# Realtime Limb Trajectory Optimization for Humanoid Running Through Centroidal Angular Momentum Dynamics

arXiv: https://arxiv.org/abs/2501.17351 · HTML: https://mlsanity.com/paper/2501.17351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [GaitSpan: Growing Humanoid Locomotion from Walking to Running](https://mlsanity.com/paper/2607.12114/) (2026)

## Abstract (arXiv)

One of the essential aspects of humanoid robot running is determining the limb-swinging trajectories. During the flight phases, where the ground reaction forces are not available for regulation, the limb swinging trajectories are significant for the stability of the next stance phase. Due to the conservation of angular momentum, improper leg and arm swinging results in highly tilted and unsustainable body configurations at the next stance phase landing. In such cases, the robotic system fails to maintain locomotion independent of the stability of the center of mass trajectories. This problem is more apparent for fast and high flight time trajectories. This paper proposes a real-time nonlinear limb trajectory optimization problem for humanoid running. The optimization problem is tested on two different humanoid robot models, and the generated trajectories are verified using a running algorithm for both robots in a simulation environment.