CROPS: Cosserat-Rod-Based Co-Design of Soft Slender Programmable Material Systems for Biomedical Applications

Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This coupling is computationally challenging: nonlinear large-deformation mechanics increase simulation cost, while contact, collision handling, and non-smooth state transitions limit the applicability of standard gradient-based approaches. We introduce a smooth, low-dimensional design embedding for soft robots that unifies shape morphing, multi-material distribution, and actuation within a single structured parameter space. Shape variation is modeled through continuous deformation maps of a reference geometry, while material properties are encoded as spatial fields. Both are constructed from shared basis functions. This representation enables expressive co-design while drastically reducing the dimensionality of the search space. In our experiments, we show that design expressiveness increases with the number of basis functions, unlike comparable neural network encodings whose representational capacity does not scale predictably with parameter count. We further show that joint co-optimization of shape, material, and actuation using our unified embedding consistently outperforms sequential strategies. All experiments are performed independently of the underlying simulator, confirming compatibility with black-box simulation pipelines. Across multiple dynamic tasks, the proposed embedding surpasses neural network and voxel-based baseline parameterizations while using significantly fewer design parameters. Together, these findings demonstrate that structuring the design space itself enables efficient co-design of soft robots.

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.

In this paper, we design feedback control laws for soft robots modelled using the Cosserat rod, which is spatially discretised using the Piecewise Constant Strain (PCS) approach. The PCS approach transforms the nonlinear PDEs describing the Cosserat rod to a system of nonlinear ODEs. This simplification results in a model describing soft robots which is similar to the serial rigid-link manipulators. We design feedback control laws for the quasi-static PCS model by using external wrenches as control inputs. The control laws are designed based on state-feedback linearisation in strain and task spaces. An extensive set of numerical results demonstrates the performance of the control laws for end-effector trajectory tracking and shape control of soft robots.