Coordinate-invariant rigid-body interpolation on a parametric C1 dual quaternion curve

Allmendinger, Felix; Eddine, Sami Charaf; Corves, Burkhard

doi:10.1016/j.mechmachtheory.2017.11.023

Cited by 9 publications

(13 citation statements)

References 8 publications

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“…Dual Quaternions can also be used in robotics to model forward and inverse kinematics [32]. Other application scenarios are designing algorithms for strapdown inertial navigation systems [33] or interpolating poses of rigid bodies [5]. They all have in common that they utilize the Dual Quaternion as a method to simultaneously describe a rotation and translation.…”

Section: A Related Workmentioning

confidence: 99%

“…This is the author's version which has not been fully edited and content may change prior to final publication. Machine learning LWPR / Kernel Density Estimation Real numbers Yes [22] Machine learning Gaussian process kernels Dual quaternions Yes [23] Machine learning RNN Dual quaternions Yes [24] Rigid body simulation -Dual quaternions No [25] Rigid body simulation -Real numbers / Quaternions No [26], [27] Rigid body simulation --No [28] Rigid body simulation -Real numbers No [29], [30], [31] Control theory -Dual quaternions No [32] Robotics -Dual quaternions No [33] Inertial navigation system -Dual quaternions No [5] Pose interpolation -Dual quaternions No [34], [37], [38] Machine learning CNN Real numbers Yes [35] Machine learning PhysNet Real numbers Yes [36] Machine learning Graph NN Real numbers Yes [39] Machine learning Hamiltonian Generative Network Real numbers Yes [40] Machine learning Hamiltonian NN Real numbers Yes [41] Machine learning MLP / Graph NN Real numbers Yes [42] Machine learning MLP Real numbers Yes [43] Machine learning MLP Quaternions Yes [44], [45] Machine learning CNN Quaternions Yes [46] Machine learning RNN Quaternions Yes…”

Section: A Quaternionsmentioning

confidence: 99%

“…R IGID body dynamics appear in a broad range of technical applications including robotics [1], [2], spacecraft dynamics [3], multi-body systems [4] rigid body interpolation [5], attitude and position tracking [6] and control [7]. Hence, the prediction of rigid body kinematics and dynamics is particularly important for design and control of rigid bodies.…”

Section: Introductionmentioning

confidence: 99%

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Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Pöppelbaum

Schwung

2022

IEEE Access

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We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements. After introducing the underlying dual quaternion math, we derive dual quaternion valued neural network layer which are generally applickable to all sorts of problems which can benefit from a mathematical description in dual quaternion space. To cover the dynamic behavior inherent to rigid body movements, we propose recurrent architectures in the neural network. To further model the rigid bodies interactions efficiently, we incorporate a novel attention mechanism employing dual quaternion algebra. The introduced architecture is trainable by means of gradient based algorithms. We apply our approach to a parcel prediction problem where a rigid body with an initial position, orientation, velocity and angular velocity moves through a fixed simulation environment which exhibits rich interactions between the parcel and the boundaries. There we can show that the dual quaternion valued models outperform their counterparts operation on the real numbers, confirming the successful introduction of an inductive bias through the usage of dual quaternion math. Furthermore, we used an advantageous custom data augmentation technique specifically tailored for the usage with our dual quaternion valued input data. INDEX TERMSdual quaternion attention, dual duaternion neural networks, hypercomplex neural networks, rigid body dynamics

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Section: A Related Workmentioning

confidence: 99%

Section: A Quaternionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Pöppelbaum

Schwung

2022

IEEE Access

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“…Implementations using B-splines, Csplines and even advanced geometrical Interpolation strategies could smooth the trajectory to the robot kinematics yet they would still be highly dependent on the adaptive control solution in real-world applications. For better comprehension of the interpolation complexity in this scenario, and possible improvements in planning (in exchange of additional computational complexity), the authors refer the reader to the excel work of Allmendinger et al [2].…”

Section: Route Planner Modulementioning

confidence: 99%

A Robot Architecture for Outdoor Competitions

Oliveira

Bauchspiess

Porto

et al. 2020

J Intell Robot Syst

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Autonomous navigation in unstructured environments is a common topic of research, being motivated by robotic competitions and involving several sets of skills. We present a modular architecture to integrate different components for path planning and navigation of an autonomous mobile robot. This architecture was developed in order to participate in the RoboMagellan competition hosted by RoboGames. It is divided in the organizational, functional and executive levels in order to secure that the developed system has programmability, autonomy, adaptability and extensibility. Global and local localization strategies use unscented and extended Kalman filters (UKF and EKF) to fuse data from a Global Positioning System (GPS) receiver, inertial measurement unit (IMU), odometry and camera. Movement is controlled by a model reference adaptive controller (MRAC) and a proportional controller. To avoid obstacles a deformable virtual zone (DVZ) approach is used. The architecture was tested in simulated environments and with a real robot, providing a very flexible approach to testing different configurations.

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“…More recently, parameterization independent motions have been produced [3]. Such interpolation however is dependent on coordinates, through a possibly ambiguous choice for the reference point with which to define the centre of rotation [8].…”

Section: Introductionmentioning

confidence: 99%