A comparative study of three methods for robot kinematics

Aspragathos, Nikos Α.; Dimitros, J.K.

doi:10.1109/3477.662755

Cited by 118 publications

(72 citation statements)

References 11 publications

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“…One set of such standard rotations is given by the Tait-Bryan rotations, i.e., the Yaw, Pitch and Roll angles. The representation through homogenous transformation matrices and especially the use of Euler angles for representing orientations has some serious disadvantages (Aspragathos and Dimitros 1998;Wang 1999;Klein Breteler and Meulenbroek 2006): -Singularities: Euler angles form a chart with the special orthogonal group of rotations in three dimensional space. This chart is mostly smooth, but there are singularities:…”

Section: Dual Quaternion Mmcsmentioning

confidence: 99%

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Universally manipulable body models—dual quaternion representations in layered and dynamic MMCs

Schilling

2011

Auton Robot

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Surprisingly complex tasks can be solved using a behaviour-based, reactive control system, i.e., a system that operates without an explicit internal representation of the environment and the own body. Nevertheless, application of internal representations has gained interest in recent years because such internal representations can be used to solve problems of perception and motor control (sensor fusion, inverse modeling) and may in addition be applied to higher cognitive functions as are the ability to plan ahead. To endow such a system with the ability to find new behavioural solutions to a given problem in a broad range of possibilities, the internal representation must be universally manipulable, i.e. the model should be able to simulate all movements that are physically possible for the body given. Using recurrent neural networks, models showing this faculty have been proposed being based on the principle of mean of multiple computation (MMC). The extension of this approach to three dimensions requires the introduction of a joint angle representation which allows for computation of mean values. Here we use dual quaternions that are singularity-free and unambiguous which allow for shortest path interpolation. In addition, it has been shown that dual quaternions are the most efficient and most compact form for representing rigid transformations. The model can easily be adapted to bodies of

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Section: Dual Quaternion Mmcsmentioning

confidence: 99%

“…Therefore, there is a high degree of unnecessary redundancy. In addition, the concatenation of two transformations becomes overly expensive (Funda and Paul 1990;Aspragathos and Dimitros 1998).…”

Section: Dual Quaternion Mmcsmentioning

confidence: 99%

Universally manipulable body models—dual quaternion representations in layered and dynamic MMCs

Schilling

2011

Auton Robot

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“…More recently similar studies have been done in research fields of robotics and graphical sciences. [19][20][21] They showed a clear advantage for geometric algebra. However, in our case we must first construct a nonrotated virtual bond vector i 0 and this results in additional operations.…”

Section: ͑31͒mentioning

confidence: 99%

Application of geometric algebra for the description of polymer conformations

Chys

2008

The Journal of Chemical Physics

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In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length (l), valence angle (theta), and rotation angle (phi) of each of the preceding bonds in the chain. Hence, the set of geometrical parameters {l(i),theta(i),phi(i)} yields all the position coordinates p(i) of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built.

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“…They have been successfully applied to inertial navigation [1], rigid body control [2], [3], [4], [5], [6], [7], spacecraft formation flying [8], inverse kinematic analysis [9], computer vision [10], [11] and animation [12]. It has been argued that dual quaternions are the most compact and efficient way to simultaneously express the translation and rotation of robotic kinematic chains [13], [14]. Moreover, it has been shown that combined position and attitude control laws based on dual quaternions automatically take into account the natural coupling between the rotational and translational motion [5], [6].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous position and attitude control without linear and angular velocity feedback using dual quaternions

Filipe

Tsiotras

2013

2013 American Control Conference

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In this paper, we suggest a new representation for the combined translational and rotational dynamic equations of motion of a rigid body in terms of dual quaternions. We show that with this representation it is relatively straightforward to extend existing attitude controllers based on quaternions to combined position and attitude controllers based on dual quaternions. We show this by developing setpoint nonlinear controllers for the position and attitude of a rigid body with and without linear and angular velocity feedback based on existing attitude-only controllers with and without angular velocity feedback. The combined position and attitude velocity-free controller exploits the passivity of the rigid body dynamics and can be used when no linear and angular velocity measurements are available. I. INTRODUCTIONDual quaternions are built on, and are an extension of, classical quaternions. They provide a compact way to represent not only the attitude but also the position of a rigid body. They have been successfully applied to inertial navigation [1], rigid body control [2], [3], [4], [5], [6], [7], spacecraft formation flying [8], inverse kinematic analysis [9], computer vision [10], [11] and animation [12]. It has been argued that dual quaternions are the most compact and efficient way to simultaneously express the translation and rotation of robotic kinematic chains [13], [14]. Moreover, it has been shown that combined position and attitude control laws based on dual quaternions automatically take into account the natural coupling between the rotational and translational motion [5], [6]. Additionally, dual quaternions allow combined position and attitude control laws to be written compactly as a single control law.However, the property that makes dual quaternions most attractive and useful is that, as it will be shown, the combined translational and rotational kinematic and dynamic equations of motion written in terms of dual quaternions have the same form as the translational kinematic and dynamic equations of motion written in terms of quaternions.In this paper, we demonstrate, and take advantage of, this analogy between quaternions and dual quaternions to develop a combined position and attitude setpoint controller that does not require linear and angular velocity measurements from an existing attitude setpoint controller that does not require angular velocity measurements [15], [16].

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A comparative study of three methods for robot kinematics

Cited by 118 publications

References 11 publications

Universally manipulable body models—dual quaternion representations in layered and dynamic MMCs

Universally manipulable body models—dual quaternion representations in layered and dynamic MMCs

Application of geometric algebra for the description of polymer conformations

Simultaneous position and attitude control without linear and angular velocity feedback using dual quaternions

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