Estimation Of Jacobian Matrix Research Articles

A visual servo reinforcement learning control of uncalibrated manipulators with multi-channel gain decision

A technology based on Kalman filtering method combined with multi-channel gain training reinforcement learning for uncalibrated camera visual servo tasks is proposed in this paper. First, a dynamic system with state variables formed from the elements of the image Jacobian matrix is constructed to describe the mapping relationship between two-dimensional images and three-dimensional poses. Kalman filter is used to estimate the state variables of the constructed system online. Next, the Jacobian matrix estimation and depth determination strategy gradient (DDPG) methods are combined to jointly train multi-channel gains by setting a reasonable segmented reward and punishment mechanism. Through training, a more effective gain decision can be obtained. The robustness of Kalman filtering to interference to a certain extent reduces the precise dependence of reinforcement learning models, thereby achieving higher robustness in intelligent visual servo control. Finally, the effectiveness and advantages of the Kalman-DDPG method have been demonstrated through simulation comparison and six-degree-of-freedom (DOF) uncalibrated manipulator physical experiments.

Improved Jacobian matrix estimation applied to snake robots.

Two manipulator Jacobian matrix estimators for constrained planar snake robots are developed and tested, which enables the implementation of Jacobian-based obstacle-aided locomotion (OAL) control schemes. These schemes use obstacles in the robot's vicinity to obtain propulsion. The devised estimators infer manipulator Jacobians for constrained planar snake robots in situations where the positions and number of surrounding obstacle constraints might change or are not precisely known. The first proposed estimator is an adaptation of contemporary research in soft robots and builds on convex optimization. The second estimator builds on the unscented Kalman filter. By simulations, we evaluate and compare the two devised algorithms in terms of their statistical performance, execution times, and robustness to measurement noise. We find that both algorithms lead to Jacobian matrix estimates that are similarly useful to predict end-effector movements. However, the unscented filter approach requires significantly lower computing resources and is not poised by convergence issues displayed by the convex optimization-based method. We foresee that the estimators may have use in other fields of research, such as soft robotics and visual servoing. The estimators may also be adapted for use in general non-planar snake robots.

A Visual Servo Control Method for Tomato Cluster-Picking Manipulators Based on a T-S Fuzzy Neural Network

HighlightsA T-S fuzzy neural network was applied to the visual servo control system of a tomato picking manipulator.The T-S fuzzy neural network structure was designed, and collected data were used to train the neural network model.A visual servo control system for the picking manipulator based on the neural network was designed and tested.The T-S fuzzy neural network was superior to a BP neural network in visual servo control of the picking manipulator.Abstract. To reduce the computational load of image Jacobian matrix estimation and to avoid the appearance of singularity of a Jacobian matrix in the visual servo control of a picking manipulator, a T-S fuzzy neural network algorithm is proposed to replace the image Jacobian matrix. This better fits the hand-eye relationship by combining the knowledge structure of fuzzy reasoning with the self-learning ability of a neural network. The T-S fuzzy neural network was trained and tested by collecting the variation data of image features and joint angles; after training, the T-S fuzzy neural network was used to predict the joint angles of the picking manipulator. Simulation results show that the square sum of training errors and testing errors were 0.017 and 0.032, respectively, after training the T-S fuzzy neural network. A T-S fuzzy neural network controller was applied to the visual servo system of the picking robot, and the test results show that the average difference between the end-effector and the ultimate target location of the visual servo system based on the T-S fuzzy neural network controller was 0.0037 m, which was 79.44% less than that of the visual servo system based on a BP neural network. The final average error of image features was between 0.52 and 3.25 pixels, which was 74.932% less than that of the visual servo system based on the BP neural network. Keywords: Picking manipulator, Tomato clusters, T-S fuzzy neural network, Visual servoing.

Compensated model-free adaptive tracking control scheme for autonomous underwater vehicles via extended state observer

This paper investigates the problem of precise trajectory tracking control of an autonomous underwater vehicle (AUV) under parameter perturbations and external disturbances. To design a data-driven control scheme with high tracking accuracy and strong robustness, a compensated model-free adaptive control (MFAC) scheme is proposed by combining an extended state observer (ESO). Specifically, a data-driven structure-improved linear ESO (SLESO) is derived to online estimate the model approximation error generated by pseudo Jacobian matrix estimation in the typical MFAC scheme. Another problem of the typical MFAC is that it cannot be directly applied to robotic systems with rotation in the inertial frame. To tackle this issue, a two-loop controller architecture is used to design the proposed SLESO-MFAC scheme. In addition, the structure of the mathematical model of AUVs and force analysis are used in MFAC design for the first time, thus providing a straightforward initial value setting method with explicit physical interpretation and helping to judge if the assumptions in the MFAC scheme can be satisfied. Furthermore, the stability analysis of the designed control system is given. Finally, the robustness and effectiveness of the proposed SLESO-MFAC scheme are substantiated via simulations and comparisons using a realistic dynamic model of the Falcon AUV.

Unscented Particle Filter for Online Total Image Jacobian Matrix Estimation in Robot Visual Servoing

The main purpose of visual servoing is to control the motion of a robot system based on visual information provided by one or more cameras. It is an important research topic in the robotics community. In uncalibrated visual servoing, the image Jacobian matrix estimation is of great importance to the success of visual servoing control. This paper addresses the online estimation of the total Jacobian matrix for robot visual servoing using the unscented particle filter. We first give the definition of the total Jacobian matrix and formulate the total Jacobian matrix estimation problem into Bayesian filtering framework. Then, we propose to estimate the total Jacobian matrix using the unscented particle filter. Each particle is propagated and updated using the unscented Kalman filter equations. Such an update can make full use of the image feature measurements and consequently generate more accurate estimation results. The simulation results on a 2DOF robot visual servoing platform show that the proposed method provides accurate and reliable performance in the object tracking task.

Measurement-Based Estimation of the Power Flow Jacobian Matrix

In this paper, we propose a measurement-based method to compute the power flow Jacobian matrix, from which we can infer pertinent information about the system topology in near real-time. A salient feature of our approach is that it readily adapts to changes in system operating point and topology; this is desirable as it provides power system operators with a way to update, as the system evolves, the models used in many reliability analysis tools. The method uses high-speed synchronized voltage and current phasor data collected from phasor measurement units to estimate entries of the Jacobian matrix through linear total least-squares (TLS) estimation. In addition to centralized TLS-based algorithms, we provide distributed alternatives aimed at reducing computational burden. Through numerical case studies, we illustrate the effectiveness of our proposed Jacobian-matrix estimation approach as compared with the conventional model-based one.

Image Jacobian Matrix Estimation Based on Online Support Vector Regression

Research into robotics visual servoing is an important area in the field of robotics. It has proven difficult to achieve successful results for machine vision and robotics in unstructured environments without using any a priori camera or kinematic models. In uncalibrated visual servoing, image Jacobian matrix estimation methods can be divided into two groups: the online method and the offline method. The offline method is not appropriate for most natural environments. The online method is robust but rough. Moreover, if the images feature configuration changes, it needs to restart the approximating procedure. A novel approach based on an online support vector regression (OL-SVR) algorithm is proposed which overcomes the drawbacks and combines the virtues just mentioned.

Unscented Kalman filter for on-line estimation of Jacobian matrix

In image based robot visual servo system,image Jacobian matrix is commonly used for calibration.Using on-line image Jacobian matrix estimation method,the complex system calibration can be avoided without knowing the accurate system models.In this paper,the author proposed to use the Unscented Kalman Filter(UKF) for on-line estimation of total Jacobian matrix for the sake of improving the tracking accuracy of the robots which is tracking a moving object.In order to evaluate the performance,three algorithms using Kalman Filter(KF),Particle Filter(PF),and UKF were used for total Jocobian matrix estimation in a 2-Degree Of Freedom(DOF) robot visual servo platform.The experimental results show that the UKF algorithm outperforms the other two in accuracy while its time cost is very much close to the KF algorithm.

Visual servoing of redundant manipulator with Jacobian matrix estimation using self-organizing map

Vision based redundant manipulator control with a neural network based learning strategy is discussed in this paper. The manipulator is visually controlled with stereo vision in an eye-to-hand configuration. A novel Kohonen’s self-organizing map (KSOM) based visual servoing scheme has been proposed for a redundant manipulator with 7 degrees of freedom (DOF). The inverse kinematic relationship of the manipulator is learned using a Kohonen’s self-organizing map. This learned map is shown to be an approximate estimate of the inverse Jacobian, which can then be used in conjunction with the proportional controller to achieve closed loop servoing in real-time. It is shown through Lyapunov stability analysis that the proposed learning based servoing scheme ensures global stability. A generalized weight update law is proposed for KSOM based inverse kinematic control, to resolve the redundancy during the learning phase. Unlike the existing visual servoing schemes, the proposed KSOM based scheme eliminates the computation of the pseudo-inverse of the Jacobian matrix in real-time. This makes the proposed algorithm computationally more efficient. The proposed scheme has been implemented on a 7 DOF PowerCube™ robot manipulator with visual feedback from two cameras.

Computing a sparse Jacobian matrix by rows and columns

Efficient estimation of large sparse Jacobian matrices has been studied extensively in the last couple of years. It has been observed that the estimation of Jacobian matrix can be posed as a graph coloring problem. Elements of the matrix are estimated by taking divided difference in several directions corresponding to a group of structurally independent columns. Another possibility is to obtain the nonzero elements by means of the so called Automatic differentiation, which gives the estimates free of truncation error that one encounters in a divided difference scheme. In this paper we show that it is possible to exploit sparsity both in columns and rows by employing the forward and the reverse mode of Automatic differentiation. A graph-theoretic characterization of the problem is given.