Repetitive learning control: a Lyapunov-based approach

Mechatronics, 2006

In this paper, a new adaptive switching learning control approach, called adaptive switching learning PD control (ASL-PD), is proposed for trajectory tracking of robot manipulators in an iterative operation mode. The ASL-PD control method is a combination of the feedback PD control law with a gain switching technique and the feedforward learning control law with the input torque profile. The torque profile is updated by the previous torque profile (which makes sense for learning). Furthermore, in this new control method, the switching control scheme is integrated into the iterative learning procedure; as such, the trajectory tracking converges very fast. The ASL-PD method achieves the asymptotical convergence based on the LyapunovÕs method. The ASL-PD method possesses both adaptive and learning capabilities with a simple control structure. The simulation study validates this new method. In particular, both position and velocity tracking errors monotonically decrease with the increase of the number of iterations. The convergence rate with the ASL-PD method is faster than that of the adaptive iterative learning control method proposed by others in literature.

International Journal of Robotics & Automation, 2010

This paper addresses the problem of position tracking control of robot manipulators in the presence of parametric uncertainty and additive periodic disturbances. Specifically, a self tuning, Lyapunov-based adaptive controller with desired dynamics compensation term and a disturbance estimator has been designed to ensure that the link position tracking error converges to zero asymptotically, despite the partially linearly parametrizable robot dynamics. Extensive experimental results are provided to illustrate the viability and performance of the proposed controller.

Automatica, 2004

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 deÿniteness 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 e ectiveness of the proposed controllers. ?

In this paper, both output-feedback iterative learning control (ILC) and repetitive learning control (RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.

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. ᭧

IEEE Transactions on Automatic Control, 1991

This note presents the proof for the exponential convergence of a class of learning and repetitive control algorithms for robot manipulators. The learning process involves the identification of the robot inverse dynamics function by having the robot execute a set of tasks repeatedly. Using the concepts of functional persistence of excitation (PE) and functional uniform complete observability (UCO), it is shown that, when a training task is selected for the robot which is persistently exciting, the learning controllers are globally exponentially stable. Repetitive controllers are always exponentially stable.

Journal of Dynamic Systems, Measurement, and Control, 1990

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit informati...

Transactions of the Institute of Measurement and Control, 2018

This paper deals with Iterative Learning Control (ILC) design to solve the trajectory tracking problem for rigid robot manipulators subject to external disturbances, and performing repetitive tasks. A high order ILC scheme is synthetized; this controller contains the information (errors) of several iterations and not only of one iteration. It has been shown that the closed loop system (robot plus controller) is 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 controller scheme. Finally, simulation results on two-link manipulator are provided to illustrate the effectiveness of the proposed controller.

Asian Journal of Control, 2017

Two important properties of industrial tasks performed by robot manipulators, namely, periodicity (i.e., repetitive nature) of the task and the need for the task to be performed by the end-effector, motivated this work. Not being able to utilize the robot manipulator dynamics due to uncertainties complicated the control design. In a seemingly novel departure from the existing works in the literature, the tracking problem is formulated in the task space and the control input torque is aimed to decrease the task space tracking error directly without making use of inverse kinematics at the position level. A repetitive learning controller is designed which "learns" the overall uncertainties in the robot manipulator dynamics. The stability of the closed-loop system and asymptotic end-effector tracking of a periodic desired trajectory are guaranteed via Lyapunov based analysis methods. Experiments performed on an in-house developed robot manipulator are presented to illustrate the performance and viability of the proposed controller.

2008 47th IEEE Conference on Decision and Control, 2008

State-periodic disturbances are frequently found in motion control systems. Examples include cogging in permanent magnetic linear motor, eccentricity in rotary machines and etc. This paper considers general form of state-dependent periodic disturbance and proposes a new high-order periodic adaptive learning compensation (HO-PALC) method for state-dependent periodic disturbance where the stored information of more than one previous periods is used. The information includes composite tracking error as well as the estimate of the periodic disturbance. This dual HO-PALC (DHO-PALC) scheme offers potential to achieve faster learning convergence. In particular, when the reference signal is also periodically changing, the proposed DHO can achieve much better convergence performance in terms of both convergence speed and final error bound. Asymptotical stability proof of the proposed DHO-PALC is presented. Extensive lab experimental results are presented to illustrate the effectiveness of the proposed DHO-PALC scheme over the first order periodic adaptive learning compensation (FO-PALC). Index Terms-State-dependent periodic disturbance, adaptive control, dual-high-order periodic adaptive learning control, dynamometer. In practice, the state-dependent periodic disturbances exist in many electromechanical systems. For example, it has been shown that the external disturbance is a state-dependent periodic disturbance for rotary systems [1], [2], [3]; in , the friction force is shown to be a state-dependent periodic parasitic effect; in [5], the engine crankshaft speed pulsation was expressed as Fourier series expansion as a periodic function of position; in [6], the tire/road contact friction was represented as a function of the system state variable; in , the friction and the eccentricity in the low-cost wheeled mobile robots is treated as the statedependent periodic disturbance; in [8], [9] and [10], the cogging force in a permanent magnetic motor was defined as a positiondependent disturbance. Since the state-dependent periodic disturbance is almost everywhere in practice, the suppression of this type of disturbance has been paid much attention to in control community. To take advantage of the state-dependent periodicity, adaptive learning control idea has been attempted. For example, an adaptive learning compensator for cogging and coulomb friction in permanent-magnet linear motors was proposed in [8] and [11]; the authors of [12] and [13] proposed an iterative learning control (ILC) algorithm and a variable step-size normalized ILC scheme to reduce periodic torque ripples from cogging and other effects of PMSM, respectively; in [9], a periodic adaptive learning compensation method for cogging was performed on the PMSM servo system. However, all these efforts did not utilize the stored information of more than one previous periods, that is, they are not high-order periodic adaptive learning control scheme for state-dependent periodic disturbance compensation. In view of this, in our previous work , a simple high order periodic adaptive learning compensator was proposed for cogging effect in PMSM position servo system, where only the stored tracking

1989

An adaptivecontrolalgorithm isproposed fora classofnonlinear systems,such as robotic manipulators,which iscapableofimproving itsperformance in repetitive motions. When thetaskisrepeated,theerrorbetween thedesiredtrajectory and thatofthesystem is guaranteed todecrease.The designisbased on thecombinationofa direct adaptivecontrol and a learning process. This method does not requireany knowledge ofthe dynamic parameters ofthesystem. l. lntroducUon

IFAC Proceedings Volumes, 2003

Operational problems with robot manipulators in space relate to several factors, one most importantly being structural flexibility and subsequently significant difficulties with the control systems, especially, position control. A control strategy is devised for positioning the endpoint of a two-link robot manipulator modeled with assumed modes flexible dynamics repetitively tracking a square trajectory. The dominant assumed modes of vibration are determined for Euler-Bernoulli cantilever beam boundary conditions then, coupled with the nonlinear dynamics for rigid links to form an Euler-Lagrange inverse flexible dynamics robot model. A Jacobian transpose control law actuates the robot links. While repetitive tracking alone achieves no improvement in control precision, adapting the control law by a fuzzy logic system achieves consistent tracking precision.

Control Theory and …, 1996

Abstract: The paper is concerned with the design of a hybrid controller structure, consisting of the adaptive contrul law and a neural-network-based learning scheme for adaptation of time-varying controller parameters. The target error vector for weight adaptation of the ...

In this paper, A new control method called nonlinear PD learning control (NPD-LC) is proposed and applied for the trajectory tracking control of a closed loop manipulator. The proposed control algorithm is a combination of a nonlinear PD feedback control and a directly iterative learning (feedforward) control. Consequently, this new control method possesses both adaptive and learning properties. One of the features of the NPD-LC controller is that the learning process is directly based on the previous torque profile of a repetitive trajectory tracking. It is proved that the asymptotic convergence for both tracking positions and tracking velocities is guaranteed based on the NPD-LC controller. Experimental studies are conducted for a closed loop manipulator under different operation conditions. It is demonstrated that the NPD-LC control method can achieve a fast convergence speed. Index Terms-Nonlinear PD control, iterative learning control, closed loop manipulator, trajectory tracking.

1997 European Control Conference (ECC), 1997

Iterative learning control applied to a simpli ed model of a robot arm is studied. The iterative learning control input signal is used in combination with conventional feedback and feed-forward control, and the aim is to let the learning control signal handle the e ects of unmodeled dynamics and friction. Convergence and robustness aspects of the choice of lters in the updating scheme of the iterative learning control signal are studied.