Adaptive Regulation of Amplitude Limited Robot Manipulators With Uncertain Kinematics and Dynamics

Common assumptions in most of the previous robot controllers are that the robot kinematics and manipulator Jacobian are perfectly known and that the robot actuators are able to generate the necessary level of torque inputs. In this note, an amplitude-limited torque input controller is developed for revolute robot manipulators with uncertainty in the kinematic and dynamic models. The adaptive controller yields semiglobal asymptotic regulation of the task-space setpoint error. The advantages of the proposed controller include the ability to actively compensate for unknown parametric effects in the dynamic and kinematic model and the ability to ensure actuator constraints are not breached by calculating the maximum required torque a priori     

A Disturbance Observer-based Robust Tracking Controller for Uncertain Robot Manipulators

This paper considers the trajectory tracking problem for uncertain robot manipulators subject to external disturbance torques. The external disturbance torques are assumed to be unknown and time-varying. We present a disturbance observer-based controller which estimates the lumped disturbance (the external disturbance torque combined with the effect of plant uncertainties), and compensates it so that the overall closed-loop system behaves like the nominal closed-loop system that is composed of the nominal model of robot manipulator and the feedback linearization-based tracking controller. A simplified implementation of the proposed controller is also introduced. Simulation results on a robot manipulator are given to validate the performance of the proposed controller.     

具有不确定雅可比矩阵机器人的鲁棒非线性PID控制器的抗饱和失效设计

对于雅克比阵不确定的操作机器人笛卡尔空间操作任务, 提出一种鲁棒非线性PID控制器的抗饱和设计方案, 解决了PID控制中的积分饱和问题. 该控制器通过引入有界递增分段连续函数于PID控制器中的积分环节, 限制了积分器的积分作用, 从而克服了积分环节对闭环系统的不利影响: 一方面使得闭环系统是渐进稳定的, 另一方面又保证了其鲁棒性; 特别是, 相比于其它的抗饱和设计方法, 显得更加简单有效.     

Data-driven Multiplayer Mixed-zero-sum Game Control of Modular Robot Manipulators with Uncertain Disturbance

International Journal of Control, Automation and Systems - This paper develops a data-driven multiplayer mixed-zero-sum game control approach of modular robot manipulators (MRMs) with uncertain...     

Global Optimal Feedback‐Linearizing Control of Robot Manipulators

The present paper offers a new optimal feedback‐linearizing control scheme for robot manipulators. The method presented aims at solving a special form of the unconstrained optimal control problem (OCP) of robot manipulators globally using the results of the Lyaponov method and feedback‐linearizing strategy and without using the calculus of variations (indirect method), direct methods, or the dynamic programming approach. Most of these methods and their sub‐branches yield a local optimal solution for the considered OCP by satisfying some necessary conditions to find the stationary point of the considered cost functional. In addition, the proposed method can be used for both set‐point regulating (point‐to‐point) tasks (e.g. pick‐and‐place operation or spot welding tasks) and trajectory tracking tasks such as painting or welding tasks. However, the proposed method can not support the physical constraints on robot manipulators and requires precise dynamics of the robot, as well. Instead, it can be used as an on‐line optimal control algorithm which produces the optimal solution without performing any kind of optimization algorithms which require time to find the optimal solution.     

A Class of OFT Controllers for Torque-Saturated Robot Manipulators: Lyapunov Stability and Experimental Evaluation

The trajectory tracking of robot manipulators is addressed in this paper. Two important practical situations are considered: the fact that robot actuators have limited power, and that only position measurements are carried out. Let us notice that a few solutions for the torque-bounded OFT (output feedback tracking) control has been proposed. In this paper we contribute to this subject by presenting a class of OFT controllers for torque-constrained robots. The theory of singularly perturbed systems is crucial in the analysis of the closed-loop system trajectories. As a second contribution of this paper, we present a detailed experimental study of six control schemes, which were tested in a two degrees-of-freedom direct-drive robot, confirming the advantages of the proposed methodology.     

离散系统LQ调节器的鲁棒性分析

本文研究了离散ＬＱ调节器系统鲁棒稳定性问题，稳定的不确定参数是通过考虑参数摄动的方向而求得的，这种方法比现有文献提供的结果具有更好的稳定范围。     

A Markov Game-Adaptive Fuzzy Controller for Robot Manipulators

This paper develops an adaptive fuzzy controller for robot manipulators using a Markov game formulation. The Markov game framework offers a promising platform for robust control of robot manipulators in the presence of bounded external disturbances and unknown parameter variations. We propose fuzzy Markov games as an adaptation of fuzzy Q-learning (FQL) to a continuous-action variation of Markov games, wherein the reinforcement signal is used to tune online the conclusion part of a fuzzy Markov game controller. The proposed Markov game-adaptive fuzzy controller uses a simple fuzzy inference system (FIS), is computationally efficient, generates a swift control, and requires no exact dynamics of the robot system. To illustrate the superiority of Markov game-adaptive fuzzy control, we compare the performance of the controller against a) the Markov game-based robust neural controller, b) the reinforcement learning (RL)-adaptive fuzzy controller, c) the FQL controller, d) the H_infin theory-based robust neural game controller, and e) a standard RL-based robust neural controller, on two highly nonlinear robot arm control problems of i) a standard two-link rigid robot arm and ii) a 2-DOF SCARA robot manipulator. The proposed Markov game-adaptive fuzzy controller outperformed other controllers in terms of tracking errors and control torque requirements, over different desired trajectories. The results also demonstrate the viability of FISs for accelerating learning in Markov games and extending Markov game-based control to continuous state-action space problems.     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

Dynamics and Noncollocated Model‐Free Position Control for a Space Robot with Multi‐Link Flexible Manipulators

In this paper, both the dynamics and noncollocated model‐free position control (NMPC) for a space robot with multi‐link flexible manipulators are developed. Using assumed modes approach to describe the flexible deformation, the dynamic model of the flexible space robotic system is derived with Lagrangian method to represent the system dynamic behaviors. Based on Lyapunov's direct method, the robust model‐free position control with noncollocated feedback is designed for position regulation of the space robot and vibration suppression of the flexible manipulators. The closed‐loop stability of the space robotic system can be guaranteed and the guideline of choosing noncollocated feedback is analyzed. The proposed control is easily implementable for flexible space robot with both uncertain complicated dynamic model and unknown system parameters, and all the control signals can be measured by sensors directly or obtained by a backward difference algorithm. Numerical simulations on a two‐link flexible space robot are provided to demonstrate the effectiveness of the proposed control.     

A Generalized Vision-based Stiffness Controller for Robot Manipulators with Bounded Inputs

Generally, stiffness and impedance control schemes require knowledge of the location of any object with which a robot interacts within its workspace; therefore, the integration of a computer vision system within the control loop allows us to know the location of the robot end effector and the object (target) simultaneously. In this paper, a generalized and saturating vision-based stiffness controller with adaptive gravity compensation is presented. The proposed control algorithm is designed to regulate robot-environment interaction in task-space, where the contact force is modeled as a vector of generalized bounded spring-like forces. In order to control nonredundant robots, the proposed controller has a nonlinear proportional-derivative structure with static model-based compensation of gravitational forces, as it includes a regressor-based adaptive term. To support the proposal, the Lyapunov stability analysis of the closed-loop equilibrium vector is presented. Finally, the suitable performance of the proposed scheme was verified by numerical simulations and experimental tests.

     

A Robust Control Law with Estimated Perturbation Compensation for Robot Manipulators

By considering the dynamic response of a robot manipulator as characterized by the sliding function, a technique is proposed to estimate the perturbation in the robot control system. Perturbation compensation is then incorporated in the design of a robust control law to cancel the effects of system parametric uncertainties and external disturbances. A normalized power rate component is introduced to replace the discontinuous control that is usually associated with variable structure system. The suggested robust control law ensures that the robot control system reaches an user specified neighbourhood of the sliding manifold in finite time and with prescribed transient behaviour. Explicit estimates of the bounds on modelling errors and external disturbances are not required while signal measurement uncertainties can be accommodated. Furthermore, using the equivalent control concept, a very simple expression is derived to estimate the system perturbation signal. Detailed computer simulation results are presented to demonstrate the effectiveness of the proposed control law.     

机械臂轨迹跟踪控制研究进展

综述了近年来刚性机械臂轨迹跟踪控制研究领域的最新进展.根据应用于机械臂的不同控制算法进行分类,从自适应PID控制、神经网络自适应控制、模糊自适应控制、滑模变结构控制和鲁棒自适应控制5种主要控制方法进行阐述.重点从关节空间出发,论述了各种控制算法在提高机械臂轨迹跟踪性能方面的各自优缺点,并分析了它们之间的相互联系.对机械...     

Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

The state estimation problem is investigated for a class of linear uncertain systems with state and noise delay. The optimal one‐step prediction algorithm is presented by introducing a fictitious noise. The predictor is designed based on the projection formula in Hilbert space and has the same dimensions as the original systems. The error covariance consists of two coupled Riccati‐type difference equations. The optimal filter and fixed‐lag smoother are provided based on the predictor. A numerical example is given to show the effectiveness of the proposed approach.     

Model‐based Prediction of Skid‐steer Robot Kinematics Using Online Estimation of Track Instantaneous Centers of Rotation

This paper presents a kinematic extended Kalman filter (EKF) designed to estimate the location of track instantaneous centers of rotation (ICRs) and aid in model‐based motion prediction of skid‐steer robots. Utilizing an ICR‐based kinematic model has resulted in impressive odometry estimates for skid‐steer movement in previous works, but estimation of ICR locations was performed offline on recorded data. The EKF presented here utilizes a kinematic model of skid‐steer motion based on ICR locations. The ICR locations are learned by the filter through the inclusion of position and heading measurements. A background on ICR kinematics is presented, followed by the development of the ICR EKF. Simulation results are presented to aid in the analysis of noise and bias susceptibility. The experimental platforms and sensors are described, followed by the results of filter implementation. Extensive field testing was conducted on two skid‐steer robots, one with tracks and another with wheels. ICR odometry using learned ICR locations predicts robot position with a mean error of ?0.42 m over 40.5 m of travel during one tracked vehicle test. A test consisting of driving both vehicles approximately 1,000 m shows clustering of ICR estimates for the duration of the run, suggesting that ICR locations do not vary significantly when a vehicle is operated with low dynamics.     

Robust Visual‐Servo Control of Robot Manipulators in the Presence of Uncertainty

This paper considers the problem of position control of planar robot manipulators via visual servoing in the presence of uncertainty associated with the robot mechanical dynamics and the camera system for both fixed‐camera and camera‐in‐hand configurations. Specifically, we first design a robust controller that compensates for uncertainty throughout the whole robot‐camera system and ensures global uniformly ultimately bounded position tracking for the fixed‐camera configuration. Under the same class of uncertainty, we then develop a setpoint controller for the camera‐in‐hand configuration that achieves global uniformly ultimately bounded regulation. Experimental results illustrating the performance of both controllers are also included. © 2003 Wiley Periodicals, Inc.     

Adaptive Non‐Backstepping Fuzzy Control for a Class of Uncertain Nonlinear Systems with Unknown Dead‐Zone Input

Based on the approximation property of fuzzy logic systems, we propose a novel non‐backstepping adaptive tracking control algorithm for a class of single input single output (SISO) strict‐feedback nonlinear systems with unknown dead‐zone input. In this algorithm, we introduce some novel state variables and coordinate transforms to convert the strict‐feedback form into a normal one, and it is not necessary to consider the traditional approximation‐based the backstepping scheme. Due to new states variables being unavailable, the tracking control is changed from a state‐feedback one to an output‐feedback one. So, observers need to be designed to estimate the indirect nonmeasurable states. According to Lyapunov stability analysis method, the developed controller can guarantee that all of the signals in the closed‐loop system will be ultimately uniformly bounded (UUB), and the output can track the reference signal very well. Simulation results are presented to show the effectiveness of the proposed approach.     

Semi‐Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi‐global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block‐backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed‐loop system is rendered semi‐globally asymptotically stable.     

An Approach of Adaptive Control for Robot Manipulators

This paper presents the study of an adaptive control which tracks a desired time-based trajectory as closely as possible for all times over a wide range of manipulator motion and payloads both in joint-variable coordinates and Cartesian coordinates. The proposed adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component computes the nominal torques from the Newton-Euler equations of motion either using the resolved joint information or the joint information from the trajectory planning program. This computation can be completed in O(n) time. The feedback component consisting of recursive least square identification and one-step optimal control algorithms for the linearized system computes the perturbation torques in O(n³) time. Because of the parallel structure, the computations of the adaptive control may be implemented in low-cost microprocessors. A computer simulation study Was conducted to evaluate the performance of the adaptive control in joint-variable coordinates for a three-joint robot arm. The feasibility of implementing the adaptive control in Cartesian coordinates using present day low-cost microprocessors is discussed.