This article presents a novel representation-free model predictive control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three-dimensional (3-D) space. Our formulation directly represents the rotational dynamics using the rotation matrix, which liberates us from the issues associated with the use of Euler angles and quaternion as the orientation representations. With a variation-based linearization scheme and a carefully constructed cost function, the MPC control law is transcribed to the standard quadratic program form. The MPC controller can operate at real-time rates of 250 Hz on a quadruped robot. Experimental results including periodic quadrupedal gaits and a controlled backflip validate that our control strategy could stabilize dynamic motions that involve singularity in 3-D maneuvers.

中文翻译：

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四足动物动态运动的无表征模型预测控制

本文提出了一种新颖的无表征模型预测控制 (RF-MPC) 框架，用于控制三维 (3-D) 空间中四足机器人的各种动态运动。我们的公式使用旋转矩阵直接表示旋转动力学，这使我们摆脱了与使用欧拉角和四元数作为方向表示相关的问题。通过基于变化的线性化方案和精心构建的成本函数，MPC 控制律被转录为标准的二次规划形式。MPC 控制器可以在四足机器人上以 250 Hz 的实时速率运行。包括周期性四足步态和受控后空翻在内的实验结果验证了我们的控制策略可以稳定涉及 3D 机动中奇点的动态运动。