# Beyond Inverted Pendulums: Task-optimal Simple Models of Legged Locomotion

arXiv: https://arxiv.org/abs/2301.02075 · HTML: https://mlsanity.com/paper/2301.02075/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Cost-Matching Model Predictive Control for Efficient Reinforcement Learning in Humanoid Locomotion](https://mlsanity.com/paper/2603.28243/) (2026)
- [Transfer Learning for a Class of Cascade Dynamical Systems](https://mlsanity.com/paper/2410.06828/) (2024)

## Abstract (arXiv)

Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM for control captures critical task-relevant aspects of the full dynamics while remaining low dimensional. However, planning within the reduced-order space unavoidably constrains the full model, and hence we sacrifice the full potential of the robot. In the community of legged locomotion, this has lead to a search for better model extensions, but many of these extensions require human intuition, and there has not existed a principled way of evaluating the model performance and discovering new models. In this work, we propose a model optimization algorithm that automatically synthesizes reduced-order models, optimal with respect to a user-specified distribution of tasks and corresponding cost functions. To demonstrate our work, we optimized models for a bipedal robot Cassie. We show in simulation that the optimal ROM reduces the cost of Cassie's joint torques by up to 23% and increases its walking speed by up to 54%. We also show hardware result that the real robot walks on flat ground with 10% lower torque cost. All videos and code can be found at https://sites.google.com/view/ymchen/research/optimal-rom.