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differential kinematics

Robotica (1)

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A new method of applying differential kinematics through dual quaternions
Andre Schneider de Oliveira, Edson Roberto De Pieri, Ubirajara Franco Moreno
Journal:

Robotica / Volume 35 / Issue 4 / April 2017

Published online by Cambridge University Press:

24 November 2015, pp. 907-921
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Differential kinematics is a traditional approach to linearize the mapping between the workspace and joint space. However, a Jacobian matrix cannot be inverted directly in redundant systems or in configurations where kinematic singularities occur. This work presents a novel approach to the solution of differential kinematics through the use of dual quaternions. The main advantage of this approach is to reduce “drift” error in differential kinematics and to ignore the kinematic singularities. An analytical dual-quaternionic Jacobian is defined, which allows for the application of this approach in any robotic system.