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

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

/pdf/nonlinear-complementary-filters-on-the-special-orthogonal-ysp0zzaoar.pdf

Nonlinear Complementary Filters on the Special Orthogonal Group

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

/pdf/handbook-of-marine-craft-hydrodynamics-and-motion-control-2qu7epb0pt.pdf

Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

/pdf/using-momentum-conservation-to-control-kinematically-erur9d59b5.pdf

Using Momentum Conservation to Control Kinematically Redundant Manipulators

A system for testing a control system (2) in a vessel (4), in which the control system (2) is arranged to control and monitor the vessel (4), comprising the following features: one or more sensors (8) on board the vessel (4) to send one or more sensor signals (7) over a signal line (12) to the control system (2); command input devices (10) on board the vessel (4) arranged to send one or more of desired position, course, velocity, (9) etc. over a command signal line (11) to the control system (2); an algorithm (31) in the control system (2) for the computation of control signals (13) to the vessel actuators (3) on basis of the sensor data (7), the command signals (9), for sending of the control signals (13) over a signal line (14) to the actuators (3); one or more communication lines (6) for sending of one or more simulated signals (7’) and/or simulated command signals (9’) from a remote test laboratory (40) to the control system (2); a simulator (30) including and algorithm (32) for the simulation of the new dynamic state (7’) of a vessel model (4’) based on a previous state (7, 7’), the control signals (13, 13’), and the dynamic parameters (5) of the vessel (4); where the communication line (6) is arranged for sending back the new simulated state of the vessel model (4’) in the form of simulated sensor signals (7’) to the control system (2), for continued computation in the control system (2) on basis of the real and/or simulated sensor signals (7, 7’) or real and/or simulated command signals (9, 9’), of the control signals (13) to achieve at least one of desired position, course, velocity etc.; and where the communication line (6) is arranged for sending the response from the control system (2) in the form of control signals (13) and control signals (13’) to the remote test laboratory (40).

Apparatus and method for testing a control system of a marine vessel

Thruster Modelling and Energy-Optimization for an Autonomous Underwater Vehicle

Passive Output Feedback and Observer Based Autopilots: A Comparative Study

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2002/data/content/01901/1901.pdf

Olav Egeland

Papers

Using Momentum Conservation to Control Kinematically Redundant Manipulators

Apparatus and method for testing a control system of a marine vessel

Thruster Modelling and Energy-Optimization for an Autonomous Underwater Vehicle

Passive Output Feedback and Observer Based Autopilots: A Comparative Study

Modeling and control of a towed seismic streamer