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
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
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.
Junru Song, Yang Yang, Jingdan Shi +6
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
Musculoskeletal robots offer intrinsic compliance and flexibility, providing a promising paradigm for versatile locomotion. However, existing research typically relies on models with fixed muscle physiological parameters. This static physical setting fails to accommodate the diverse dynamic demands of complex tasks, inherently limiting the robot's performance upper bound. In this work, we focus on the morphology and control co-design of musculoskeletal systems. Unlike previous studies that optimize single physiological attributes such as stiffness, we introduce a Complete Musculoskeletal Morphological Evolution Space that simultaneously evolves muscle strength, velocity, and stiffness. To overcome the exponential expansion of the exploration space caused by this comprehensive evolution, we propose Spectral Design Evolution (SDE), a high-efficiency co-optimization framework. By integrating a bilateral symmetry prior with Principal Component Analysis (PCA), SDE projects complex muscle parameters onto a low-dimensional spectral manifold, enabling efficient morphological exploration. Evaluated on the MyoSuite framework across four tasks (Walk, Stair, Hilly, and Rough terrains), our method demonstrates superior learning efficiency and locomotion stability compared to fixed-morphology and standard evolutionary baselines.
Lidong Sun, Wentao Zhao, Ye Wang +2
Naval University of Engineering, Wuhan 430033, China · Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China · Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
In the automated co-design of soft robots, precisely adapting the material stiffness field to task environments is crucial for unlocking their full physical potential. However, mainstream platforms (e.g., EvoGym) strictly discretize the material dimension, artificially restricting the design space and performance of soft robots. To address this, we propose EvoGymCM (EvoGym with Continuous Materials), a benchmark suite formally establishing continuous material stiffness as a first-class design variable alongside morphology and control. Aligning with real-world material mechanisms, EvoGymCM introduces two settings: (i) EvoGymCM-R (Reactive), motivated by programmable materials with dynamically tunable stiffness; and (ii) EvoGymCM-I (Invariant), motivated by traditional materials with invariant stiffness fields. To tackle the resulting high-dimensional coupling, we formulate two Morphology-Material-Control co-design paradigms: (i) Reactive-Material Co-Design, which learns real-time stiffness tuning policies to guide programmable materials; and (ii) Invariant-Material Co-Design, which jointly optimizes morphology and fixed material fields to guide traditional material fabrication. Systematic experiments across diverse tasks demonstrate that continuous material optimization boosts performance and unlocks synergy across morphology, material, and control.
Le Shen, Kangyao Huang, Wentao Zhao +1
College of Control Science and Engineering, Zhejiang University. · Department of Computer Science and Technology, Tsinghua University.