Generative Evolutionary Design of Voxel-Based Soft Robots with Provable Optimality

Junru Song; Huan Xiao; Yang Yang; Guozhen Li; Wei Peng; Xiaoya Zhang; Tingsong Jiang; Weien Zhou

cs.ROAug 24, 2026

Generative Evolutionary Design of Voxel-Based Soft Robots with Provable Optimality

Authors: Junru Song, Huan Xiao, Yang Yang, Guozhen Li, Wei Peng, Xiaoya Zhang, Tingsong Jiang, Weien Zhou,

Organizations: School of Computer Science, Shanghai Jiao Tong University, Shanghai 200240, China · School of Statistics, Renmin University of China, Beijing 100872, China · Intelligent Game and Decision Laboratory, Beijing 100071, China · School of Statistics and the Center for Applied Statistics, Renmin University of China, Beijing 100872, China

Abstract

Voxel-based soft robots (VSRs) present a promising avenue for developing artificial organisms with lifelike intelligence. However, the vast design spaces and expensive evaluations substantially challenge their design optimization. Here we develop MISCO, a novel evolutionary framework empowered by deep generative models to optimize VSR designs with theoretical guarantees. MISCO integrates an estimation-of-distribution algorithm with a meticulously designed variational autoencoder featuring multi-task learning, position awareness, and inter-voxel signaling. These key components enhance the representational capacity of VSR morphologies and facilitate highly efficient sampling and optimization of morphological distributions. We provide theoretical guarantees for MISCO's asymptotic convergence to globally optimal designs, alongside a favorable convergence rate. Extensive simulated experiments further demonstrate MISCO's exceptional effectiveness in navigating vast design spaces, evolving high-performing VSRs for diverse tasks while flexibly balancing optimization efficiency and morphological diversity. Being validated both empirically and theoretically, MISCO represents a step change towards more scalable and reliable soft robot development.

Figures & tables

Fig. 1 : Algorithm overview . a, In each generation, MISCO iterates over four stages: (1) Robot proposal by MEC-VAE; (2) Control optimization and fitness evaluation; (3) Natural selection with an adjustable balance between exploitation and exploration; (4) Model update. b, The process of robot proposal by MEC-VAE.

Fig. 2 : Illustration of model update via variational inference.

Fig. 3 : Comparisons of best fitness and cumulative fitness time average (CFTA). a, A brief introduction of the selected task instances. b, Comparison of best fitness. Best fitness (vertical axis) is plotted against the cumulative count of up to 1,000 robot evaluations (horizontal axis). c, Comparison of CFTA, which reflects how the average fitness of evaluated robot designs evolves over time.

Fig. 4 : Best-performing morphologies evolved by MISCO.

Fig. 5 : Comparisons of evolutionary outcomes. a, left: Comparative results of eventually achieved best fitness, as well as average ranks across all tasks. The best results are in bold while the best-performing baselines are underlined (the same is true for panel b ). a, right: Normalized best-fitness performances showcased in radar plots, with MISCO-A serving as one unit. b, left: Comparative results of average fitness of all evaluated designs, as well as average ranks across all tasks. b, right: Normalized average-fitness performances showcased in radar plots, with MISCO-A serving as one unit. c, Kernel density estimations of fitness distributions. Probability density (vertical axis) is plotted against fitness (horizontal axis).

TABLE I : Performance comparison of diversity. In some cases the algorithm fails to produce more than one high-performing robot design, so diversity is not available ("NA").

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Fig. 6 : Shared structures across tasks. Note that ’DS-v0’ and ’PJ-v0’ are short for DownStepper-v0 and PlatformJumper-v0, respectively. a, Overlapping of robot designs in multiple tasks. b, Perplexity of robot designs in multiple tasks. c, Dimension-wise average KL divergence of task latent variables. The bubble plot illustrates the average KL divergence for each of the 128 dimensions of the task latent variable in our multi-task VAE framework. The $x$ -axis shows the dimension index, ranging from 1 to 128, while the $y$ -axis represents average KL divergence, with the bubble size and color intensity corresponding to divergence magnitude.

Fig. 7 : Illustration of various tasks in the EvoGym environment.

TABLE II : Results of the ablation study. Best fitness achieved at the end of evolution is compared between both of the two variants and their ablated versions.

Hyperparameter	Value
Number of tasks optimized together in multi-task learning	3
Size of robot design space	5 $\times$ 5
Number of voxel type	5

Appendix

TABLE III : Definition of VSR design problem.

Hyperparameter	Notation	Value
Task embedding dimension	$Y_{t}$	128
Task latent dimension	$H_{t}$	128
Position embedding dimension	$P_{v}$	128
Voxel-specific latent dimension	$h_{v}$	64
Voxel-specific steady state dimension	$H_{v}$	64

Appendix

TABLE IV : Model hyperparameters.

MLP Type	Structure
MLP in task awareness	[input size, 128, ReLU, 128, ReLU, 128, ReLU, output size, output transform]
MLP in NCA	[input size, 128, ReLU, 128, ReLU, 128, ReLU, output size]
MLP in shared output layer	[input size, 128, ReLU, 128, ReLU, 128, ReLU, output size]
MLP in encoder	[input size, 128, ReLU, 128, ReLU, 128, ReLU, output size, output transform]

Appendix

TABLE V : MLP architectures.

Soft Robotics

Soft robotics studies robots with compliant bodies and actuators that deform to move, sense, and interact with uncertain environments.

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Aug 24, 2026J/K move · Enter open · S save

RoboLDA: A Probabilistic Generative Model for Uncovering Embodied Hierarchical Structures in Voxel-based Soft Robots

Junru Song, Yang Yang, Jingdan Shi, Guozhen Li+5

School of Computer Science, Shanghai Jiao Tong University, Shanghai, 200240, China · Intelligent Game and Decision Laboratory, Beijing, 100071, China · School of Statistics, Renmin University of China, Beijing, 100872, China+3

Generative Modeling Soft Robotics Robot Morphology-Control Co-Design

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Recent advances in robotics highlight hierarchical configurations of robot morphology, where multiple levels of functional substructures synergize to facilitate intelligent behaviors. This hierarchical perspective, while particularly advantageous for voxel-based soft robots (VSRs) to ease design and control complexities, is hindered by its heavy reliance on domain expertise. In this work, we address the following question: can we derive such hierarchical design principles solely from existing successful designs? We answer affirmatively by presenting RoboLDA, a Bayesian probabilistic model that decomposes VSR morphology generation into a four-level hierarchy: "task-robot-organ-voxel", and is trained via variational inference. Through extensive experiments on simulated VSRs, we verify the presence of consistent, intuitive hierarchical patterns underlying high-performing VSR designs and showcase RoboLDA's proficiency to extract and leverage these hierarchical priors for zero-shot robot design in unseen tasks. The generated designs, even without further optimization, achieve on average 106.4% of the optimized performance produced by evolutionary algorithms. Additionally, the organ structures inferred by RoboLDA serve as valid functional substructures, significantly enhancing synergistic motion control when integrated with modular control policies. Our work pioneers hierarchical generative modeling of robot morphology, offering a promising pathway towards more interpretable and generalizable development of embodied agents.

Abstract

Soft Robotics

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