Approximate Jacobian control with task-space damping for robot manipulators

In this note, we propose two new approximate Jacobian control laws with task-space damping for setpoint control of robot manipulators. The proposed controllers do not require exact knowledge of the Jacobian matrix and dynamics of the robots. We will show that the end-effector's position converges to a desired position in a finite task space even when the kinematics and Jacobian matrix are uncertain. Experimental results are presented to illustrate the performance of the proposed controllers.     

Adaptive sliding mode control of n$n$ flexible-joint robot manipulators in the presence of structured and unstructured uncertainties

Multibody System Dynamics - This study investigates a voltage-based adaptive sliding mode control (VB-ASMC) to tracking the position of an $n$ rigid-link flexible-joint (RLFJ) robot manipulator...     

Neural network-based sliding mode adaptive control for robot manipulators

This paper addresses the robust trajectory tracking problem for a robot manipulator in the presence of uncertainties and disturbances. First, a neural network-based sliding mode adaptive control (NNSMAC), which is a combination of sliding mode technique, neural network (NN) approximation and adaptive technique, is designed to ensure trajectory tracking by the robot manipulator. It is shown using the Lyapunov theory that the tracking error asymptotically converge to zero. However, the assumption on the availability of the robot manipulator dynamics is not always practical. So, an NN-based adaptive observer is designed to estimate the velocities of the links. Next, based on the observer, a neural network-based sliding mode adaptive output feedback control (NNSMAOFC) is designed. Then it is shown by the Lyapunov theory that the trajectory tracking errors, the observer estimation errors asymptotically converge to zero. The effectiveness of the designed NNSMAC, the NN-based adaptive observer and the NNSMAOFC is illustrated by simulations.     

An exponentially convergent adaptive sliding mode control of robot manipulators

A new robust adaptive algorithm for control of robot manipulators is proposed to account for a desired transient response with global exponential convergence of tracking errors without any persistent excitating assumption on the regressor. Its novelty lies in a new dynamic sliding surface that allows a systematic combination of adaptive control and variable structure control to yield a sliding mode inside an adaptive control loop. During sliding mode, parameter uncertainty appears in terms of known variables in such a manner that a new robust parameter estimator with enhanced stability properties is established. On the other hand, if the regressor meets the persistent exciting condition, the global uniform exponential stability of the equilibrium concerning the adaptive closed-loop error equation is easily established. The proposed controller from the VSS viewpoint relaxes the longstanding condition on a priori knowledge of the size of the parametric uncertainty to induce a sliding mode. On the other hand, from the adaptive control viewpoint it relaxes the standard assumption of the persistent excitation on the regressor to obtain the exponential convergence of tracking errors. Also, the stability against time-varying parameters is briefly discussed. Concluding remarks concerning its structural behaviour are given, and computer simulation data show a robust performance.     

Simple sliding mode control scheme applied to robot manipulators!

We present a simple sliding mode control scheme for robot manipulators that does not rely upon the construction of individually stable discontinuity surfaces, thus greatly reducing the complexity of design. We utilize the structure of the manipulator dynamics and Lyapunov's second method in order to establish a sliding surface on the intersection of the switching surfaces in a direct manner. A simple numerical example accompanies the theoretical development.     

输入受限机器人的鲁棒自适应输出反馈跟踪控制

在输入受限的情况下，通过一个线性一阶滤波器，实现机器人的鲁棒自适应输出反馈跟踪控制，解决了自适应控制算法的鲁棒性问题，即当满足持续激励条件及估计参数域包含参数真实值时，闭环系统能够实瑰渐近穗定跟踪，本算法简单有效，不仅提高了鲁棒性，改善了控制品质，同时对于参数域估计误差也具有很强的鲁棒性，仿真算饲验证了算法的有效性。     

performance control of robot manipulators with kinematics,dynamics and actuator uncertainties

This paper deals with the task‐space trajectory tracking control problem of robot manipulators. An improved adaptive backstepping controller is proposed to deal with the uncertainties in kinematics, dynamics, and actuator modeling. To avoid the explosion of computation in conventional backstepping techniques, a modified dynamic surface control algorithm is proposed, which guarantees the asymptotic convergence rather than the uniformly ultimately boundedness of tracking errors in conventional dynamic surface control methods. Furthermore, the expression of the norm of tracking errors is explicitly derived in relation to the controller parameters, which provides instructions on tuning controller parameters to adjust the system performance. Moreover, the passivity structure of the designed adaptation law is thoroughly analyzed. Simulation of a free‐floating space robot is used to verify the effectiveness of the proposed control strategy in comparison with the conventional tracking control schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

Flexible control for robot manipulators

We designed, implemented, and tested a real-time flexible controller for manipulating different types of robots and control algorithms. The robot-independent, IBM PC-based multiprocessor system contains a DSP56001 master controller, six independent HCTL-1100 joint processors for accurate robotic joint control, and an interface computer board for processor communication. The joint processors operate in four user-defined modes and can be connected directly to an incremental optical encoder, which accommodates specialized applications and eliminates extra hardware     

Finite-time control for robot manipulators

Finite-time control of the robot system is studied through both state feedback and dynamic output feedback control. The effectiveness of the proposed approach is illustrated by both theoretical analysis and computer simulation. In addition to offering an alternative approach for improving the design of the robot regulator, this research also extends the study of the finite-time control problem from second-order systems to a large class of higher order nonlinear systems.     

神经网络自适应滑模控制的不确定机器人轨迹跟踪控制

提出一种针对机器人跟踪控制的神经网络自适应滑模控制策略。该控制方案将神经网络的非线性映射能力与滑模变结构和自适应控制相结合。对于机器人中不确定项,通过RBF网络分别进行自适应补偿,并通过滑模变结构控制器和自适应控制器消除逼近误差。同时基于Lyapunov理论保证机器手轨迹跟踪误差渐进收敛于零。仿真结果表明了该方法的优越性和有效性。     

Vsc motion and force control of robot manipulators in the presence of environmental constraint uncertainties

Due to task kinematic modelling inaccuracy, constraint functions imposed on robot manipulators may not be known exactly. In this article, a variable structure control (VSC) method is developed for robust motion and constrained force control of robot manipulators in the presence of parametric uncertainties, external disturbances, and constraint function uncertainties. The method is based on a particular structure of the constrained robot, in which motion control and force control are treated together. The proposed VSC controller provides the sliding mode and reaching transient response with prescribed qualities. A sufficient condition to guarantee the robot does not lose contact with the constraint surface is given. Detailed simulation results illustrate the proposed method. © 1994 John Wiley & Sons, Inc.     

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.     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

Digital control of space robot manipulators with velocity type joint controller using transpose of generalized Jacobian matrix

For free floating space robots having manipulators, we have proposed a discrete-time tracking control method using the transpose of Generalized Jacobian Matrix (GJM). Control inputs of the control method are joint torques of the manipulator. In this paper, the control method is augmented for angular velocity inputs of the joints. Computer simulations have shown the effectiveness of the augmented method. This work was presented in part and awarded as Best Paper Award at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Global sliding mode with fractional operators and application to control robot manipulators

In this paper, a novel fractional-order global sliding-mode control scheme is presented. It is first used to stabilise a coupled second-order nonlinear system, and then it is generalised to control a class of multi-input and multi-output nonlinear systems with the model uncertainties and external disturbances. The proposed sliding manifold, which will converge to the origin in finite time by utilising a classical quadratic Lyapunov function, ensures global stabilisation of the system and the reduction of the chattering phenomenon during the control processes. Based on input-to-state stability and Lyapunov's stability theorem, the closed-loop system can be globally uniformly asymptotically stabilised to the origin in the future time. Some results about the control and stabilisation of integer-order nonlinear systems, when the fractional-order sliding-mode controller is used, are illustrated in this paper. Finally, an application to two-degree of freedom polar robot manipulator is provided to show the validity and feasibility of the proposed method.     

Integrated adaptive-robust control of robot manipulators

In this article, an integrand adaptive-robust approach along with a smooth adaptive-robust friction compensation strategy are applied to tracking control of robot manipulators with joint stick-slip friction. The designed controller takes advantage of both adaptive and robust approaches. It has the ability to learn and the ability to reject disturbance and to handle various uncertainties including stick-slip friction. The uncertainties due to unknown robot link parameters, unknown viscous friction coefficient, and unknown maximum static friction, which are linear in parameters, are compensated by the integrated adaptive-robust control method. On the other hand, the exponential friction (used to model the Stribeck effect: the downward bend of friction torque at low velocities), which are nonlinear in parameters, and external disturbances, are compensated by a robust compensator with a self-learning upper bounding function when no a priori knowledge on the exponential friction and disturbances are available. The employed robust compensators produce smooth control action, and avoid motion intermittency, which are commonly associated with stick-slip friction. The proposed controller guarantees global asymptotic stability of the closed-loop system, as proved by Lyapunov's direct method. © 1998 John Wiley & Sons, Inc.     

Robust microprocessor control of robot manipulators

In this paper the problem of robust tracking for robot manipulators in the presence of uncertainty and input constraints is studied. Using the theory of uncertain dynamical systems, robust non-linear control strategies, with guaranteed tracking properties that can be quantified given bounds on the extent of model uncertainty, sensor noise, input disturbances, etc., are derived. A torque optimization strategy is also utilized to optimize the joint torques in the event of actuator saturation. The algorithm has been implemented using a single Motorola 12 MHz MC68000 microprocessor on a three-link revolute joint manipulator constructed by the School of Mechanical Engineering at Cornell University. Experimental results are presented here showing the feasibility and performance of the control stragegy.     

Decentralized adaptive control of robot manipulators

A decentralized adaptive control scheme is proposed for the trajectory tracking of a general n-degree-of-freedom robot manipulator. The robot is considered as a set of decoupled second-order systems with disturbances. The controller consists of feedforward from the desired trajectory based on the “inverse system” of the model, PID feedback from the actual trajectory, and auxiliary input for the compensation of the neglected terms in modeling in each subsystem. The gain is derived in diagonal matrix form, and is adjusted by the model reference adaptive control theory based on the Lyapunov's direct method. The result is high accuracy in path tracking despite the high speed, load change, and sudden torque disturbances. Numerical simulations on.a planar two-link robot manipulator are presented to show the performance under various practical considerations.     

Handling uncertainties of robot manipulators and active vision by constraint propagation

Joint errors are inevitable in robot manipulation. These uncertainties propagate to give rise to translational and orientational errors in the position and orientation of the robot end‐effector. The displacement of the active vision head mounted on the robot end‐effector produces distortion of the projected object on the image. Upon active visual inspection, the observed dimension of a mechanical part is given dimension by the measurement on the projected edge segment on the image. The difference between the observed dimension and the actual dimension is the displacement error in active vision. For different motion of the active vision head, the resulting displacement errors are different. Given the uncertainties of the robot manipulator's joint errors, constraint propagation can be employed to assign the motion of the active sensor in order to satisfy the tolerance of the displacement errors for inspection. In this article, we define the constraint consistency and network satisfaction in the constraint network for the problem of displacement errors in active vision. A constraint network is a network where the nodes represent variables, or constraints, and the arcs represent the relationships between the output variables and the input variables of the constraints. In the displacement errors problem, the tolerance of the displacement errors and the translational and orientational errors of robot manipulators have interval values while the sensor motion has real values. Constraint propagation is developed to propagate the tolerance of displacement errors in the hierarchical interval constraint network in order to find the feasible robot motion. © 2002 Wiley Periodicals, Inc.