Invariant body kinematics. II: reaching and neurogeometry
Neural Networks
Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration
Journal of Mathematical Imaging and Vision
Mechanics of robotic manipulation
Mechanics of robotic manipulation
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Geometric Fundamentals of Robotics (Monographs in Computer Science)
Geometric Fundamentals of Robotics (Monographs in Computer Science)
Avoiding Spurious Submovement Decompositions II: A Scattershot Algorithm
Biological Cybernetics
Arm trajectory modifications during reaching towards visual targets
Journal of Cognitive Neuroscience
The superposition strategy for arm trajectory modification inrobotic manipulators
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Motor algebra, a 4D degenerate geometric algebra, offers a rigorous yet simple representation of the 3D velocity of a rigid body. Using this representation, we study 3D extended arm pointing and reaching movements. We analyze the choice of arm orientation about the vector connecting the shoulder and the wrist, in cases for which this orientation is not prescribed by the task. Our findings show that the changes in this orientation throughout the movement were very small, possibly indicating an underlying motion planning strategy. We additionally examine the decomposition of movements into submovements and reconstruct the motion by assuming superposition of the velocity profiles of the underlying submovements by analyzing both the translational and rotational components of the 3D spatial velocity. This movement decomposition method reveals a larger number of submovement than is found using previously applied submovement extraction methods that are based only on the analysis of the hand tangential velocity. The reconstructed velocity profiles and final orientations are relatively close to the actual values, indicating that single-axis submovements may be the basic building blocks underlying 3D movement construction.