Adaptive iterative learning control for robot manipulators

In this paper, we propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.     

Further results on adaptive iterative learning control of robot manipulators

Based on a combination of a PD controller and a switching type two-parameter compensation force, an iterative learning controller with a projection-free adaptive algorithm is presented in this paper for repetitive control of uncertain robot manipulators. The adaptive iterative learning controller is designed without any a priori knowledge of robot parameters under certain properties on the dynamics of robot manipulators with revolute joints only. This new adaptive algorithm uses a combined time-domain and iteration-domain adaptation law allowing to guarantee the boundedness of the tracking error and the control input, in the sense of the infinity norm, as well as the convergence of the tracking error to zero, without any a priori knowledge of robot parameters. Simulation results are provided to illustrate the effectiveness of the learning controller.     

Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.     

基于改进涡流搜索算法的外骨骼迭代学习控制

为提升康复外骨骼机器人的步态跟踪性能,提出一种基于改进涡流搜索算法的迭代学习控制方法。首先针对传统迭代学习控制抗扰性差和控制信息缺失问题,引入PD控制器、自适应遗忘因子、误差过渡曲线和控制信息搜索等策略,改进迭代学习控制律;其次,基于多种策略对涡流搜索算法进行改进,提出了一种改进涡流搜索算法,改进后的算法可优化迭代学习控制的PD参数;最后进行行走实验,将提出的迭代学习控制方法与现有的同类算法进行仿真和数值比较,并测试了扰动情况下的跟踪性能。实验结果表明,所提方法的误差更小,跟踪性能更强。该算法改进了迭代学习控制的不足,具有较强的抗扰性能,保证了使用时的稳定性。     

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.     

Design of robot control systems

An expository discussion on practical aspects of the design problems of robot control systems is presented. The first section discusses the present status of robot control methodology based on the so-called 'teaching and playback' control scheme. It is pointed out that PTP (point to point) control is still central in practice because only a sort of pulse-incremental servo controller is implemented for each joint actuator in actual industrial robots. The second section points out that servo controllers of this kind perform approximately as a PD or PID controller, and demonstrates that such PD and PID control schemes can work well even if the robot dynamics are non-linear and have strong couplings between the joint variables. The third section deals with path-tracking and trajectory-tracking control problems when teaching by human operators is not possible. This is then followed by a final but substantial section on recent results on learning control and adaptive control. An example of learning control for robot motions is given and its potential applicability in robotic systems is discussed.     

基于层迭CMAC网络的6-DOF机器人自适应控制

研究了标称自适应+迭代学习控制算法的稳定性,并利用层迭CMAC网络的优良特性, 提出了基于层迭CMAC的标称自适应+迭代学习控制方法．此方法将标称自适应控制中确定的 模型信息与未知的信息分离,充分利用模型中确定的信息进行前馈控制;而对于未知信息, 则利用层迭CMAC进行自适应学习．仿真实验表明用本文所设计的控制系统对6 DOF并行机器 人进行轨线控制,可获得比以往的普通CMAC+PD控制系统更好的控制效果．     

Scalable Techniques from Nonparametric Statistics for Real Time Robot Learning

Locally weighted learning (LWL) is a class of techniques from nonparametric statistics that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional belief that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested on up to 90 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing by a humanoid robot arm, and inverse-dynamics learning for a seven and a 30 degree-of-freedom robot. In all these examples, the application of our statistical neural networks techniques allowed either faster or more accurate acquisition of motor control than classical control engineering.     

分数阶迭代学习控制的收敛性分析

本文将传统的迭代学习控制时域和频域分析方法扩展到一类针对分数阶非线性系统的分数阶迭代学习控制时域分析方法.提出了一类新的分数阶迭代学习控制框架并简化了收敛条件,且证明了常增益情况下两类分数阶迭代学习控制收敛条件的等价性问题.该讨论进一步引出了如下两个结果:分数阶不确定系统的分数阶自适应迭代学习控制的可学习区域以及理想带阻型分数阶迭代学习控制的框架.上述结果均得到了仿真验证.     

Adaptive control of robot manipulator using fuzzy compensator

This paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncertainties. In order to compensate these uncertainties, we use the FLS (fuzzy logic system) that has the capability to approximate any nonlinear function over the compact input space. In the proposed control schemes, we need not derive the linear formulation of robot dynamic equation and tune the parameters. We also suggest the robust adaptive control laws in all proposed schemes for decreasing the effect of approximation error. To reduce the number of fuzzy rules of the FLS, we consider the properties of robot dynamics and the decomposition of the uncertainty function. The proposed controllers are robust not only to the structured uncertainty such as payload parameter, but also to the unstructured one such as friction model and disturbance. The validity of the control scheme is shown by computer simulations of a two-link planar robot manipulator     

A comparison of model-based path control algorithms for direct-drive SCARA robots

Various advanced control strategies are applied to a direct-drive SCARA robot and studied in computer simulations. Besides computed torque control and direct adaptive control, heuristic optimal control, a new path control scheme for robotic manipulators, is included in the comparison study. PD control, the traditional robot control method, is used for generating a comparing baseline. While all schemes are applied for the same tracking task, the effect of modelling errors and measurement noise is considered in robot performance evaluation. Simulation results show that (1) without model errors, all advanced control schemes can achieve higher tracking accuracy than PD control; (2) with a random measurement error of 1%, computed torque and direct adaptive control methods are inferior to PD control; (3) heuristic control proves to be the most robust control scheme in case of mixed model and measurement errors.     

An adaptive friction compensator for global tracking in robot manipulators

A novel adaptive friction compensator based on a dynamic model recently proposed in the literature is presented in this paper. The compensator ensures global position tracking when applied to an n degree of freedom robot manipulator perturbed by friction forces with only measurements of position and velocity, and all the system parameters (robot and friction model) unknown. Instrumental for the solution of the problem is the observation that friction compensation can be recasted as a disturbance rejection problem. The control signal is then designed in two steps, first a classical adaptive robot controller that (strictly) passifies the system, and then a relay-based outer-loop that rejects the disturbance.     

环卫车辆轨迹跟踪系统的无模型自适应迭代学习控制

针对环卫车辆周期重复性工作特点,考虑模型时变以及未知扰动问题,提出一种基于无模型自适应迭代学习的环卫车辆轨迹跟踪控制方法.首先,针对环卫车辆建立了两轮移动机器人的运动学模型,然后,给出带时变参数和非线性不确定项的迭代域下全格式动态线性化数据模型,引入时间差分估计算法,设计基于最优性能指标的轨迹跟踪无模型自适应迭代学习控...     

On the P-type and Newton-type ILC schemes for dynamic systems with non-affine-in-input factors

In this paper, P-type learning scheme and Newton-type learning scheme are proposed for quite general nonlinear dynamic systems with non-affine-in-input factors. Using the contraction mapping method, it is shown that both schemes can achieve asymptotic convergence along learning repetition horizon. In order to quantify and evaluate the learning performance, new indices—Q-factor and Q-order—are introduced in particular to evaluate the learning convergence speed. It is shown that the P-type iterative learning scheme has a linear convergence order with limited learning convergence speed under system uncertainties. On the other hand, if more of system information such as the input Jacobian is available, Newton-type iterative learning scheme, which is originated from numerical analysis, can greatly speed up the learning convergence speed. The effectiveness of the two learning control methods are demonstrated through a switched reluctance motor system.     

Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov–Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L²_{[0, T]} convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.     

基于迭代学习控制的鳗鱼机器人切向速度跟踪控制

鳗鱼机器人的动力学模型非线性强、高度欠驱动,导致多关节鳗鱼机器人的切向速度跟踪控制极具挑战．本文采用P型迭代学习控制与步态生成器相结合的方法对多关节鳗鱼机器人的切向速度进行跟踪控制．首先,采用解析牛顿-欧拉法建立非惯性系下的鳗鱼机器人动力学模型,直接获得切向速度子动力学模型;然后,利用带饱和函数的P型迭代学习控制器控制步态参数,并且利用复合能量函数和切向速度子动力学模型分析该控制器的收敛性,得到切向速度跟踪误差的收敛条件;最后,提出鳗鱼机器人的运动控制框架,并对多模块的鳗鱼机器人进行仿真和实验．实验结果表明,实际的切向速度随着迭代次数的增加而逐渐跟踪上了期望的切向速度,故而验证了鳗鱼机器人切向速度跟踪控制器的有效性．     

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

Adaptive control of a robot arm using driver programs

Most successful state-of-the-art robotic manipulators have the characteristic of producing precise, fast, smooth and reproducible movements. Their drawback is that they tend to have a limited repertoire which can only be extended by costly inverse kinematics calculations or direct teach-in sessions. The goal of our project is to develop a flexible open world robot, which adapts to its task and environment progressively and in an iterative manner. It begins carefully and slowly, with small jagged movements, but, after repetition, reaches an acceptable level of smoothness and execution speed. It can be placed in new surroundings with new task definitions, requiring only a further practice time before becoming expert. Similarities from other sub-tasks are recognized and may be transferred to the new domains. The basic constituents of the adaptive robot are simple iterative inverse kinematics and driver programs. In this paper the idea of driver programs for robot arm control is introduced and their properties investigated.     

Adaptive dynamic surface control for linear multivariable systems

In this paper, an output-feedback adaptive control is presented for linear time-invariant multivariable plants. By using the dynamic surface control technique, it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated. The proposed scheme has the following features: (1) The L_∞ performance of the system’s tracking error can be guaranteed, (2) it has least number of updated parameters in comparison with other multivariable adaptive schemes, and (3) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning

This paper describes the fractional modeling and control of an industrial selective compliant assembly robot arm (SCARA); the fractional model was obtained by using the Euler–Lagrange and Hamilton formalisms. Each joint of the robot manipulator was driven by an induction motor. In this work, the fractional model of each induction motor was formulated, and the matching of the induction motors with the SCARA robot is shown. For comparison purposes, the SCARA robot control was formulated by conventional PI and PD and by fractional PI ^? and PD ^δ controllers. So each induction motor was controlled by using PI and fractional PI ^? controllers, and for trajectory tracking control, PD and fractional PD ^δ controllers were designed. For tuning the PI, PI ^? , PD, and PD ^δ controllers, the PSO algorithm was used; the same restrictions were used for the PI and PD classical controllers, and ITAE index was used as a cost function to be minimized. For computing the fractional derivatives and to obtain the numerical solution of the system, the Riemann–Liouville and Grünwald–Letnikov approaches were used. The numerical simulations have shown the effectiveness of the use of fractional PI ^? and PD ^δ controllers.