The ability of executing multiple tasks simultaneously is an important feature of redundant robotic systems. As a matter of fact, complex behaviors can often be obtained as a result of the execution of several tasks. Moreover, in safety-critical applications, tasks designed to ensure the safety of the robot and its surroundings have to be executed along with other nominal tasks. In such cases, it is also important to prioritize the former over the latter. In this paper, we formalize the definition of extended set-based tasks, i.e., tasks which can be executed by rendering subsets of the task space asymptotically stable or forward invariant. We propose a mathematical representation of such tasks that allows for the execution of more complex and time-varying prioritized stacks of tasks using kinematic and dynamic robot models alike. We present and analyze an optimization-based framework which is computationally efficient, accounts for input bounds, and allows for the stable execution of time-varying prioritized stacks of extended set-based tasks. The proposed framework is validated using extensive simulations and experiments with robotic manipulators.

翻译：多任务并行执行能力是冗余机器人系统的重要特性。实际上，复杂行为往往源于多个任务的协同执行。在安全关键型应用中，确保机器人及其环境安全的任务必须与常规任务同步执行，且前者需具有更高优先级。本文正式定义了扩展集合型任务——即通过使任务空间子集渐近稳定或前向不变来实现的任务类型。我们提出此类任务的数学表征方法，可同时利用运动学与动力学模型构建更复杂、时变的优先级任务栈。通过优化框架的设计与分析，该方法兼具计算高效性、输入约束适应能力，并支持扩展集合型任务时变优先级栈的稳定执行。通过机器人操作臂的仿真与实验验证了该框架的有效性。