Kinematic problems are fundamental and inevitable for theory and applications of robots consisting of manipulators. While kinematics of single groundmounted manipulators are well studied and solved since decades, this investigation considers kinematics at a higher level of generality. In particular, it is assumed that a considered robot consists of a base and multiple serial manipulators and floats freely, e.g., as in the case of near-zero gravity. The work justifies such an assumption by application of the developed kinematic models to space robots for on-orbit servicing. The obtained kinematic models can be easily reduced to the case of ground-mounted manipulator, as a special case. Such general kinematics have been already solved using the classical approach, i.e., using matrices – homogeneous transforms in particular – while this work employs dual quaternions instead of homogeneous transforms as a tool for representation of spatial transformations; the work also exploits an adjusted dual inertia operator as representation of free-floating robot inertia. Besides author’s preliminary investigation, such approach to free-floating robot kinematics is the first in the literature, according to the author’s knowledge. The application of dual quaternions was motivated mainly by a popular conjecture that they imply better computational efficiency than homogeneous transforms. However, this opinion will be challenged in this work.
The direct kinematics problem considers solving for pose of a frame affixed to manipulator, given joint variables. As the name suggests, inverse kinematics is concerned by solving for joint variables given the pose. In an analogous manner, direct velocity kinematics problem solves for linear and angular velocities of some frame attached to the manipulator, given joint variable rates. Finally, inverse velocity kinematics gives us joint variable rates provided linear and angular velocities of a frame attached to a manipulator component.
The main differences between free-floating robots and ground-based manipulators are that the base of free-floating robot is not fixed and gravity forces are reduced. In a consequence, movements of a manipulator disturb position and attitude of the base, what makes the kinematic problems significantly more difficult. In particular, the inverse velocity kinematic problem cannot be solved using solely kinematic parameters – the momentum conservation law needs to be used together with knowledge on the system’s inertia parameters.