Formalization of Temporal and Spatial Constraints of Bimanual Manipulation Categories

Executing bimanual manipulation tasks on humanoid robots introduces additional challenges due to inherent spatial and temporal coordination between both hands. In our previous work, we proposed the Bimanual Manipulation Taxonomy, which defines categories of bimanual manipulation strategies based on the coordination and physical interaction between both hands, the role of each hand in the task, and the symmetry of arm movements during task execution. In this work, we build upon this taxonomy and provide a formalization of temporal and spatial constraints associated with each category of the taxonomy. This formalization uses Petri nets to represent temporal constraints and differentiates between relative and global targets. We incorporate these constraints in a category-specific controller to enable reactive adaptation of the behavior according to the respective coordination constraints. We evaluated our approach in simulation and in real-world experiments on the humanoid robot ARMAR-6. The results demonstrate that category-specific constraints can be enforced when needed while maintaining flexibility to accommodate additional constraints.