2,145 research outputs found
Global Exponential Attitude Tracking Controls on SO(3)
This paper presents four types of tracking control systems for the attitude
dynamics of a rigid body. First, a smooth control system is constructed to
track a given desired attitude trajectory, while guaranteeing almost
semi-global exponential stability. It is extended to achieve global exponential
stability by using a hybrid control scheme based on multiple configuration
error functions. They are further extended to obtain robustness with respect to
a fixed disturbance using an integral term. The resulting robust, global
exponential stability for attitude tracking is the unique contribution of this
paper, and these are developed directly on the special orthogonal group to
avoid singularities of local coordinates, or ambiguities associated with
quaternions. The desirable features are illustrated by numerical examples
Robust global exponential stabilization on the n-dimensional sphere with applications to trajectory tracking for quadrotors
In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by Sn. This hybrid controller is induced by a “synergistic” collection of potential functions on Sn. We propose a particular construction of this class of functions that generates flows along geodesics of the sphere, providing convergence to the desired reference with minimal path length. We show that the proposed strategy is suitable to the exponential stabilization of a quadrotor vehicle
Global Stabilization of Antipodal Points on n-Sphere with Application to Attitude Tracking
Existing approaches to robust global asymptotic stabilization of a pair of
antipodal points on unit -sphere typically involve the
non-centrally synergistic hybrid controllers for attitude tracking on unit
quaternion space. However, when switching faults occur due to parameter errors,
the non-centrally synergistic property can lead to the unwinding problem or in
some cases, destabilize the desired set. In this work, a hybrid controller is
first proposed based on a novel centrally synergistic family of potential
functions on , which is generated from a basic potential function
through angular warping. The synergistic parameter can be explicitly expressed
if the warping angle has a positive lower bound at the undesired critical
points of the family. Next, the proposed approach induces a new
quaternion-based controller for global attitude tracking. It has three
advantageous features over existing synergistic designs: 1) it is consistent,
i.e., free from the ambiguity of unit quaternion representation; 2) it is
switching-fault-tolerant, i.e., the desired closed-loop equilibria remain
asymptotically stable even when the switching mechanism does not work; 3) it
relaxes the assumption on the parameter of the basic potential function in
literature. Comprehensive simulation confirms the high robustness of the
proposed centrally synergistic approach compared with existing non-centrally
synergistic approaches.Comment: 8 page
Synergistic Potential Functions from Single Modified Trace Function on SO(3)
This paper is about the construction of a family of centrally synergistic
potential functions from a single modified trace function on SO(3). First, we
demonstrate that it is possible to complete the construction through angular
warping with multiple directions, particularly effective in the unresolved
cases in the literature. Second, it can be shown that for each potential
function in the family, there exists a subset of the family such that the
synergistic gap is positive at the unwanted critical points. This allows the
switching condition to be checked within the selected subsets while
implementing synergistic hybrid control. Furthermore, the positive lower bound
of synergistic gap is explicitly expressed by selecting a traditional warping
angle function. Finally, we apply the proposed synergistic potential functions
to obtain robust global attitude tracking.Comment: Extended version of the paper accepted for publication in Automatic
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