Convergent Functions, Divergent Forms

2025-05-27

AI Summary

To address poor generalizability and low sample efficiency in morphology-control co-design, this paper proposes the LOKI framework. LOKI clusters structurally similar morphologies in a morphology latent space and reuses shared control policies—termed “convergent functions”—while replacing global mutation with dynamic local search—termed “divergent morphology”—to jointly enable cross-morphology policy transfer and broad morphological exploration. This “convergent function + divergent morphology” paradigm mitigates premature convergence and enables scalable discovery of high-diversity, high-performance morphologies. In UNIMAL simulations, LOKI achieves a 780× increase in morphology exploration over baselines, reduces per-design simulation steps by 78%, and cuts computational cost by 40%. Discovered morphologies span quadrupeds, bipeds, crabs, and rotating bodies, and demonstrate a 2× improvement in transfer reward on downstream tasks—including obstacle traversal, box pushing, and slope climbing.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Evolutionary Learning

Application Category

• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We introduce LOKI, a compute-efficient framework for co-designing morphologies and control policies that generalize across unseen tasks. Inspired by biological adaptation -- where animals quickly adjust to morphological changes -- our method overcomes the inefficiencies of traditional evolutionary and quality-diversity algorithms. We propose learning convergent functions: shared control policies trained across clusters of morphologically similar designs in a learned latent space, drastically reducing the training cost per design. Simultaneously, we promote divergent forms by replacing mutation with dynamic local search, enabling broader exploration and preventing premature convergence. The policy reuse allows us to explore 780$ imes$ more designs using 78% fewer simulation steps and 40% less compute per design. Local competition paired with a broader search results in a diverse set of high-performing final morphologies. Using the UNIMAL design space and a flat-terrain locomotion task, LOKI discovers a rich variety of designs -- ranging from quadrupeds to crabs, bipedals, and spinners -- far more diverse than those produced by prior work. These morphologies also transfer better to unseen downstream tasks in agility, stability, and manipulation domains (e.g., 2$ imes$ higher reward on bump and push box incline tasks). Overall, our approach produces designs that are both diverse and adaptable, with substantially greater sample efficiency than existing co-design methods. (Project website: https://loki-codesign.github.io/)

Problem

• Efficient co-design of morphologies and control policies
• Overcoming inefficiencies in evolutionary algorithms
• Enhancing adaptability and diversity in robotic designs

Innovation

• Learning convergent functions for shared policies
• Dynamic local search replaces mutation for diversity
• Policy reuse reduces training cost significantly