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.     

Decentralized adaptive control of a class of large-scaleinterconnected nonlinear systems

Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Output feedback tracking control of robot manipulators with model uncertainty via adaptive fuzzy logic

Many robot controllers require not only joint position measurements but also joint velocity measurements; however, most robotic systems are only equipped with joint position measurement devices. In this paper, a new output feedback tracking control approach is developed for the robot manipulators with model uncertainty. The approach suggested herein does not require velocity measurements and employs the adaptive fuzzy logic. The adaptive fuzzy logic allows us to approximate uncertain and nonlinear robot dynamics. Only one fuzzy system is used to implement the observer-controller structure of the output feedback robot system. It is shown in a rigorous manner that all the signals in a closed loop composed of a robot, an observer, and a controller are uniformly ultimately bounded. Finally, computer simulation results on three-link robot manipulators are presented to show the results which indicate good position tracking performance and robustness against payload uncertainty and external disturbances.     

A partial state feedback controller for tajectory tracking of rigid-link fiexible-joint robot using an observed backstepping approach

This article presents a partial state feedback controller for a rigid-link flexible-joint (RLFJ) robot using an observed integrator backstepping approach. The robot controller requires only link position and actuator position measurements, and eliminates the need for measuring link velocity and actuator velocity. The controller uses two exact knowledge, second-order nonlinear observers to estimate the link and actuator velocities. The overall control system achieves a semiglobal exponential stability result for the link position and velocity tracking errors as well as the velocity observation errors. A stability proof and simulation results for the proposed partial state feedback controller are included in the article. © 1995 John Wiley & Sons, Inc.     

Adaptive tracking control of leader–follower systems with unknown dynamics and partial measurements

In this paper, a decentralized adaptive tracking control is developed for a second-order leader–follower system with unknown dynamics and relative position measurements. Linearly parameterized models are used to describe the unknown dynamics of a self-active leader and all followers. A new distributed system is obtained by using the relative position and velocity measurements as the state variables. By only using the relative position measurements, a dynamic output–feedback tracking control together with decentralized adaptive laws is designed for each follower. At the same time, the stability of the tracking error system and the parameter convergence are analyzed with the help of a common Lyapunov function method. Some simulation results are presented to validate the proposed adaptive tracking control.     

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

Adaptive λ-tracking for a class of infinite-dimensional systems

For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius λ>0. This control strategy, called λ-tracking, combines proportional error feedback with a simple nonlinear adaptation of the feedback gain. It does not involve any parameter estimation algorithms, nor is it based on the internal model principle. The class of reference signals is W^1,∞, the Sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative. The control strategy is robust with respect to output measurement noise in W^1,∞ and bounded input disturbances. We apply our results to retarded systems and integrodifferential systems.     

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.     

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.     

Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines

The problem of state observation and position control by output feedback for a nonlinear three degrees-of-freedom (3-DOF) parallel kinematic machine (PKM) system is considered, based on the limited signal availability (only the moving platform displacement measurements are assumed available). Unknown velocity signals are estimated via a nonlinear robust observer that is designed for the nonlinear system with observable linear dynamics part and bounded nonlinearities and disturbances, and that guarantees global exponential stability of the observation error. A proportional-derivative (PD) controller is designed to solve the position control problem, utilizing the estimated velocity, as well as the gravitation compensation, dynamic friction and external disturbance compensation for the PKM. The closed-loop system is proven to have global asymptotical stability according to the Lyapunov analysis method and LaSalle’s invariance principle. Performance of the resulting observer and controller is illustrated in a simulation study of a 3-DOF PKM. Modifications to the nonlinear observer and control law are discussed, that assure convergence of the position error and state observation error to zero when the upper bounds on the model uncertainties/disturbances are not known a priori.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Nonlinear adaptive control for teleoperation systems with symmetrical and unsymmetrical time-varying delay

The stability and trajectory tracking control problem of passive teleoperation systems with the presence of the symmetrical and unsymmetrical time-varying communication delay is addressed in this paper. The proposed teleoperator is designed by coupling local and remote sites by delaying position signals of the master and slave manipulator. The design also comprises local proportional and derivative signals with nonlinear adaptive terms to cope with parametric uncertainty associated with the master and slave dynamics. The Lyapunov–Krasovskii function is employed to establish stability conditions for the closed-loop teleoperators under both symmetrical and unsymmetrical time-varying communication delay. These delay-dependent conditions allow the designer to estimate the control gains a priori in order to achieve asymptotic property of the position, velocity and synchronisation errors of the master and slave systems. Finally, simulation results along with comparative studies are presented to illustrate the effectiveness of the proposed method.     

多智能体系统自适应跟踪控制

基于带有非线性动态的二阶多智能体系统,研究了在有动态领导者条件下的跟踪一致性问题。假设跟随者只能获取邻居智能体的相对状态信息,只有一部分跟随者可以获得领导者的位置和速度信息,领导者的控制输入非零且不被任何一个跟随者可知。在通信拓扑为无向连通图的条件下,为了避免全局信息的不确定性,设计了分布式自适应控制协议。将系统的一致性问题转化为误差系统的一致性问题,通过Lyapunov稳定性理论和矩阵理论分析得到了该协议使系统达到一致的充分条件。最后用仿真例子证明了设计方法的有效性。     

ADRC Law of Spacecraft Rendezvous and Docking in Final Approach Phase

This article addresses the high-precision coordinated control problem of spacecraft autonomous rendezvous and docking, which couple the relative position and attitude in the final approach phase. The coupled dynamics equations of the tracking-target spacecrafts is derived by using dual quaternions. Then, a cascade Active Disturbance Rejection Controller is proposed, by which the extended state observer and nonlinear error feedback law is designed, the virtual value on which the actual control volume tracking is calculated to ensure the finite time convergence of the relative position and attitude tracking errors in spite of parametric uncertainties and external disturbances. Finally, numerical simulations are performed to demonstrate that the proposed approaches, which can avoid the coupling effect and restrain the interference, can track the target spacecraft in a relatively short period of time, and the control precision can satisfy the requirements of docking.     

Robust integral control for a class of nonlinear systems with unknown control coefficients

The robust integral control problem is studied for a class of nonlinear systems with input-to-state stable (ISS)unmodeled dynamics in this paper.It does not require a priori knowledge of the control coefficients.Combining the Nussbaum-type gain technique and the backstepping design,we propose a state feedback controller,which could achieve the global asymptotic tracking for any constant reference signal,irrespective of the unmeasured dynamic disturbance.It is shown that the proposed methodology further extends the existing robust nonlinear integral control results.Simulation results verify the correctness of the theoretical analysis.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

Stability and control aspects of flexible link robot manipulators during constrained motion tasks

The effect of robotic manipulator structural compliance on system stability and trajectory tracking performance and the compensation of this structural compliance has been the subject of a number of publications for the case of robotic manipulator noncontact task execution. The subject of this article is the examination of dynamics and stability issues of a robotic manipulator modeled with link structural flexibility during execution of a task that requires the robot tip to contact fixed rigid objects in the work environment. The dynamic behavior of a general n degree of freedom flexible link manipulator is investigated with a previously proposed nonlinear computed torque constrained motion control applied, computed based on the rigid link equations of motion. Through the use of techniques from the theory of singular perturbations, the analysis of the system stability is investigated by examining the stability of the “slow” and “fast” subsystem dynamics. The conditions under which the fast subsystem dynamics exhibit a stable response are examined. It is shown that if certain conditions are satisfied a control based on only the rigid link equations of motion will lead to asymptotic trajectory tracking of the desired generalized position and force trajectories during constrained motion. Experiments reported here have been carried out to investigate the performance of the nonlinear computed torque control law during constrained motion of the manipulator. While based only on the rigid link equations of motion, experimental results confirm that high-frequency structural link modes, exhibited in the response of the robot, are asymptotically stable and do not destabilize the slow subsystem dynamics, leading to asymptotic trajectory tracking of the overall system. © 1992 John Wiley & Sons, Inc.     

ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS WITH TRACKING ERRORS SQUARE

In this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.