Diverse and Adaptable Arm Coordination for Octopus-Crawling via Diffusion-Based Uncertainty-Aware Optimization

Seung Hyun Kim; Heng-Sheng Chang; Kimia Kazemi; Prashant Mehta; Mattia Gazzola

cs.ROSep 17, 2026

Diverse and Adaptable Arm Coordination for Octopus-Crawling via Diffusion-Based Uncertainty-Aware Optimization

Authors: Seung Hyun Kim, Heng-Sheng Chang, Kimia Kazemi, Prashant Mehta, Mattia Gazzola

Organizations: Mechanical Science and Engineering, University of Illinois Urbana-Champaign · Coordinated Science Laboratory, University of Illinois Urbana-Champaign · Carl R. Woese Institute for Genomic Biology, University of Illinois Urbana-Champaign · National Center for Supercomputing Applications, University of Illinois Urbana-Champaign

Abstract

Octopus crawling motivates soft robots that exploit redundancy, yet discovering and organizing diverse coordination modes for adaptation remains challenging. To address this, we introduce a Diffusion-based Uncertainty-aware Optimization (DUO) algorithm that learns demonstration-free crawling controllers for a simulated, muscle-actuated CyberOctopus. This work represents the first application of diffusion-based control to soft multi-arm robots in contact-rich simulations. By embedding a variety of locomotion behaviors within a shared control distribution, this approach enables the simulated octopus to navigate dynamic physical constraints, demonstrating that learned coordination diversity inherently facilitates robust adaptation. The main contributions include: (i) a symmetry-structured policy representation that folds radially equivalent controllers into a canonical directional sector, (ii) an online black-box optimization strategy, the DUO algorithm, that discovers and retains diverse coordination modes, and (iii) a control editing technique that adapts existing controllers to novel actuator constraints without retraining. These results show how learned coordination diversity makes motor abundance a practical resource for adaptation in soft multi-arm robots.

Figures & tables

Fig. 1: CyberOctopus. The eight-arm soft-body model crawls on a frictional plane following waypoint sequences, requiring coordinated distributed actuation in a hyper-redundant control space. A diffusion model is chosen to handle a variety of feasible coordination modes, and the trained model can then be leveraged for adaptive control editing when an arm fails or surface friction changes, without requiring retraining.

Fig. 2: Cyber-octopus model and actuation. (a) Cosserat-rod soft-arm model. (b) Eightfold radial symmetry. (c) Control-induced translation and body rotation. (d) Arm coordination through pulling, pushing, and alternating recruitment. (e) Muscular-hydrostat cross-section: longitudinal (LM), transverse (TM), and oblique (OM) muscles, axial nerve cord, and suction cups. (f) Muscle-driven bending (LM), extension (TM), and twisting (OM and LM); tapered arms and muscle paths follow a spiral construction [ 23 ] . (g) Muscle arrangement, arm-body coupling, internal loading, and floor contact. Within the capture distance, sucker adhesion attracts the arm to the floor while tangential damping suppresses slip.

Fig. 3: Control discovery and constrained reuse. (a) Control generation and denoiser training. (b) Candidate selection and evaluation. Candidates are ranked by acquisition score $\alpha$ , and the top $I$ candidates are evaluated. Simulating the crawling motion in both the center and boundary directions yields the objective values for the next iteration. (c) Control reuse by editing. Shaded grid entries illustrate constrained actuation coordinates. The landscape depicts a schematic objective, and the pink hyperplane denotes the constrained control subspace. Through repeated noising and denoising, a previous control can be adjusted to satisfy the constraints while improving performance, without retraining.

Fig. 4: Directional crawling and control diversity. (a) Crawling objective over $\phi\in[-22.5^{\circ},22.5^{\circ}]$ with (blue) and without (orange) the boundary objective; shading indicates standard deviation over $32$ seeds. (b) Angular deviation (solid, left scale) and body rotation (dashed, right scale). (c) Waypoint tracking with the same color convention as (a); black dashed lines mark the commanded paths. (d) Crawling along a curved target path (black dashed), showing successive body configurations, trajectories from $128$ controls (gray), and best control (red); inset: best control values. (e) Arm-averaged time-integrated activation of TM, LM, suction, and OM recruitment across the control family. The family is clustered using the k-nearest neighbors (KNN) algorithm ( $\text{k}=6$ ). (f) Per-iteration objective ranges (left) and maxima (right) for the compared methods. (g) PCA of the generated control distribution across training iterations, $1,800$ samples per iteration. PC1 and PC2 indicate the first and second principal components.

Fig. 5: Adaptive control editing under actuation constraints. Performance objective recovery outcomes produced by the trained and fixed DUO denoiser: (a) $25\%$ muscle-amplitude reduction across all arms; (b) $75\%$ suction-amplitude reduction across all arms; (c) zero muscle and suction amplitudes on arms $1$ , $3$ , $5$ , and $7$ . On the left, dark cells mark constrained channels. On the right, blue violin plots show retained-outcome objective distributions over $64$ generated controls; black markers show means. The plotted points illustrate the performance across the adaptation process: starting from the initial control, applying the constraint, and showing the subsequent edited versions across the iterative denoising steps. Red percentages report the mean of recovery, $(y_{\mathrm{adapted}}-y_{\mathrm{constrained}})/(y_{\mathrm{initial}}-y_{\mathrm{constrained}})\times 100\%$ .

Variation	Final best	$\Delta$ (%)
DUO	$\mathbf{0.384}$	–
- sample $u^{i}$ from $p_{\theta_{e}}(\cdot\|y_{\text{max}})$ instead	$0.256$	$-33.3$
- without $\alpha^{\text{control}}$	$0.243$	$-36.7$
- without $\alpha^{\text{target}}$	$0.328$	$-14.6$

TABLE I: Ablation study of DUO components. Values are mean over five independent runs, each of

100

iterations.

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This paper proposes SoftGM, an octopus-inspired distributed control architecture for segmented soft robotic arms that learn to reach targets in contact-rich environments using online obstacle discovery without assuming full obstacle geometry at the start of each episode. SoftGM formulates each arm section as a cooperative agent and represents the arm-environment interaction as a graph. SoftGM uses a two-stage graph attention message passing scheme following a Centralised Training Decentralised Execution (CTDE) paradigm with a centralised critic and decentralised actor. We evaluate SoftGM in a Cosserat-rod simulator (PyElastica) across three tasks that increase the complexity of the environment: obstacle-free, structured obstacles, and a wall-with-hole scenario. Compared with six widely used MARL baselines (IDDPG, IPPO, ISAC, MADDPG, MAPPO, MASAC) under identical information content and training conditions, SoftGM matches strong CTDE methods in simpler settings and achieves the best performance in the wall-with-hole task. Robustness tests with observation noise, single-section actuation failure, and transient disturbances show that SoftGM maintains comparable performance under non-ideal simulated conditions while keeping control effort bounded, suggesting that selective contact-relevant information routing improves resilience in the tested settings.

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