well‐known bounds extracted from robot dynamics and kinematics. Simulations performed on a two degree‐of‐freedom manipulator are provided to illustrate the effectiveness of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Model-free robot joint position regulation and tracking with prescribed performance guarantees

The problem of robot joint position control with prescribed performance guarantees is considered; the control objective is the error evolution within prescribed performance bounds in both problems of regulation and tracking. The proposed controllers do not utilize either the robot dynamic model or any approximation structures and are composed by simple PID or PD controllers enhanced by a proportional term of a transformed error through a transformation related gain. Under a sufficient condition for the damping gain, the proposed controllers are able to guarantee (i) predefined minimum speed of convergence, maximum steady state error and overshoot concerning the position error and (ii) uniformly ultimate boundedness (UUB) of the velocity error. The use of the integral term reduces residual errors allowing the proof of asymptotic convergence of both velocity and position errors to zero for the regulation problem under constant disturbances. Performance is a priori guaranteed irrespective of the selection of the control gain values. Simulation results of a three dof spatial robotic manipulator and experimental results of one dof manipulator are given to confirm the theoretical findings.     

对气动肌肉驱动器快速准确定位控制的研究

针对气动人工肌肉(PAM)驱动器,将机器人受驱关节的转角位置误差、位置误差变化速率和负载变化等,作为控制器的内环反馈量,建立了一种能自适应调节比倒压力阀输入控制量大小的算法,模拟人类手臂两点间的运动特点,同时通过外环反馈的角位置,控制电磁开关阀的开合,使受控关节能快捷、稳定和准确地定位于目标位置,解决了由于气体的可压缩...     

Polynomial family of PD-type controllers for robot manipulators

This paper addresses the problem of position control for robot manipulators. A new polynomial family of PD-type controllers with gravity compensation for the global position of robots manipulators is presented. The previous results on the linear PD controller are extended to the proposed polynomial family. The classical PD controller can be found among this large class of controllers when its proportional gain is a diagonal matrix. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the proposed family of controllers is globally asymptotically stable in agreement with Lyapunov's direct method and LaSalle's invariance principle. Besides the theoretical results, a real-time experimental comparison is also presented to illustrate the performance of the proposed family with other well-known control algorithms such as PD and PID schemes on a three degrees of freedom direct-drive arm.