On the adaptive control of robot manipulators with velocity observers

To achieve accurate tracking control of robot manipulators many schemes have been proposed. A common approach is based on adaptive control techniques, which guarantee trajectory tracking under the assumption that the robot model structure is perfectly known and linear in the unknown parameters, while joint velocities are available. Despite tracking errors tend to zero, parameter errors do not unless some persistent excitation condition is fulfilled. There are few works dealing with velocity observation in conjunction with adaptive laws. In this note, an adaptive control/observer scheme is proposed for tracking position of robot manipulators. It is shown that tracking and observation errors are ultimately bounded, with the characteristic that when a persistent excitation condition is matched then they, as well as the parameter errors, tend to zero. Simulation results are in good agreement with the developed theory.     

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.     

Hybrid adaptive control for robot manipulators

A hybrid adaptive control scheme is proposed for robot manipulators. Unmodelled dynamics have been considered in the robot model. The standard RLS algorithm has been modified to take into account these unmodelled dynamics. Global stability of the system is ensured.     

Adaptive synchronization control of networked robot systems without velocity measurements

This paper addresses the adaptive synchronization control problem of networked robot systems characterized by the Lagrangian function, where exact dynamic models are unknown and velocity measurements are unavailable. A class of distributed observers, comprised of multiple dynamic variables and static variables, are established based on no a priori restriction on the boundness of the observer states. The observer is compatible for different control schemes with or without structure uncertainties. Using the estimated states given by the observer, adaptive distributed control input is developed, and then, closed‐loop dynamic models for filtered vectors are established. It is proven that our proposed control scheme permits global exact state estimation and global asymptotic synchronization while compensating for structure uncertainties. Simulations are provided to demonstrate the effectiveness of the results.     

A new adaptive tracking control scheme of wheeled mobile robot without longitudinal velocity measurement

This paper proposes a new adaptive trajectory tracking control scheme of the wheeled mobile robot without longitudinal velocity measurement. First, based on a kinematic controller, we obtain a new tracking error equation, which is suitable to develop an adaptive controller. Then, we develop a new adaptive trajectory tracking controller, which does not need any accurate values of the wheeled mobile robot parameters, including the driving motor parameters. Moreover, as the longitudinal velocity measurement is still difficult, this controller is developed without longitudinal velocity measurement. In addition, this new adaptive controller introduces a method to improve the control performance. The stability of the closed‐loop system is presented using the direct Lyapunov method. Finally, numerous simulations verify the effectiveness of the new controller.     

神经网络自适应滑模控制的不确定机器人轨迹跟踪控制

提出一种针对机器人跟踪控制的神经网络自适应滑模控制策略。该控制方案将神经网络的非线性映射能力与滑模变结构和自适应控制相结合。对于机器人中不确定项,通过RBF网络分别进行自适应补偿,并通过滑模变结构控制器和自适应控制器消除逼近误差。同时基于Lyapunov理论保证机器手轨迹跟踪误差渐进收敛于零。仿真结果表明了该方法的优越性和有效性。     

Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator

This article presents a robust adaptive controller for electrically driven robots using Bernstein polynomials as universal approximator. The lumped uncertainties including unmodeled dynamics, external disturbances, and nonimplemented control signals (they assumed as a function of time, instead a function of several variables) are represented with this powerful mathematical tool. The polynomial coefficients are then tuned based on the adaptation law obtained in the stability analysis. A comprehensive approach is adopted to include the saturated and unsaturated areas and also the transition between these areas in the stability analysis. As a result, the stability and the performance of the proposed controller have been improved considerably in dealing with actuator saturation. Also, in comparison with a recent paper based on uncertainty estimation using Taylor series, the proposed controller is less computational due to reducing the size of the matrix of convergence rate. A performance evaluation has been carried out to verify satisfactory performance of transient response of the controller. Simulation results on a Puma560 manipulator actuated by geared permanent magnet dc motors have been presented to guarantee its satisfactory performance.     

Switched adaptive tracking control of robot manipulators with friction and changing loads

A switched adaptive controller is designed for robot manipulators with friction and changing loads. The nonlinear friction is depicted by a nonlinear friction model, and a switched nonlinear system is used to model the parameter jump caused by load change. Hyperstability theory is used in the designing procedure, which provides more options for adaptive laws than Lyapunov theory. In the presence of friction and changing loads, asymptotic tracking is achieved under arbitrary switching, which is not able to accomplish by a non-switched adaptive controller. The proposed method is validated by a simulation of a 2 degree of freedom manipulator.     

Trajectory tracking control for robot manipulators using only position measurements

In the paper, the trajectory tracking control problem is investigated for robotic manipulators which are not equipped with the tachometers. Our contribution consists in establishing uniform asymptotic stability in closed-loop system by using the dynamic position-feedback controller with feedforward. Using Lyapunov vector function and comparison principle, we construct the non-linear controller with variable gain matrices and first-order linear dynamic compensator such that the origin of the closed-loop system is uniformly asymptotically stable. The controller is shown to be robust with respect to parameters incertainties. We illustrate the utility of our result by simulation tests with reference to a two-link planar elbow robot manipulator.     

Task-space fully distributed tracking control of networked uncertain robotic manipulators without velocity measurements

This paper investigates the task-space synchronised tracking problem of uncertain networked manipulators interconnected on directed graphs, where the dynamic leader is available to only a subset of followers and followers have only local interaction. A fully distributed tracking controller is proposed, which is composed of a distributed desired trajectory estimator, a joint-space velocity observer and an adaptive cooperative control algorithm. Specifically, the proposed controller allows each manipulator to track the dynamic leader solely using local task-space position measurements. Besides, in the presence of both dynamic and kinematic uncertainties, the adaptive cooperative control algorithm indeed improves the system's robustness. Furthermore, it is strictly proved that the proposed control scheme ensures that both task-space position and velocity tracking errors converge to zero as time tends to infinity. In the end, simulation results are provided to demonstrate the effectiveness of the proposed controller.     

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.     

Tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy

This paper discusses the tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy. This control strategy consists of two steps; first, the classical MIMO dynamical system is decomposed into a set of nonlinear interconnected subsystems. Each subsystem has one joint. Second, the distributed adaptive control strategy is introduced. This control strategy consists of controlling the last subsystem while assuming that the remaining subsystems are stable. Then, going backward to the second last subsystem, the same strategy is applied and so on until the first one. The system parameters are assumed to be unknown. An adaptive control is used to estimate these parameters. Indeed, the unknown parameters existing in the equation of motion of the last subsystem are first estimated and the control law is developed based on these estimated parameters. Then, going backward to the before last joint, the control law is developed using its own estimated parameters and the ones already estimated in the upper level subsystem. Asymptotical stability of the error dynamics is proved using Lyapunov approach. The developed algorithm is experimented on a 4 DOF hyper redundant articulated nimble adaptable trunk robot and compared with the classical computed torque approach. Good tracking in the workspace and joint space is obtained and effectiveness of the results is shown.     

Repetitive control of electrically driven robot manipulators

This article presents a novel robust discrete repetitive control of electrically driven robot manipulators for tracking of a periodic trajectory. We propose a novel model, which presents the highly non-linear dynamics of robot manipulator in the form of linear discrete-time time-varying system. Based on the proposed model, we develop a two-term control law. The first term is an ordinary time-optimal and minimum-norm (TOMN) control by employing parametric controllers to guarantee stability. The second term is a novel robust control to improve the control performance in the face of uncertainties. The robust control estimates and compensates uncertainties including the parametric uncertainty, unmodelled dynamics and external disturbances. Performance of the proposed method is compared with two discrete methods, namely the TOMN control and an adaptive iterative learning (AIL) control. Simulation results confirm superiority of the proposed method in terms of the convergence speed and precision.     

Adaptive hybrid force/position control of robot manipulators using an adaptive force estimator in the presence of parametric uncertainty

This study is devoted to sensorless adaptive force/position control of robot manipulators using a position-based adaptive force estimator (AFE) and a force-based adaptive environment compliance estimator. Unlike the other sensorless method in force control that uses disturbance observer and needs an accurate model of the manipulator, in this method, the unknown parameters of the robot can be estimated along with the force control. Even more, the environment compliance can be estimated simultaneously to achieve tracking force control. In fact, this study deals with three challenging problems: No force sensor is used, environment stiffness is unknown, and some parametric uncertainties exist in the robot model. A theorem offers control laws and updating laws for two control loops. In the inner loop, AFE estimates the exerted force, and then, the force control law in the outer loop modifies the desired trajectory of the manipulator for the adaptive tracking loop. Besides, an updating law updates the estimated compliance to provide an accurate tracking force control. Some experimental results of a PHANToM Premium robot are provided to validate the proposed scheme. In addition, some simulations are presented that verify the performance of the controller for different situations in interaction.     

模糊自适应在机器人行走平衡控制中的应用

针对多变量、非线性的两轮机器人系统的行走平衡控制问题,提出一种基于Backstepping（反推）方法和PID的控制策略。该策略在Backstepping控制器中加入模糊自适应部分,利用模糊系统逼近Backstepping设计过程中的未知非线性函数,模糊系统中的参数基于自适应律调整,解决了Backstepping控制器中因含有未知参数难以实现的困难,避免了两轮机器人系统不满足严格三角结构的问题。针对两轮机器人的仿真实验结果表明：采用设计的控制策略,可以实现两轮机器人的行走平衡控制任务。     

Differentiator-based time delay control for uncertain robot manipulators

High-quality acceleration signal plays a significant role in fast and precise trajectory tracking of robot manipulators via time delay control (TDC). This paper proposes a fast transient tracking differentiator (FTD) for obtaining the noise-less time derivative from a noisy measurement within the framework of tracking differentiator (TD) design methodology. Global asymptotic convergence of the proposed FTD is proven by Lyapunov's direct method and TD theory. The proposed FTD is cascaded to construct an acceleration estimation and is integrated with the commonly used TDC for an improved trajectory tracking of robot manipulators in the presences of parametric uncertainties and bounded disturbances. Numerical simulations and real-time experimental validation comparisons demonstrate that the proposed approach provides an easy-going model-free improved design for fast and accurate trajectory tracking of robot manipulators with position measurement only.     

A robust adaptive control of a parallel robot

The work presented in this article deals with the robust adaptive control tracking of a 6 degree of freedom parallel robot, called C5 parallel robot. The proposed approach is based on the coupling of sliding modes and multi-layers perceptron neural networks (MLP-NNs). It does not require the inverse dynamic model for deriving the control law. The MLP-NN is added in the control scheme to estimate the gravitational and frictional forces along with the non-modelled dynamic effects. The nonlinearity problem, present in neural networks, is resolved using Taylor series expansion. The proposed approach allows to adjust the parameters of neural network and sliding mode control terms by taking into account a reference model and the closed-loop stability in the Lyapunov sense. We implemented our approach on the C5 parallel robot of LISSI laboratory and performed experiments to observe its effectiveness and the robust behaviour of the controller against external disturbances.     

基于Lagrangian支持向量机的机械手鲁棒自适应控制

提出了一种基于Lagrangian支持向量机的不确定机械手鲁棒自适应控制方法。Lagrangian支持向量机采用梯度投影法学习机械手系统的未知部分,来对机械手系统进行非线性补偿。根据Lyapunov稳定性理论设计自适应律进一步在线调整支持向量机的参数,并叠加一个滑模控制项,以保证控制系统的稳定性和鲁棒性。对两关节机械手的仿真结果证明了以上控制方法的有效性。     

机器人自适应PID饱和输出反馈控制

针对机器人系统在仅有位置传感、驱动器饱和、存在建模不确定性及干扰等条件下的轨迹跟踪控制问题,提出了一种新的自适应PID控制方案。采用高精度滤波器估计机器人关节速度,采用带饱和函数的控制器限制输出力矩,采用自适应PID控制器补偿建模不确定性和干扰。通过Lyapunov直接法,证明系统的稳定性。最后以两关节机器人为例,给出仿真实验结果,验证了算法的有效性。     

A fully adaptive decentralized control of robot manipulators

In this paper, we develop a fully adaptive decentralized controller of robot manipulators for trajectory tracking. With high-order and adaptive variable-structure compensations, the proposed scheme makes both position and velocity tracking errors of robot manipulators globally converge to zero asymptotically while allowing all signals in closed-loop systems to be bounded, even without any prior knowledge of robot manipulators. Thus this control scheme is claimed to be fully adaptive. Even when the proposed scheme is modified to avoid the possible chattering in actual implementations, the overall performance will remain appealing. Finally, numerical results are provided to verify the effectiveness of the proposed schemes at the end.