# LEGO: Latent-space Exploration for Geometry-aware Optimization of Humanoid Kinematic Design

arXiv: https://arxiv.org/abs/2604.08636 · HTML: https://mlsanity.com/paper/2604.08636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [HybrIK: A Hybrid Analytical-Neural Inverse Kinematics Solution for 3D Human Pose and Shape Estimation](https://mlsanity.com/paper/2011.14672/) (2020)
- [SynBody: Synthetic Dataset with Layered Human Models for 3D Human Perception and Modeling](https://mlsanity.com/paper/2303.17368/) (2023)
- [Differentiable Dynamics for Articulated 3d Human Motion Reconstruction](https://mlsanity.com/paper/2205.12256/) (2022)
- [Trajectory Optimization for Physics-Based Reconstruction of 3d Human Pose from Monocular Video](https://mlsanity.com/paper/2205.12292/) (2022)
- [GLSO: Grammar-guided Latent Space Optimization for Sample-efficient Robot Design Automation](https://mlsanity.com/paper/2209.11748/) (2022)
- [On Explicit Curvature Regularization in Deep Generative Models](https://mlsanity.com/paper/2309.10237/) (2023)
- [COIL: Constrained Optimization in Learned Latent Space: Learning Representations for Valid Solutions](https://mlsanity.com/paper/2202.02163/) (2022)
- [N-LIMB: Neural Limb Optimization for Efficient Morphological Design](https://mlsanity.com/paper/2207.11773/) (2022)
- [A Geometric Perspective on Autoencoders](https://mlsanity.com/paper/2309.08247/) (2023)
- [MORPH: Design Co-optimization with Reinforcement Learning via a Differentiable Hardware Model Proxy](https://mlsanity.com/paper/2309.17227/) (2023)
- [MMP++: Motion Manifold Primitives with Parametric Curve Models](https://mlsanity.com/paper/2310.17072/) (2023)
- [The igus Humanoid Open Platform: A Child-sized 3D Printed Open-Source Robot for Research](https://mlsanity.com/paper/1809.11110/) (2018)

## Abstract (arXiv)

Designing robot morphologies and kinematics has traditionally relied on human intuition, with little systematic foundation. Motion-design co-optimization offers a promising path toward automation, but two major challenges remain: (i) the vast, unstructured design space and (ii) the difficulty of constructing task-specific loss functions. We propose a new paradigm that minimizes human involvement by (i) learning the design search space from existing mechanical designs, rather than hand-crafting it, and (ii) defining the loss directly from human motion data via motion retargeting and Procrustes analysis. Using screw-theory-based joint axis representation and isometric manifold learning, we construct a compact, geometry-preserving latent space of humanoid upper body designs in which optimization is tractable. We then solve design optimization in this latent space using gradient-free optimization. Our approach establishes a principled framework for data-driven robot design and demonstrates that leveraging existing designs and human motion can effectively guide the automated discovery of novel robot design.