Comments on “Robust tracking control for rigid roboticmanipulators”

In the original paper by M. Zhihong and M. Palaniswami (ibid., vol.39, p.154-9, 1994), a robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics was presented. It is assumed that the model uncertainty is bounded. The author claims that this assumption is not necessarily correct and that the results obtained are therefore untenable     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Robot discrete adaptive control based on dynamic inversion using dynamical neural networks

A stable discrete time adaptive control approach using dynamic neural networks (DNNs) is developed in this paper for the trajectory tracking of a robotic manipulator with unknown nonlinear dynamics. By using dynamic inversion constructed by a DNN, the assumption under which the system state should be on a compact set can be removed. This assumption is usually required in neuro-adaptive control. The NN-based variable structure control is designed to guarantee the stability and improve the dynamic performance of the closed-loop system. The proposed control scheme ensures the global stability and desired tracking as well.     

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.     

Towards nonadaptive and adaptive control of manipulation robots

Control synthesis for robotic systems with a variable payload is considered. First, we synthesize a robust, nonadaptive decentralized control using an approximative system model. Then, we analyze the stability of an exact system model. We thus check whether the robotic manipulator is stabilized for all allowable payload variations. If the simple decentralized control cannot accommodate all expected payload variations we introduce additional load, nonadaptive, feedback loop. This global control requires force transducers to be implemented in manipulator joints. If such nonadaptive control cannot stabilize robotic manipulator trajectories we suggest another adaptive control scheme. This control scheme includes an algorithm for on-line identification of variable payload and adaptation of local gains.     

Unconstrained and constrained motion control of a planar two-link structurally flexible robotic manipulator

Unconstrained and constrained motion control of a planar two-link structurally-flexible robotic manipulator are considered in this study. The dynamic model is obtained by using the extended Hamilton's principle and the Galerkin criterion. A method is presented to obtain the linearized equations of motion in Cartesian space for use in designing the control system. The approach to solving the control problem is to use feedforward and feedback control torques. The feedforward torques maneuver the flexible manipulator along a nominal trajectory and the feedback torques minimize any deviations from the nominal trajectory. The feedforward and feedback torques are obtained by solving the inverse dynamics problem for the rigid manipulator and designing linear quadratic Gaussian with loop transfer recovery (LQG/LTR) compensators, respectively. The LQG/LTR design methodology is exploited to design a robust feedback control system that can handle modeling errors and sensor noise, and operate on Cartesian space trajectory errors. Computer simulated results are presented for an example planar, two-link, structurally flexible robotic manipulator. © 1994 John Wiley & Sons, Inc.     

基于模糊变结构的机械臂控制

现有的机械臂模糊变结构控制方法大都计算复杂或需要检测滑模面的微分信号.本文将机械臂模型分为确定部分和不确定部分进行研究,对确定部分采用一般反馈控制,对不确定部分采用变结构集中补偿控制,为了消除变结构控制器的抖震引入模糊控制方法,将滑模面作为模糊控制器的输入,补偿控制器权值作为输出.本方案不仅不需要检测滑模面微分信号,而且计算简单,易于实现.仿真结果表明,在存在模型误差和外部扰动的情况下,该方案既能达到快速跟踪,又能很好的消除控制器的抖震.     

指数稳定的机器人鲁棒跟踪控制

本文提出了一种用于控制具有参数不确性机器人轨迹踊跃的鲁棒控制策略，该控制器的设计根据Ｌｙａｐｕｎｏｖ理论，由一个基于Ｓｌｏｔｉｎｅ方法的标称控制器和一个非线性连续反馈补偿器组成。     

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.     

Adaptive PI Hermite neural control for MIMO uncertain nonlinear systems

This paper presents an adaptive PI Hermite neural control (APIHNC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The proposed APIHNC system is composed of a neural controller and a robust compensator. The neural controller uses a three-layer Hermite neural network (HNN) to online mimic an ideal controller and the robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Moreover, a proportional–integral learning algorithm is derived to speed up the convergence of the tracking error. Finally, the proposed APIHNC system is applied to an inverted double pendulums and a two-link robotic manipulator. Simulation results verify that the proposed APIHNC system can achieve high-precision tracking performance. It should be emphasized that the proposed APIHNC system is clearly and easily used for real-time applications.     

基于PD控制的机器人轨迹跟踪性能研究与比较

定义同一个Lyapunov函数，分析了基于PD的3种常用机器人轨迹跟踪算法的稳定性和鲁棒性，得到了新的结论，PD加前馈控制按指数收敛到0，PD及修改的PD加前馈控制收敛到一封闭球，增大反馈系数可使球半径任意小，基于PD的轨迹跟踪算法对模型误差及有界不确定性干扰具有鲁棒性，实验研究验证了分析结果，并对3种轨迹跟踪算法的控制性能进行比较。     

Projection operator-based robust adaptive control of an aerial robot with a manipulator

This paper describes a quadcopter manipulator system, an aerial robot with an extended workspace, its controller design, and experimental validation. The aerial robot is based on a quadcopter with a three degree of freedom robotic arm connected to the base of the vehicle. The work aims to create a stable airborne robot with a robotic arm that can work above and below the airframe, regardless of where the arm is attached. Integrating a robotic arm into an underactuated, unstable system like a quadcopter can enhance the vehicle's functionality while increasing instability. To execute a mission with accuracy and reliability during a real-time task, the system must overcome the inter-coupling effects and external disturbances. This work presents a novel design for a robust adaptive feedback linearization controller with a model reference adaptive controller and hardware implementation of the quadcopter manipulator system with plant uncertainties. The closed-loop stability of the aerial robot and the tracking error convergence with the robust controller is analyzed using Lyapunov stability analysis. The quadcopter manipulator system is custom developed in the lab with an off-the-shelf quadcopter and a 3D-printed robotic arm. The robotic system architecture is implemented using a Jetson Nano companion computer for autonomous onboard flight. Experiments were conducted on quadcopter manipulator system to evaluate the autonomous aerial robot's stability and trajectory tracking with the proposed controller.     

Bio-harmonized control experiments of a carangiform robotic fish underwater vehicle

This paper presents experimental implementation and comparison of three different control schemes of a bio-inspired robotic fish underwater vehicle. The dynamics model is obtained by unifying conventional rigid body dynamics and bio-fluid dynamics of a carangiform fish swimming given by Lighthill’s(LH) slender body theory. It proposes an inclusive mathematical design for better control and energy efficient path travel for the robotic fish. The system is modeled as an two-link robot manipulator (caudal tail) with a mobile base (head). This forward thrust drives the robotic fish head represented by a combined non-linear equation of motion in earth fixed frame. We develop and compare the dynamic motion closed loop control strategy of the bio-harmonized robotic fish based on three different non-linear control schemes using CTM (Computed Torque Method), FF (Feed-Forward) controllers both with dynamic PD compensation and finally a proposed combination of CTM with FF. An inverse dynamic control method based on non-linear state function model including hydrodynamics is proposed to improve tracking performance. CTM control generates a feedback loop for linearization and decoupling robot dynamic model with a shorter response time, while a dynamic PD compensation in the FF path is employed by FF scheme through the desired trajectories. FF model-based strategy results in an improved tracking and shorter route to travel between two points. Overall results indicate that performances of the proposed control schemes based on the inverse dynamic model are comparable and useful for robotic fish motion tracking in fluid environment.     

A simulational comparison of intelligent control algorithms on a direct drive manipulator

This paper investigates the control of nonlinear systems by neural networks and fuzzy logic. As the control methods, Gaussian neuro-fuzzy variable structure (GNFVS), feedback error learning architecture (FELA) and direct inverse modeling architecture (DIMA) are studied, and their performances are comparatively evaluated on a two degrees of freedom direct drive robotic manipulator with respect to trajectory tracking performance, computational complexity, design complexity, RMS errors, necessary training time in learning phase and payload variations.     

A Robust Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators

In this paper, a robust adaptive terminal sliding mode controller is developed for n-link rigid robotic manipulators with uncertain dynamics. An MIMO terminal sliding mode is defined for the error dynamics of a closed loop robot control system, and an adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties in the Lyapunov sense. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated and a finite time error convergence in the terminal sliding mode can be guaranteed. Also, a useful bounded property of the derivative of the inertial matrix is explored, the convergence rate of the terminal sliding variable vector is investigated, and an experiment using a five bar robotic manipulator is carried out in support of the proposed control scheme.     

A robust MIMO terminal sliding mode control scheme for rigidrobotic manipulators

In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero     

Adaptive tracking control of rigid manipulators using only position measurements

This article presents a new approach to trajectory tracking control of uncertain rigid manipulators using only position measurements. The proposed control strategy is an adaptive scheme that is very general and computationally efficient, requires virtually no information regarding the manipulator dynamic model, and is implementable without calculation of the robot inverse dynamics or inverse kinematic transformations. It is shown that the controller ensures semiglobal uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Additionally, it is demonstrated that the proposed strategy can be used as the basis for developing controllers for “cascaded” robotic systems, such as manipulators with significant actuator dynamics or joint flexibility. The efficacy of this approach to manipulator control is illustrated through both computer simulations and hardware experiments. © 1997 John Wiley & Sons, Inc.     

一类奇异非线性变结构控制系统的跟踪问题

首次利用变结构控制方法研究了一类奇异非线性系统的模型跟踪问题，在不同情况下，通过引入动态补偿器的概念，设计了奇异模型跟踪系统的切换函数，得到了在切换面上实现跟踪的条件，然后利用趋近律方法设计了变结构控制，以保证在切换面外的运动在有限时间到达切换面，通过滑动运动实现跟踪，最后讨论了参数模型为正常系统的线性定常奇异系统的跟踪问题。