# Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control

arXiv: https://arxiv.org/abs/1807.08037 · HTML: https://mlsanity.com/paper/1807.08037/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Robust and Versatile Bipedal Jumping Control through Reinforcement Learning](https://mlsanity.com/paper/2302.09450/) (2023)
- [Autonomous Navigation of Underactuated Bipedal Robots in Height-Constrained Environments](https://mlsanity.com/paper/2109.05714/) (2021)

## Abstract (arXiv)

This paper presents the design and validation of controlling hopping on the 3D bipedal robot Cassie. A spring-mass model is identified from the kinematics and compliance of the robot. The spring stiffness and damping are encapsulated by the leg length, thus actuating the leg length can create and control hopping behaviors. Trajectory optimization via direct collocation is performed on the spring-mass model to plan jumping and landing motions. The leg length trajectories are utilized as desired outputs to synthesize a control Lyapunov function based quadratic program (CLF-QP). Centroidal angular momentum, taking as an addition output in the CLF-QP, is also stabilized in the jumping phase to prevent whole body rotation in the underactuated flight phase. The solution to the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping behaviors on bipedal robots with compliance. The framework presented in this paper is verified experimentally on the bipedal robot Cassie.