Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization

Yanning Dai1†, Yuhui Wang1†, Dylan R. Ashley1,2,3,4, Jürgen Schmidhuber1,2,3,4,
1KAUST, Thuwal, Saudi Arabia. 2IDSIA, Lugano, Switzerland. 3USI, Lugano, Switzerland. 4SUPSI, Lugano, Switzerland.
†Equal contribution.
Paper arXiv Code
Stackelberg PPO Framework

Stackelberg PPO. An efficient Stackelberg-based formulation that mitigates the non-differentiable coupling in morphology–control co-design by leveraging their inherent leader–follower hierarchy.

Co-Designed Agents

(3D Tasks)

Pusher

Task 1

Stepper-Regular

Task 1

Stepper-Hard

Task 1

Crawler

Task 1

(2D Tasks)

Cheetah

Task 1

Terrain Crosser

Task 1

Walker-Hard

Task 1

Glider-Hard

Task 1

Designed Morphologies Across Diverse Tasks

creatures

Evolution Process

evolve

BibTeX


@inproceedings{dai2026efficient,
  title     = {Efficient Morphology--Control Co-Design via Stackelberg {PPO}},
  author    = {Dai, Yanning and Wang, Yuhui and Ashley, Dylan R. and Schmidhuber, J{\"u}rgen},
  booktitle = {The Fourteenth International Conference on Learning Representations},
  year      = {2026}
}