Globally exponential continuous controller/observer for position tracking in robot manipulators with hysteretic joint friction

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.

SUMMARYIn most dynamic adaptive control simulation of robotic manipulators, the Langrange–Euler (L–E) dynamic equations are first piecewise linearized about the desired reference and then discretized and rewritten in a state space form. This makes things very complicated and it is easy to make errors. What is more is that with a different reference this work must be done again. A new simulation scheme – Backward Recursive Self-Tuning Adaptive (BRSTA) – as it will be called, is suggested in this paper for adaptive controller design of robot manipulators. A two degree of freedom robot manipulator is used to verify the scheme in the condition of highly nonlinear and highly coupled system. A one degree of freedom robot manipulator is used for comparing both the forward and backward methods. The main advantages of this scheme include that it can be used for evaluating the self-tuning adaptive control laws and provide the initial process parameters for real-time control. And it is concluded here that the Newton–Euler (N–E) dynamic equations are equally well qualified as the Langrange–Euler (L-E) equations for the simulation of self-tuning adaptive control of robot manipulators.

A new evolutionary-based algorithm is proposed to solve the robot manipulator optimal path generation problem. The following scenario is considered: given a learnt joint path describing a robot manipulator simple task in the Cartesian space, an optimal path is calculated when a different initial joint configuration is considered. The optimization problem is formulated as the minimization of both the end-effector pose error and the total joint displacement so as to ensure convergence towards the learnt path and a smooth joint motion. To solve the optimization problem an algorithm based on an evolutionary method called Differential Evolution (DE) is used. DE is a stochastic direct search optimization method based on the evolution of a candidate solution population in an iterative process of mutation, recombination, and selection. Since the algorithm does not require the use of the Jacobian matrix during the kinematic inversion, singularities problems are overcome. Results on the optimal path generation of a six degrees of freedom robot manipulator are also presented.

In the impedance control scheme in robotic manipulation applications, the interaction force can be indirectly controlled by acting on the manipulator reference position trajectory. However, the reference position depends on the environment parameters, like location and stiffness, which in practice are not exactly known. To deal with those uncertainties, this paper presents a fuzzy adaptive approach which determines the appropriate reference (target) positions to an impedance controller in order to obtain the desired force/position trajectory. Moreover, only an estimate of the environment location is necessary, and so the fuzzy adaptive controller corrects this estimated position based on the force error. The fuzzy adaptive controller is a kind of self organizing controller, which consists of a direct fuzzy controller and an adaptation mechanism, (the fuzzy inverse model) which adjusts the membership functions of the consequent parts of the direct fuzzy controller. To validate the proposed control scheme, simulation results with a two degree of freedom robot manipulator are presented where it is shown a good force/tracking performance with uncertainties on the environment location and on the stiffness value.

In the paper fuzzy logic controller for rehabilitation robot manipulator is presented. The control object is two degree of freedom robot manipulator. In this case there are two main problems. The first is, that the object is for rehabilitation process so the quality of control system is very important problem. The next problem is with the highly nonlinear dynamics of a robot manipulator. Suggest fuzzy logic control system for that reasons. The model-based Takagi-Sugeno fuzzy control strategy is applied. Described model have two inputs (error and derivation) and one output. The first part of research, was the simulation tests. For this part simulation model was prepare. The dynamic equations was used to build a model in Matlab. During this research the main problem was suitable control quality. It is very important because control quality is connected with rehabilitation process. The control algorithms enable to movement realization and obtain set position given by the physiotherapist. The tests results show that the fuzzy logic control have good control quality.

In this study, trajectory tracking control of six–degrees of freedom robotic manipulator has been performed using the proposed fractional-order adaptive integral sliding mode control scheme. The proposed method is first composed by fractional-order and adaptive integral sliding mode control to achieve the finite-time convergence, chattering-free control inputs, better tracking performance and robustness for the robotic manipulator. Furthermore, an adaptive method has been utilized to evaluate and compensate the uncertain and unknown dynamics of the system without relying on the prior knowledge of the upper bounds. To illustrate the efficiency of the proposed fractional-order adaptive integral sliding mode control method, the real-time experimental studies have been performed for the six–degrees of freedom industrial robot manipulator. The experimental outcomes strongly verified that the proposed controller gives quite well trajectory tracking response and faster convergence compared with the classical integral sliding mode control under the external payload.

This paper presents a decentralized control scheme, based on a recurrent neural identifier with a block control structure, and its application to robotics manipulators. A local joint controller is proposed for each joint, using only local angular position and velocity measurements. These very simple local joint controllers allow trajectory tracking, with reduced computations. The applicability of the proposed scheme is illustrated, via simulations, first by the applications to a two degree of freedom robotic manipulator and then to a seven degree of freedom one.

This work presents the design and the corresponding stability analysis of a model-based, joint position tracking error constrained, adaptive output feedback (OFB) controller for robot manipulators. Specifically, provided that the initial joint position tracking error starts within a predefined region, the proposed controller algorithm ensures that the joint tracking error remains inside this region and asymptotically approaches zero, despite the lack of joint velocity measurements and uncertainties associated with the system dynamics. The constraint imposed on the position tracking error term ensures predictable overshoot for the overall system and enables a predetermined transient performance. The need for the joint velocity measurements is removed via the use of a surrogate filter formulation in conjunction with the use of desired model compensation. The stability and the convergence of the closed-loop system are proved via a barrier Lyapunov function (BLF)-based argument. Extensive numerical simulations and experimental studies performed on a two-link, direct-drive robotic manipulator are provided to illustrate the feasibility and effectiveness of the proposed method.

Predictive Control Architecture for Visual Servoing of Robot Manipulators

The authors analyse the contour error dynamics in contouring control of dual‐arm robotic manipulators with holonomic constraints. With the modified dynamics of robot, the dynamics of dual‐arm robot with holonomic constraints is symetrically transformed into dynamics error problem by considering the equivalent error method. It becomes the control problem of stabilisation such that it is suitable for robust control approach to improve control performance in terms of contouring control, i.e. contour accuracy with high speed. The proposed method can deal with both analytic and non‐analytic functions of desired path in task space. The experimental results reveal that the proposed method yields excellent performance in comparison to conventional distributed control. As a result, the proposed method can lead to the development of a modified distributed control for high degree of freedom robot manipulators.

Visual servoing control of robot manipulators represents a natural option in unstructured environments and it is specially attractive when the task to achieve can be expressed directly in image coordinates. In the present work a control law is developed for trajectory tracking of three degrees of freedom robot manipulators. The main characteristic of the proposed algorithm is that it does not need any dynamic model of the system and image coordinates are employed directly for feedback, while an observer is designed for velocity estimation. To carry out 3D movements no stereoscopic vision is used. Rather, a simpler configuration employing two fixed cameras is proposed which makes unnecessary their calibration and helps avoid occlusions for most of the robots workspace. The developed theory was successfully tested in an industrial manipulator.

This paper presents a general methodology and accompanying formulation for planning kinematically smooth path trajectories for serial robot manipulators. Starting from an initial point on the path, it is required to traverse a path trajectory without halting the motion (typically due to switch from one inverse solution to another). The problem focuses on determining a starting configuration at the initial point on the path. The problem is formulated in terms of a constraint function and characterized by a system of differential-algebraic equations (DAEs) of index 2. These DAEs are solved numerically by Runge-Kutta (RK) methods while a best starting configuration is chosen using a cost-function driven optimization method. The formulation is demonstrated through a planar 3 degree of freedom robot manipulator.

This paper presents a stability analysis of nonlinear bang-bang impact control for a one degree of freedom robotic manipulator based on an analysis in L/sub 2/ space. The physical implications of sufficient stability conditions are explained in terms of sampling time, accuracy of inertia estimation, control gains, and rate of change in the Coriolis, centrifugal, and disturbance forces. The stability conditions are not stringent and are verified by simulations.

A robust controller is proposed for the accurate trajectory control of a general n degree of freedom robotic manipulator, using feedback of task space coordinates, in the presence of large perturbations of the manipulator dynamic parameters. The controller is shown to consist of two separate devices: 1) a robust compensator which makes the system insensitive to parameter perturbation and causes asymptotic regulation to occur for a certain class of reference input/disturbance signals, and 2) a stabilizing compensator which stabilizes the closed-loop system. Asymptotic stability of the closed-loop system is demonstrated, using a Lyapunov approach, for large perturbations of the plant parameters. A numerical simulation of a two degree of freedom manipulator, with a large unknown payload mass is used to demonstrate the effectiveness of the controller.

Performing tracking tasks in robotic manipulators presents many challenges for the controller design, especially in presence of external disturbances that affects the dynamical behavior of the robotic system. This paper presents the design of a Fractional-Order PID controller with the computed torque control strategy for the tracking control of a two degree of freedom robotic manipulator. The proposed technique is contrasted against the classical PID controller with the computed torque control strategy. To validate the proposed controllers, the robotic system is simulated using an MSC-ADAMS/MATLAB co-simulation model, which is employed for identification and control tasks. The proposed model is tested in presence of external disturbances in the applied torque, random noise in the feedback loop and payload variations. Obtained results show that the Fractional-Order PID controller with the computed torque control strategy has a better performance in presence of the analyzed external disturbances for tracking tasks.