  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.
