Related papers: Special Orthogonal Group SO(3), Euler Angles, Angl…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
This paper reviews the attitude control problems for rigid-body systems, starting from the attitude representation for rigid body kinematics. Highly redundant rotation matrix defines the attitude orientation globally and uniquely by 9…
Successful control of a rigid-body rotating in three dimensional space requires accurate estimation of its attitude. The attitude dynamics are highly nonlinear and are posed on the Special Orthogonal Group $SO(3)$. In addition, measurements…
This paper provides new results for a tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and…
This paper proposes two novel nonlinear attitude filters evolved directly on the Special Orthogonal Group SO(3) able to ensure prescribed measures of transient and steady-state performance. The tracking performance of the normalized…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
This paper provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid…
Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of…
This paper formulates the pose estimation problem as nonlinear stochastic filter kinematics evolved directly on the Special Euclidean Group SE(3). Proposed filter guarantees that the errors present in position and Rodriguez vector estimates…
We derive explicitly the structural properties of the $p$-adic special orthogonal groups in dimension three, for all primes $p$, and, along the way, the two-dimensional case. In particular, starting from the unique definite quadratic form…
This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and…
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…
This paper addresses the distributed attitude synchronization problem for a network of rigid-body systems on the special orthogonal group SO(3). Each agent measures, in its body frame, its own angular velocity and a set of vectors whose…
This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the…
Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…
An arbitrary rigid transformation in $\mathbf{SE}(3)$ can be separated into two parts, namely, a translation and a rigid rotation. This technical report reviews, under a unifying viewpoint, three common alternatives to representing the…
We propose a 12-dimensional, global, continuous, and exponentially convergent observer for gyro bias and attitude of a rigid body. Any attitude observer developed on the special orthogonal group suffers from the topological restriction that…
The general 4D rotation matrix is specialised to the general 3D rotation matrix by equating its leftmost top element (a00) to 1. Its associate matrix of products of the left-hand and right-hand quaternion components is specialised…
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…
This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the…