Hybrid Attitude Control and Estimation On SO(3)

This thesis presents a general framework for hybrid attitude control and estimation design on the Special Orthogonal group SO(3). First, the attitude stabilization problem on SO(3) is considered. It is shown that, using a min-switch hybrid control strategy designed from a family of potential functions on SO(3), global exponential stabilization on SO(3) can be achieved when this family of potential functions satisfies certain properties. Then, a systematic methodology to construct these potential functions is developed. The proposed hybrid control technique is applied to the attitude tracking problem for rigid body systems. A smoothing mechanism is proposed to filter out the discrete behaviour of the hybrid switching mechanism leading to control torques that are continuous. Next, the problem of attitude estimation from continuous body-frame vector measurements of known inertial directions is considered. Two hybrid attitude and gyro bias observers designed directly on SO(3) are proposed. The first observer uses a set of innovation terms and a switching mechanism that selects the appropriate innovation term. The second observer uses a fixed innovation term and allows the attitude state to be reset (experience discrete transition or jump) to an adequately chosen value on SO(3). Both hybrid observers guarantee global exponential stability of the zero estimation errors. Finally, in the case where the body-frame vector measurements are intermittent, an event-triggered attitude estimation scheme on SO(3) is proposed. The observer consists in integrating the continuous angular velocity during the interval of time where the vector measurements are not available, and updating the attitude state upon the arrival of the vector measurements. Both cases of synchronous and asynchronous vector measurements with possible irregular sampling periods are considered. Moreover, some modifications to the intermittent observer are developed to handle different practical issues such as discrete-time implementation, noise filtering and gyro bias compensation

Geometric State Observers for Autonomous Navigation Systems

The development of reliable state estimation algorithms for autonomous navigation systems is of great interest in the control and robotics communities. This thesis studies the state estimation problem for autonomous navigation systems. The first part of this thesis is devoted to the pose estimation on the Special Euclidean group \SE(3). A generic globally exponentially stable hybrid estimation scheme for pose (orientation and position) and velocity-bias estimation on \SE(3)\times \mathbb{R}^6 is proposed. Moreover, an explicit hybrid observer, using inertial and landmark position measurements, is provided. The second part of this thesis is devoted to the problem of simultaneous estimation of the attitude, position and linear velocity for inertial navigation systems (INSs). Three different types of nonlinear observers are developed to handle the following cases: continuous landmark position measurements, intermittent landmark position measurements and continuous stereo bearing measurements. First, a class of nonlinear geometric hybrid observers on the Lie group \SE_2(3), with GES guarantees, using continuous IMU and landmark position measurements is developed. Then, a class of nonlinear state observers, with strong stability guarantees, using intermittent landmark measurements is proposed. Finally, a class of state observers, with strong stability guarantees, directly incorporating body-frame stereo-bearing measurements, is proposed

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Nonlinear Attitude Estimation Using Intermittent and Multi-Rate Vector Measurements

This paper considers the problem of nonlinear attitude estimation for a rigid body system using intermittent and multi-rate inertial vector measurements as well as continuous (high-rate) angular velocity measurements. Two types of hybrid attitude observers on Lie group $SO(3)$ are proposed. First, we propose a hybrid attitude observer where almost global asymptotic stability is guaranteed using the notion of almost global input-to-state stability on manifolds. Thereafter, this hybrid attitude observer is extended by introducing a switching mechanism to achieve global asymptotic stability. Both simulation and experimental results are presented to illustrate the performance of the proposed hybrid observers.Comment: 22 pages, 7 figures, submitted to IEEE TAC for possible publicatio

State Estimation for a Humanoid Robot

This paper introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in [1] on a quadruped platform by incorporating the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter (EKF) accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. The filter employs a sensor-based prediction model which uses inertial data from an IMU and corrects for integrated error using a kinematics-based measurement model which relies on joint encoders and a kinematic model to determine the relative position and orientation of the feet. A nonlinear observability analysis is performed on both the original and updated filters and it is concluded that the new filter significantly simplifies singular cases and improves the observability characteristics of the system. Results on simulated walking and squatting datasets demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.Comment: IROS 2014 Submission, IEEE/RSJ International Conference on Intelligent Robots and Systems (2014) 952-95

Aeronautical Engineering: A continuing bibliography, supplement 120

This bibliography contains abstracts for 297 reports, articles, and other documents introduced into the NASA scientific and technical information system in February 1980