This paper proposes an MPC-based controller to efficiently execute multiple hierarchical tasks for underactuated and constrained robotic systems. Existing task-space controllers or whole-body controllers solve instantaneous optimization problems given task trajectories and the robot plant dynamics. However, the task-space control method we propose here relies on the prediction of future state trajectories and the corresponding costs-to-go terms over a finite time-horizon for computing control commands. We employ acceleration energy error as the performance index for the optimization problem and extend it over the finite-time horizon of our MPC. Our approach employs quadratically constrained quadratic programming, which includes quadratic constraints to handle multiple hierarchical tasks, and is computationally more efficient than nonlinear MPC-based approaches that rely on nonlinear programming. We validate our approach using numerical simulations of a new type of robot manipulator system, which contains underactuated and constrained mechanical structures.

中文翻译：

---

基于 MPC 的欠驱动和受约束机器人执行多任务的分层任务空间控制

本文提出了一种基于 MPC 的控制器，以有效地为欠驱动和受限机器人系统执行多个分层任务。现有的任务空间控制器或全身控制器解决了给定任务轨迹和机器人工厂动力学的瞬时优化问题。然而，我们在此提出的任务空间控制方法依赖于对未来状态轨迹的预测以及有限时间范围内相应的成本项来计算控制命令。我们采用加速能量误差作为优化问题的性能指标，并将其扩展到 MPC 的有限时间范围内。我们的方法采用二次约束二次规划，其中包括二次约束来处理多个层次任务，并且在计算上比依赖非线性规划的基于非线性 MPC 的方法更有效。我们使用新型机器人机械手系统的数值模拟来验证我们的方法，该系统包含欠驱动和受约束的机械结构。