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260
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 989 (4 self)
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squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best
Unit Quaternions and the Bloch Sphere
"... Abstract. The spinor representation of spin1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Blochsphere rotations to be represented as quaternionic multiplicatio ..."
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Abstract. The spinor representation of spin1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Blochsphere rotations to be represented as quaternionic
The parameterization of joint rotation with the unit quaternion
 In DICTA
, 2003
"... Abstract. Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S 3 group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation li ..."
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Cited by 3 (0 self)
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Abstract. Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S 3 group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation
Unit QuaternionBased Output Feedback for the Attitude Tracking Problem
, 2008
"... In this note, we propose a quaternionbased dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement. Our approach consists of introducing an auxiliary dynamical system whose output (which is also a unit quaternion) is used in the control law together w ..."
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Cited by 12 (1 self)
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In this note, we propose a quaternionbased dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement. Our approach consists of introducing an auxiliary dynamical system whose output (which is also a unit quaternion) is used in the control law together
Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors
, 2006
"... We present the three main mathematical constructs used to represent the attitude of a rigid body in threedimensional space. These are (1) the rotation matrix, (2) a triple of Euler angles, and (3) the unit quaternion. To these we add a fourth, the rotation vector, which has many of the benefits of b ..."
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Cited by 43 (0 self)
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We present the three main mathematical constructs used to represent the attitude of a rigid body in threedimensional space. These are (1) the rotation matrix, (2) a triple of Euler angles, and (3) the unit quaternion. To these we add a fourth, the rotation vector, which has many of the benefits
TRIANGULATION OF AIRBORNE THREELINE IMAGES USING UNIT QUATERNION
"... In this paper the unit quaternion is used as a substitute for describing the attitude of a camera to overcome the shortcomings of Euler angles on the description and interpolation of orientation, corresponding collinearity equation is then derived and linearized. At the same time the Spherical linea ..."
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In this paper the unit quaternion is used as a substitute for describing the attitude of a camera to overcome the shortcomings of Euler angles on the description and interpolation of orientation, corresponding collinearity equation is then derived and linearized. At the same time the Spherical
1Rotation Optimization on the Unit Quaternion Manifold and its Application for Robotic Grasping
"... In this paper we consider blackbox optimization of objects ’ grasp density functions relative to a gripper’s orientation. For this, we introduce MonteCarlo Tree Search on the unit quaternion manifold. Our experimental evaluation shows that our method is feasible and allows finding grasps of arbitr ..."
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In this paper we consider blackbox optimization of objects ’ grasp density functions relative to a gripper’s orientation. For this, we introduce MonteCarlo Tree Search on the unit quaternion manifold. Our experimental evaluation shows that our method is feasible and allows finding grasps
A Compact Differential Formula for the First Derivative of a Unit Quaternion Curve
, 1996
"... This paper presents a compact differential formula for the first derivative of a unit quaternion curve defined on SO(3) or S 3 . The formula provides a convenient way to compute the angular velocity of a rotating 3D solid. We demonstrate the effectiveness of this formula by deriving the differenti ..."
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Cited by 8 (3 self)
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This paper presents a compact differential formula for the first derivative of a unit quaternion curve defined on SO(3) or S 3 . The formula provides a convenient way to compute the angular velocity of a rotating 3D solid. We demonstrate the effectiveness of this formula by deriving
A General Construction Scheme for Unit Quaternion Curves with Simple High Order Derivatives
, 1995
"... This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R 3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to wellknown spline curves (such as Bezier, Hermite, and B ..."
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Cited by 70 (7 self)
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This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R 3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to wellknown spline curves (such as Bezier, Hermite
Results 1  10
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260