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.

中文翻译：

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任务数学：基于约束的任务规范的领域特定语言

本文提出了一种领域特定语言，以综合和全面的方式描述机器人系统的复杂控制问题。建议的语言，命名为任务数学, 摘自数学的问题的描述，很大程度上取决于选择解决问题的特定算法，依赖于一组运算符和实体，它们组合在一起，描述行为的控制问题。这任务数学可以描述任何类型的瞬时控制器，而不考虑特定的受控变量（例如，关节速度、关节加速度、接触力）。本文使用来自不同类型机器人平台（如机械手、人形双足动物和四足动物）的经典控制问题的示例，展示了所提出的形式主义的便利性。