Achieving both target accuracy and robustness in dynamic maneuvers with long flight phases, such as high or long jumps, has been a significant challenge for legged robots. To address this challenge, we propose a novel learning-based control approach consisting of model learning and model predictive control (MPC) utilizing an adaptive frequency scheme. Compared to existing MPC techniques, we learn a model directly from experiments, accounting not only for leg dynamics but also for modeling errors and unknown dynamics mismatch in hardware and during contact. Additionally, learning the model with adaptive frequency allows us to cover the entire flight phase and final jumping target, enhancing the prediction accuracy of the jumping trajectory. Using the learned model, we also design an adaptive-frequency MPC to effectively leverage different jumping phases and track the target accurately. In hardware experiments with a Unitree A1 robot, we demonstrate that our approach outperforms baseline MPC using a nominal model, reducing the jumping distance error up to 8 times. We achieve jumping distance errors of less than 3 percent during continuous jumping on uneven terrain with randomly-placed perturbations of random heights (up to 4 cm or 27 percent of the robot's standing height). Our approach obtains distance errors of 1-2 cm on 34 single and continuous jumps with different jumping targets and model uncertainties.

翻译：在具有长飞行阶段的动态机动（如高跳或远跳）中，同时实现目标精度和鲁棒性一直是腿式机器人面临的重大挑战。为应对这一挑战，我们提出了一种新颖的基于学习的控制方法，该方法包含模型学习和模型预测控制（MPC），并采用自适应频率方案。与现有MPC技术相比，我们直接从实验中学习模型，不仅考虑了腿部动力学，还考虑了硬件及接触过程中的建模误差和未知动力学失配。此外，通过自适应频率学习模型，使我们能够覆盖整个飞行阶段和最终跳跃目标，从而提高了跳跃轨迹的预测精度。利用学习到的模型，我们还设计了一种自适应频率MPC，以有效利用不同的跳跃阶段并精确跟踪目标。在Unitree A1机器人上的硬件实验中，我们证明了我们的方法优于使用标称模型的基线MPC，将跳跃距离误差降低了多达8倍。在具有随机放置、随机高度（最高达4厘米或机器人站立高度的27%）扰动的非平坦地形上进行连续跳跃时，我们实现了小于3%的跳跃距离误差。我们的方法在34次具有不同跳跃目标和模型不确定性的单次及连续跳跃中，获得了1-2厘米的距离误差。