Towards the use of dual quaternions for motion generation of nonholonomic mobile manipulators

Kinematic control based on dual quaternion algebra and its application to robot manipulators

“…Therefore, the three-dimensional rotation 11 operation must be defined in a subgroup of O(3) with determinant restricted to 1-this group, SO(3), is called the special orthogonal group or rotation group of R 3 . Definition 2.15 (Rotation group).…”

“…In summary, this section presents three different numerical examples implemented in Open Robotics Automation Virtual Environment (OpenRAVE) without a physics engine to simulate rigid body dynamics, and two more realistic simulations devised and implemented in the Virtual Experimentation Platform (VREP) from Coppelia RObotics GmbH (see, [90]) using Bullet Physics Library 10 as the physics engine. For examples using OpenRAVE, all controllers were implemented using Matlab and the DQ_Robotics toolbox 11 ; whereas the V-REP simulations were implemented using The Robot Operating System (ROS) 12 and the DQ_Robotics toolbox with a sampling time of 5ms. The desired end-effector position and orientation configuration is given by…”

“…Neste sentido, esta tese também pode ser vista como uma sequência do trabalho e da obra de Adorno [1] com referência a utilização da álgebra de quatérnios duais para a robótica. De fato, o uso de quatérnios duais unitários em robótica pode ser rastreado até as obras de [8][9][10][11], contudo apenas a partir do trabalho de Adorno uma estrutura completa para modelagem cinemática de robôs por meio de quatérnios duais unitários foi estabelecida e devidamente normalizada. Uma análise cuidadosa sobre as contribuições decorrentes do trabalho [1] lançam alguma luz sobre a mudança de paradigma promovida no sentido de representação de corpos rígidos no contexto de robótica.…”

“…Moreover, to cope with the challenges arising from robust, optimal and flexible control of robot manipulators in the task-space, this thesis exploits the advantages of dual quaternion algebra to model and control the robot coupled translation and rotation kinematics, following the steps and continuing the history introduced in Adorno's work [1]. The use of unit dual quaternions in robotics can be traced back to the works of [8][9][10][11], but only in Adorno's work a complete framework for robot kinematic modeling by means of unit dual quaternion is properly formalized. A careful analysis on the contributions stemming from [1] shed some light on its paradigm shift characteristics for rigid body representation in robotics.…”