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.     

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.     

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.     

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.     

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     

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.     

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     

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.     

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.     

Hybrid adaptive control for robot manipulators

A hybrid adaptive control scheme is proposed for robot manipulators. Unmodelled dynamics have been considered in the robot model. The standard RLS algorithm has been modified to take into account these unmodelled dynamics. Global stability of the system is ensured.     

Observer based adaptive neuro-sliding mode control for MIMO nonlinear systems

In this paper, a stable adaptive neural sliding mode controller is developed for a class of multivariable uncertain nonlinear systems. For these systems not all state variables are available for measurements. By designing a state observer, adaptive neural systems, which are used to model unknown functions, can be constructed using the state estimations. Based on Lyapunov stability theorem, the proposed adaptive neural control system can guarantee the stability of the whole closed loop system and obtain good tracking performances. Adaptive laws are proposed to adjust the free parameters of the neural models. Simulation results illustrate the design procedure and demonstrate the tracking performances of the proposed controller.     

Globally robust nonlinear PID controllers for robot manipulators with an uncertain Jacobian matrix

Based on a continuous piecewise-differentiable increasing functions vector, a class of robust nonlinear PID (RN-PID) controllers is proposed for setpoint control with uncertain Jacobian matrix. Globally asymptotic stability is guaranteed and only position and joint velocity measurements are required. And stability problem arising from integral action and integrator windup, are consequently resolved. Furthemnore, RN-PID controllers can be of effective alternative for anti-integrator-wind-up,the control performance would not be very bad in the presence of rough parameter tuning.     

Adaptive Jacobian position/force tracking control of free-flying manipulators

This paper solves the problem of position/force tracking control of a free-flying space manipulator with uncertain kinematics and dynamics. A free-flying manipulator interacting with an uncertain compliant surface is considered. To cope with the uncertainties arising from free-flyer’s kinematics, dynamics and surface stiffness and position, an adaptive Jacobian controller is devised. The convergence of the force and position tracking errors is proved based on Lyapunov stability analysis. Numerical simulation is presented to show the performance of the controller.     

Decentralized adaptive fuzzy control of robot manipulators

This paper develops a decentralized adaptive fuzzy control scheme for robot manipulators via a combination of genetic algorithm and gradient method. The controller for each link consists of a feedforward fuzzy torque-computing system and a feedback fuzzy PD system. The feedforward fuzzy system is trained and optimized off-line by an improved genetic algorithm, that is to say, not only the parameters but also the structure of the fuzzy system are self-organized. Because genetic algorithm can operate successfully without the system model, no exact inverse dynamics of the robot system are required. The feedback fuzzy PD system, on the other hand, is tuned on-line using gradient method. In this way, the proportional and derivative gains are adjusted properly to keep the closed-loop system stable. The proposed controller has the following merits: (1) it needs no exact dynamics of the robot systems and the computation is time-saving because of the simple structure of the fuzzy systems; and (2) the controller is insensitive to various dynamics and payload uncertainties in robot systems. These are demonstrated by analyses of the computational complexity and various computer simulations.     

On the robust control of robot manipulators

A simple robust nonlinear control law for n-link robot manipulators is derived using the Lyapunov-based theory of guaranteed stability of uncertain systems. The novelty of this result lies in the fact that the uncertainty bounds needed to derive the control law and to prove uniform ultimate boundedness of the tracking error depend only on the inertial parameters of the robot. In previous results of this type, the uncertainty bounds have depended not only on the inertia parameters but also on the reference trajectory and on the manipulator state vector. The presented result also removes previous assumptions regarding closeness in norm of the computed inertia matrix to the actual inertial matrix. The design used thus provides the simplest such robust design available to date     

Perfomance-based adaptive tracking control of robot manipulators

This article presents two new adaptive schemes for the motion control of robot manipulators. The proposed controllers are very general and computationally efficient because they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies are globally stable in the presence of bounded disturbances, and that in the absence of disturbances the ultimate bound on the size of the tracking errors can be made arbitrarily small. Computer simulation results are given for a PUMA 560 manipulator, and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers. Experimental results are presented for an IMI Zebra Zero manipulator and confirm that the control schemes provide a simple and effective means of obtaining high-performance trajectory tracking. © 1995 John Wiley & Sons, Inc.     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.