There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This article is the second of a two-part tutorial on visual servo control. In this tutorial, we have only considered velocity controllers. It is convenient for most of classical robot arms. However, the dynamics of the robot must of course be taken into account for high speed task, or when we deal with mobile nonholonomic or underactuated robots. As for the sensor, geometrical features coming from a classical perspective camera is considered. Features related to the image motion or coming from other vision sensors necessitate to revisit the modeling issues to select adequate visual features. Finally, fusing visual features with data coming from other sensors at the level of the control scheme will allow to address new research topics

https://hal.inria.fr/inria-00350638/document

Visual servo control. II. Advanced approaches [Tutorial]

1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

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Power Electronics Converters Applications And Design

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L2 Gain And Passivity Techniques In Nonlinear Control

In this note, we present a new continuous control mechanism that compensates for uncertainty in a class of high-order, multiple-input-multiple-output nonlinear systems. The control strategy is based on limited assumptions on the structure of the system nonlinearities. A new Lyapunov-based stability argument is employed to prove semiglobal asymptotic tracking.

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

A new method for the state of charge (SOC) estimation of lithium-ion batteries is proposed based on an inclusive equivalent circuit model in this brief. In particular, we propose to utilize the neural network to estimate the uncertainties in the battery model online. A radial basis function neural network-based nonlinear observer is then designed to estimate the battery’s SOC. Following Lyapunov stability analysis, it is proved that the SOC estimation error is ultimately bounded and the error bound can be arbitrarily small. Experimental and simulation results illustrate the performance of the proposed approach. Furthermore, we compare the SOC estimation results of the extended Kalman filter with the proposed radial basis function neural network-based nonlinear observer. The proposed approach has faster convergence speed and higher precision.

Neural Network-Based State of Charge Observer Design for Lithium-Ion Batteries

In this paper, we propose an adaptive control approach with fuzzy logic parameter tuning (AFLPT) for the energy management of electric vehicles that are using fuel cell battery hybrid systems. The controller is adaptive to different driving conditions including normal, regenerative, and overload conditions. Specifically, the power flow between the fuel cell (FC) and the Li-ion battery is controlled in real time to maintain the battery state of charge (SOC) at a desirable level while satisfying the FC dynamic constraints. For guaranteeing performance in different driving conditions, the FLPT is integrated with the adaptive controller. Moreover, theoretical properties of the designed controller are analyzed. Simulation and experiment results illustrate the effectiveness of the proposed strategy for FC-battery hybrid systems in electric vehicles.

Adaptive Fuzzy Logic Control of Fuel-Cell-Battery Hybrid Systems for Electric Vehicles

A visual servo tracking controller is developed in this paper for a monocular camera system mounted on an underactuated wheeled mobile robot (WMR) subject to nonholonomic motion constraints (i.e., the camera-in-hand problem). A prerecorded image sequence (e.g., a video) of three target points is used to define a desired trajectory for the WMR. By comparing the target points from a stationary reference image with the corresponding target points in the live image and the prerecorded sequence of images, projective geometric relationships are exploited to construct Euclidean homographies. The information obtained by decomposing the Euclidean homography is used to develop a kinematic controller. A Lyapunov-based analysis is used to develop an adaptive update law to actively compensate for the lack of depth information required for the translation error system. Experimental results are provided to demonstrate the control design.

/pdf/homography-based-visual-servo-tracking-control-of-a-wheeled-4at6rlqz4w.pdf

Homography-based visual servo tracking control of a wheeled mobile robot

In this paper, a feedback linearization controller is proposed for the van compressor in the air supply system of a proton exchange membrane fuel cell. The control goal is to avoid oxygen starvation and reduce power consumption by tracking an optimal reference oxygen excess ratio. Specifically, an improved control-oriented third-order model of the air supply system is proposed with the model identification of the air compressor. The optimal reference oxygen excess ratio is obtained from experiments to maintain a maximum net power. Based on the air supply system model, a nonlinear controller is designed to track the optimal oxygen excess ratio using feedback linearization. Lyapunov-based technique is utilized to analyze the stability of the closed-loop system. Effectiveness of the proposed approach is illustrated by experimental results.

Jian Chen

Papers

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

Neural Network-Based State of Charge Observer Design for Lithium-Ion Batteries

Adaptive Fuzzy Logic Control of Fuel-Cell-Battery Hybrid Systems for Electric Vehicles

Homography-based visual servo tracking control of a wheeled mobile robot

Optimal Oxygen Excess Ratio Control for PEM Fuel Cells