The Math of Tasks: A Domain Specific Language for Constraint-Based Task Specification

This paper proposes a Domain Specific Language to describe in a synthetic and comprehensive way, complex control problems for robotic systems. The proposed language, named Math of Tasks, abstracts from the mathematical description of the problem, which heavily depends on the particular algorithm chosen to solve it, relying on a set of operators and entities which instead, composed together, describes the behavior of the control problem. The Math of Tasks can describe any type of instantaneous controller regardless of the particular controlled variable (e.g., joint velocity, joint acceleration, contact forces). This paper shows the convenience of the proposed formalism using examples from classical control problems for different types of robotic platforms such as manipulators, humanoid bipeds, and quadrupeds.