974 research outputs found
Global Finite-Time Attitude Tracking via Quaternion Feedback
This paper addresses the attitude tracking of a rigid body using a quaternion
description. Global finite-time attitude controllers are designed with three
types of measurements, namely, full states, attitude plus constant-biased
angular velocity, and attitude only. In all three scenarios hybrid control
techniques are utilized to overcome the well-known topological constraint on
the attitude manifold, while coupled nonsmooth feedback inputs are designed via
homogeneous theory to achieve finite-time stability. Specially, a finite-time
bias observer is derived in the second scenario and a quaternion filter is
constructed to provide damping in the absence of velocity feedback. The
proposed methods ensure bounded control torques a priori and, in particular,
include several existing attitude controllers as special cases.Comment: 14 pages, 5 figures, to appear in Systems and Control Letter
Global Finite-Time Attitude Consensus of Leader-Following Spacecraft Systems Based on Distributed Observers
This paper addresses the leader-following attitude consensus problem for a
group of spacecraft when at least one follower can access the leader's attitude
and velocity relative to the inertial space. A nonlinear distributed observer
is designed to estimate the leader's states for each follower. The observer
possesses one important and novel feature of keeping attitude and angular
velocity estimation errors on second-order sliding modes, and thus provides
finite-time convergent estimates for each follower. Further, quaternion-based
hybrid homogeneous controllers recently developed for single spacecraft are
extended and then applied, by establishing a separation principle with the
proposed observer, to track the leader's attitude motion. As a result, global
finite-time attitude consensus is achieved on the entire attitude manifold,
with either full-state measurements or attitude-only measurements, as long as
the network topology among the followers is undirected and connected. Numerical
simulations are presented to demonstrate the performance of the proposed
methods.Comment: 13 pages, 12 figure
Construction of Synergistic Potential Functions on SO(3) with Application to Velocity-Free Hybrid Attitude Stabilization
We propose a systematic and comprehensive procedure for the construction of
synergistic potential functions, which are instrumental in hybrid control
design on SO(3). A new map via angular warping on SO(3) is introduced for the
construction of such a family of potential functions allowing an explicit
determination of the critical points and the synergistic gap. Some optimization
results on the synergistic gap are also provided. The proposed synergistic
potential functions are used for the design of a global velocity-free hybrid
attitude stabilization scheme relying solely on inertial vector measurements.
Comparative simulation results between the proposed global hybrid control
scheme and the almost global smooth control scheme have been carried out
A Central Synergistic Hybrid Approach for Global Exponential Stabilization on SO(3)
We propose a new central synergistic hybrid approach for global exponential
stabilization on the Special Orthogonal group SO(3). We introduce a new
switching concept relying on a central family of (possibly) non-differentiable
potential functions that enjoy (as well as their gradients) the following
properties: 1) being quadratic with respect to the Euclidean attitude distance,
and 2) being synergistic with respect to the gradient's singular and/or
critical points. The proposed approach is used to solve the attitude tracking
problem, leading to global exponential stability results
Inertial Measurements Based Velocity-free Attitude Stabilization
The existing attitude controllers (without angular velocity measurements)
involve explicitly the orientation (\textit{e.g.,} the unit-quaternion) in the
feedback. Unfortunately, there does not exist any sensor that directly measures
the orientation of a rigid body, and hence, the attitude must be reconstructed
using a set of inertial vector measurements as well as the angular velocity
(which is assumed to be unavailable in velocity-free control schemes). To
overcome this \textit{circular reasoning}-like problem, we propose a
velocity-free attitude stabilization control scheme relying solely on inertial
vector measurements. The originality of this control strategy stems from the
fact that the reconstruction of the attitude as well as the angular velocity
measurements are not required at all. Moreover, as a byproduct of our design
approach, the proposed controller does not lead to the unwinding phenomenon
encountered in unit-quaternion based attitude controllers.Comment: Submitted for Journal publication on December 18, 2011. Partial and
preliminary results related to this work have been presented in ACC-201
On the Design of Globally Exponentially Stable Hybrid Attitude and Gyro-bias Observers
This paper presents hybrid attitude and gyro-bias observers designed directly
on the Special Orthogonal group SO(3). The proposed hybrid observers, enjoying
global exponential stability, rely on a hysteresis-based switching between
different configurations derived from a set of potential functions on SO(3).
Different sets of potential functions have been designed via an appropriate
angular warping transformation applied to some smooth and non-smooth potential
functions on SO(3). We show that the proposed hybrid observers can be expressed
solely in terms of inertial vector measurements and biased angular velocity
readings. Simulation results are given to illustrate the effectiveness of the
proposed attitude estimation approach
Robust Collaborative Object Transportation Using Multiple MAVs
Collaborative object transportation using multiple Micro Aerial Vehicles
(MAVs) with limited communication is a challenging problem. In this paper we
address the problem of multiple MAVs mechanically coupled to a bulky object for
transportation purposes without explicit communication between agents. The
apparent physical properties of each agent are reshaped to achieve robustly
stable transportation. Parametric uncertainties and unmodeled dynamics of each
agent are quantified and techniques from robust control theory are employed to
choose the physical parameters of each agent to guarantee stability. Extensive
simulation analysis and experimental results show that the proposed method
guarantees stability in worst case scenarios
Sliding Motions on SO(3), Sliding Subgroups
We propose a sliding surface for systems on the Lie group . The sliding surface is shown to be a Lie subgroup. The
reduced-order dynamics along the sliding subgroup have an almost globally
asymptotically stable equilibrium. The sliding surface is used to design a
sliding-mode controller for the attitude control of rigid bodies. The
closed-loop system is robust against matched disturbances and does not exhibit
the undesired unwinding phenomenon.Comment: Submitted to the 58th Conference on Decision and Control - Nice,
Franc
Feedback Particle Filter on Matrix Lie Groups
This paper is concerned with the problem of continuous-time nonlinear
filtering for stochastic processes on a compact and connected matrix Lie group
without boundary, e.g. SO(n) and SE(n), in the presence of real-valued
observations. This problem is important to numerous applications in attitude
estimation, visual tracking and robotic localization. The main contribution of
this paper is to derive the feedback particle filter (FPF) algorithm for this
problem. In its general form, the FPF provides a coordinate-free description of
the filter that furthermore satisfies the geometric constraints of the
manifold. The particle dynamics are encapsulated in a Stratonovich stochastic
differential equation that preserves the feedback structure of the original
Euclidean FPF. Specific examples for SO(2) and SO(3) are provided to help
illustrate the filter using the phase and the quaternion coordinates,
respectively.Comment: 7 pages, submitted for 2016 American Control Conferenc
Sliding on Manifolds: Geometric Attitude Control with Quaternions
This work proposes a quaternion-based sliding variable that describes
exponentially convergent error dynamics for any forward complete desired
attitude trajectory. The proposed sliding variable directly operates on the
non-Euclidean space formed by quaternions and explicitly handles the double
covering property to enable global attitude tracking when used in feedback.
In-depth analysis of the sliding variable is provided and compared to others in
the literature. Several feedback controllers including nonlinear PD, robust,
and adaptive sliding control are then derived. Simulation results of a rigid
body with uncertain dynamics demonstrate the effectiveness and superiority of
the approach
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