A new algebraic approach for the description of robotic manipulation tasks

This paper introduces the Manipulation Task Model (MTM), an algebraic approach to describe manipulation tasks for robotic systems. The model is based on dual quaternion algebra to describe poses, linear and angular velocities, and forces and moments, all of which are joined to form the algebraic group of actions. We then use this group together with process algebra to describe temporal and logical relations between actions composing manipulation tasks. A simulation example of a cleaner robot shows that the proposed model is comprehensive and expressive enough, and that it provides robustness in relation to perturbations at the task level. Future developments will include merging the model with underlying controllers in order to provide a unified means for description, planning, and execution of manipulation tasks for robotic systems.