# Online Trajectory Optimization for Dynamic Aerial Motions of a Quadruped Robot

arXiv: https://arxiv.org/abs/2110.06330 · HTML: https://mlsanity.com/paper/2110.06330/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2021.

## Built on by (most cited first, 5 of 5)

- [RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion](https://mlsanity.com/paper/2305.17842/) (2023)
- [Guided Reinforcement Learning for Omnidirectional 3D Jumping in Quadruped Robots](https://mlsanity.com/paper/2507.16481/) (2025)
- [Efficient Reinforcement Learning for Jumping Monopods](https://mlsanity.com/paper/2309.07038/) (2023)
- [Impedance Matching: Enabling an RL-Based Running Jump in a Quadruped Robot](https://mlsanity.com/paper/2404.15096/) (2024)
- [Learn to Swim: Data-Driven LSTM Hydrodynamic Model for Quadruped Robot Gait Optimization](https://mlsanity.com/paper/2505.03146/) (2025)

## Abstract (arXiv)

This work presents a two part framework for online planning and execution of dynamic aerial motions on a quadruped robot. Motions are planned via a centroidal momentum-based nonlinear optimization that is general enough to produce rich sets of novel dynamic motions based solely on the user-specified contact schedule and desired launch velocity of the robot. Since this nonlinear optimization is not tractable for real-time receding horizon control, motions are planned once via nonlinear optimization in preparation of an aerial motion and then tracked continuously using a variational-based optimal controller that offers robustness to the uncertainties that exist in the real hardware such as modeling error or disturbances. Motion planning typically takes between 0.05-0.15 seconds, while the optimal controller finds stabilizing feedback inputs at 500 Hz. Experimental results on the MIT Mini Cheetah demonstrate that the framework can reliably produce successful aerial motions such as jumps onto and off of platforms, spins, flips, barrel rolls, and running jumps over obstacles.