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Convergent Functions, Divergent Forms
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Proposes LOKI, a compute-efficient morphology-control co-design method that clusters morphologies in a VAE latent space, trains shared transformer policies per cluster, and uses dynamic local search instead of mutation to evolve diverse, transferable robot designs in the UNIMAL space.
Problem
Brain-body co-design of robot morphology and control is computationally expensive because each morphology is trained from scratch, and evolutionary/quality-diversity methods trade off diversity against the number of designs evaluated; resulting designs often overfit to the training task.
Approach
Train shared multi-design transformer policies per cluster of morphologically similar designs in a learned VAE latent space, and replace mutation with dynamic local search that samples random designs per cluster and swaps top ones into a dynamic elite pool, so each policy serves as a cheap surrogate evaluator.
Key results
- LOKI explores about 3.12M morphologies versus 4,000 for DERL, using 4.62B interactions versus 20B, and about 102B FLOPs per morphology versus 159B.
- LOKI achieves the highest QD-score (60.9) and 100% coverage, while DERL reaches 37.5% coverage and max fitness is slightly higher for DERL and MAP-Elites.
- On unseen tasks, LOKI improves bump from 981 to 1908 and push box incline from 1519 to 3148 relative to DERL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use LOKI instead of DERL | UNIMAL co-design on flat terrain · UNIMAL flat terrain (FT) | searched morphologies: 4000 -> 3,120,000 | Helped |
| use LOKI instead of DERL | UNIMAL co-design on flat terrain · UNIMAL flat terrain (FT) | interactions (B): 20 -> 4.62 | Helped |
| use LOKI instead of DERL | UNIMAL co-design on flat terrain · UNIMAL flat terrain (FT) | QD-score: 26.2 -> 60.9 | Helped |
| use LOKI instead of MAP-Elites | UNIMAL co-design on flat terrain · UNIMAL flat terrain (FT) | QD-score: 43.5 -> 60.9 | Helped |
| use LOKI instead of MAP-Elites | UNIMAL co-design on flat terrain · UNIMAL flat terrain (FT) | Max Fitness: 5807.3 -> 5671.9 | Hurt |
| use LOKI instead of DERL | final evolved morphologies · Bump | reward: 981 -> 1908 | Helped |
| use LOKI instead of DERL | final evolved morphologies · Push box incline | reward: 1519 -> 3148 | Helped |
| use LOKI instead of DERL | final evolved morphologies · Manipulate ball | reward: 142 -> 172 | Helped |
| remove clustering (ablation) | LOKI · UNIMAL flat terrain (FT) | QD-score: 60.9 -> 40.0 | Hurt |
| use 10 clusters instead of 40 (ablation) | LOKI · UNIMAL flat terrain (FT) | QD-score: 60.9 -> 21.6 | Hurt |
| use 20 clusters instead of 40 (ablation) | LOKI · UNIMAL flat terrain (FT) | QD-score: 60.9 -> 26.6 | Hurt |
| replace learned latent-space clusters with raw-parameter clusters (ablation) | LOKI · UNIMAL flat terrain (FT) | QD-score: 60.9 -> 27.5 | Hurt |
Surprising findings
- Max fitness of LOKI is slightly lower than DERL and MAP-Elites despite higher QD-score.
- Raw-parameter clustering variant performs worse than latent-space clustering on quality and diversity.
Limitations
- Number of clusters must be fixed at the start of training; adding clusters later may require costly retraining.
- Training cost scales linearly with the number of clusters.
- Max fitness is slightly lower than DERL and MAP-Elites on flat terrain.
Experimental setup
Datasets: UNIMAL morphology space (500k random morphologies)
Benchmarks: flat-terrain locomotion Patrol Incline Push Box Incline Obstacle Bump Manipulate Ball Exploration
Metrics: max fitness QD-score coverage (%) sparseness downstream reward number of searched morphologies simulation interactions FLOPs per morphology
Baselines: DERL MAP-Elites Latent-MAP-Elites Random LOKI (w/o cluster)
Builds on: DERL MAP-Elites PPO UNIMAL
Closest papers by meaning
- BodyGen: Advancing Towards Efficient Embodiment Co-Design (ICLR 2025 · similarity 0.88)
- DittoGym: Learning to Control Soft Shape-Shifting Robots (ICLR 2024 · similarity 0.87)
- MorphVAE: Advancing Morphological Design of Voxel-Based Soft Robots with Variational Autoencoders (AAAI 2024 · similarity 0.87)
- Embracing Evolution: A Call for Body-Control Co-Design in Embodied Humanoid Robot (NeurIPS 2026 · similarity 0.87)
- DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations (NeurIPS 2026 · similarity 0.86)
- Distilling Morphology-Conditioned Hypernetworks for Efficient Universal Morphology Control (ICML 2024 · similarity 0.86)
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