Neural-network-based two-loop control of robotic manipulators including actuator dynamics in task space

A neural-network-based motion controller in task space is presented in this paper. The proposed controller is addressed as a two-loop cascade control scheme. The outer loop is given by kinematic control in the task space. It provides a joint velocity reference signal to the inner one. The inner loop implements a velocity servo loop at the robot joint level. A radial basis function network （RBFN） is integrated with proportional-integral （PI） control to construct a velocity tracking control scheme for the inner loop. Finally, a prototype technology based control system is designed for a robotic manipulator. The proposed control scheme is applied to the robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.     

Adaptive control of robot manipulators in task space

Adaptive control of robotic manipulators in task space or Cartesian space is considered. A general Lyapunov-like concept is used to design an adaptive control law. It is shown that the global stability and convergence can be achieved for the adaptive control algorithm. The algorithm has the advantage that the inverse of Jacobian matrix is not required. The algorithm is further modified so that the requirement for the bounded inverse of estimated inertia matrix is also eliminated. In addition, two approaches are presented to achieve robustness to bounded disturbances     

用于刚性机械手的无抖振快速终端滑模控制

提出一种用于刚性机械手的无抖振动终端滑模鲁棒控制器。快速终端滑模综合了终端滑模和传统线性滑模的优，能在有限时间内到达平衡点，并降低系统稳态误差。采用优化方法推导出系统的跟踪精度和用于消除抖振的饱和函数和函数宽度之间的数学关系。利用系统的参数化模型，可将参数的不确定部分从回归矩阵中分离出来.根据每个参数不确定范围设计鲁棒控制器。仿真结果证明了该方法的有效性。     

Robust neural control for robotic manipulators

A robust neural control scheme for mechanical manipulators is presented. The design basically consists of an adaptive neural controller which implements a feedback linearization control law for a generic manipulator with unknown parameters, and a sliding-mode control which robustifies the design and compensates for the neural approximation errors. It is proved that the resulting closed-loop system is stable and that the trajectory-tracking control objective is achieved. Some simulation results are also provided to evaluate the design.     

Global stability analysis for some trajectory‐tracking control schemes of robotic manipulators

With a same Lyapunov function defined, the stability, robustness, and convergence speed of three widely used trajectory‐tracking control schemes, i.e., the proportional‐derivative (PD) control, the PD control with a feedforward compensation, and the PD control with a calculated feedforward compensation, are presented. All three control schemes are globally exponentially convergent. The trajectory‐tracking features of the three control schemes are theoretically analyzed and compared. Suggestions are given for the choices of the control parameters. © 2001 John Wiley & Sons, Inc.     

Discrete-time modeling and control of robotic manipulators

A general approach is presented to derive discrete-time models of robotic manipulators. Such models are obtained by applying numerical discretization techniques directly to the problem of the minimization of the Lagrange action functional. Although these models are in implicit form, they own a dynamic structure that allows us to design discrete-time feedback linearizing control laws. The proposed models and control algorithms are validated by simulation with reference to a three link robot.     

Computer control of robotic manipulators using predictors

Model-based robot control algorithms require the on-line evaluation of robot dynamics, leading to hybrid continuous/discrete-time implementations. The performance of these fixed-gain control algorithms varies in the workspace and it is not adequate for trajectory-tracking. In this paper, we present a coherent discrete-time framework for the analysis of model-based algorithms and introduce predictors to compensate for modeling and discretization errors. The basic controller structure is not altered; an added supervisory module is proposed to monitor performance and adjust the command signal accordingly. The module injects a degree of adaptiveness in the controller and reduces the sensitivity of the design to unmodeled dynamics. Our preliminary simulation experiments confirm that one-step-ahead predictors lead to a more uniform performance and are suitable for trajectory-tracking applications.A preliminary version of this paper appeared in the Proceedings of the IEEE International Symposium on Intelligent Control, Philadelphia, Pennsylvania, 19–20 January 1987. Research supported in part by the National Science Foundation under Grant No. DMC-8707622.     

No-overshoot control of robotic manipulators in the presence of obstacles

The long standing problem of guiding robotic manipulators in cluttered workspaces is treated here by a unified approach, taking into account both motion planning and control aspects. Planning the collision-free operation is based on the notion of roadmaps. To reduce the complexity of the roadmaps, the real problem is approximated by a simplified but still realistic graph structure. Motion planning relies on the robot closely following the defined collison-free path, so the errors in robot control must be contained within bounded regions. Satisfying this assumption ideally requires no-overshoot control. Overshooting demands special attention in tasks that require high speed operations of robots in the presence of obstacles. To stabilize at the specified collision-free trajectory, before going actually beyond it, joint control schemes demand slow movements through a number of intermediate subgoals. This significantly delays the completion of the task. By using ideas from variable structure control (VSC), a control policy is suggested here that switches between PD⁺ and CEA⁺ (constant error acceleration) schemes, where the CEA + scheme applies a “constant error acceleration” of the largest possible magnitude in the appropriate direction. The performance of the path planning and the control algorithms is presented through simulations of a four-link SCARA robot in various cluttered workspaces. © 1994 John Wiley & Sons, Inc.     

机器人机械手的离散时间学习控制*

本文为机器人机械手提出了一种基于离散时间的重复学习控制法，这种学习控制法利用机器人动力学模型的部分知识，从它的特性和实用观点看，这种控制法比现有的其它学习控制法更有吸引力，本文还给出了学习控制法的收敛性证明和计算机仿真结果。     

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.     

Robust tracking control for rigid robotic manipulators

The problem of robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics is addressed in this note. It is shown that the effects of large system uncertainties can be eliminated and asymptotic convergence of the output tracking error can be guaranteed by using a variable structure compensator in the closed loop feedback control system for the rigid robotic manipulator     

Robust fuzzy tracking control for robotic manipulators

In this paper, a stable adaptive fuzzy-based tracking control is developed for robot systems with parameter uncertainties and external disturbance. First, a fuzzy logic system is introduced to approximate the unknown robotic dynamics by using adaptive algorithm. Next, the effect of system uncertainties and external disturbance is removed by employing an integral sliding mode control algorithm. Consequently, a hybrid fuzzy adaptive robust controller is developed such that the resulting closed-loop robot system is stable and the trajectory tracking performance is guaranteed. The proposed controller is appropriate for the robust tracking of robotic systems with system uncertainties. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

Reliability maps for probabilistic guarantees of task motion for robotic manipulators

There are many applications for which reliable and safe robots are desired. For example, assistant robots for disabled or elderly people and surgical robots are required to be safe and reliable to prevent human injury and task failure. However, different levels of safety and reliability are required for different tasks so that understanding the reliability of robots is paramount. Currently, it is possible to guarantee the completion of a task when the robot is fault tolerant and the task remains in the fault-tolerant workspace (FTW). The traditional definition of FTW does not consider different reliabilities for the robotic manipulator's different joints. The aim of this paper is to extend the concept of a FTW to address the reliability of different joints. Such an extension can offer a wider FTW while maintaining the required level of reliability. This is achieved by associating a probability with every part of the workspace to extend the FTW. As a result, reliable fault-tolerant workspaces (RFTWs) are introduced by using the novel concept of conditional reliability maps. Such a RFTW can be used to improve the performance of assistant robots while providing the confidence that the robot remains reliable for completion of its assigned tasks.     

Gain adaptation in sliding mode control of robotic manipulators

In this paper, a novel scheme is proposed to adapt the gains of a sliding mode controller (SMC) so that the problems faced in its practical implementations as a motion controller are overcome. A Lyapunov function is selected for the design of the SMC and an MIT rule is used for gain adaptation. The criterion that is minimized for gain adaptation is selected as the sum of the squares of the control signal and the sliding surface function. This novel approach is tested on a scara-type robot manipulator. The experimental results presented prove its efficacy.     

Robust control of robotic manipulators without velocity feedback

This study concerns the problem of robust control of robotic manipulators without joint velocity feedback. A robust lead + bias controller is studied. The bias signal is intended to compensate the nonlinear dynamics of the robot. The focus of this study is robustness when the nonlinear compensation is not perfect and the external disturbances are not negligible. A conservative polynomial bound is introduced to describe the worst feedback effect of the compensation error and the external disturbances. The polynomial bound covers a class of possible bias signals, synthesized according to the available knowledge about the robot dynamics. Based on the polynomial bound, the tracking errors of a lead + bias controller are proved to be uniformly bounded. They can be minimized by a proper design of the bias signal. In the ideal case where the bias signal compensates the robot dynamics perfectly, the tracking errors will converge to zero.     

An approach to adaptive control of robotic manipulators

The control synthesis for the robotic systems in which parameters are partially unknown is considered. We propose synthesis of robust, non-adaptive, decentralized control which has to stabilize robots for all allowable variations of the parameters. If the robust non-adaptive control cannot withstand all expected variations of parameters, we propose synthesis of indirect adaptive control, i.e. the estimation of the robot parameters is performed first and then used for adjusting the decentralized control gains. The non-adaptive and adaptive control syntheses are illustrated by simulation of an industrial robot with unknown payload mass.     

Scaled Jacobian transpose based control for robotic manipulators

This paper presents a scaled Jacobian transpose based control method for robotic manipulators as a modification of a conventional Jacobian transpose based method. The proposed method has several advantages such as it shows faster convergence and better tracking performance than the conventional method, furthermore, it does not have any singularity problem similar to the conventional method. The scaled Jacobian transpose is obtained by collecting each pseudoinverse of the column vector of the Jacobian matrix. The proposed method performs a given task well under singular configurations while minimizing the task error. Finally, a few comparative studies with the conventional method are provided to show the effectiveness of the proposed method through simulations.     

A global adaptive learning control for robotic manipulators

This paper addresses the problem of designing a global adaptive learning control for robotic manipulators with revolute joints and uncertain dynamics. The reference signals to be tracked are assumed to be smooth and periodic with known period. By developing in Fourier series expansion the input reference signals of every joint, an adaptive learning PD control is designed which ‘learns’ the input reference signals by identifying their Fourier coefficients: global asymptotic and local exponential stability of the tracking error dynamics are obtained when the Fourier series expansion of each input reference signal is finite, while arbitrary small tracking errors are achieved otherwise. The resulting control is not model based and depends only on the period of the reference signals and on some constant bounds on the robot dynamics.     

Robust discrete nonlinear feedback control for robotic manipulators

Nonlinear feedback control algorithms for manipulators utilize a complete (coupled and nonlinear) dynamic robot model to decouple the robot joints. In the companion article¹ we outlined the practical problems introduced by modeling inaccuracies, unmodeled dynamics and parameter errors. We then introduced the α-computed-torque nonlinear feedback control algorithm which is robust in the presence of the aforementioned error sources. In this article, we apply the insight gained from the α-computed-torque algorithm to design a robust discrete-time (accelerometer-free) computed-torque robot-control algorithm founded upon our discrete dynamic robot model.² Numerical experiments with the cylindrical robot confirm both the robust disturbance rejection characteristics and the practical applicability of our discrete-time computer-torque control algorithm.     

Adaptive learning tracking control of robotic manipulators with uncertainties

An adaptive learning tracking control scheme is developed for robotic manipulators by a synthesis of adaptive control and learning control approaches. The proposed controller possesses both adaptive and learning properties and thereby is able to handle robotic systems with both time-varying periodic uncertainties and time invariant parameters. Theoretical proofs are established to show that proposed controllers ensure asymptotical tracking performance. The effectiveness of the proposed approaches is validated through extensive numerical simulation results.