Design Optimization for Large High-Force Soft Robot Manipulators Under Gravitational Loads

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.

Typically, heuristic/trial-based approaches are used to design soft pneumatic grippers (SPGs). This paper presents a systematic topology optimization framework for developing SPGs. The design-dependent nature of actuating load is modeled using Darcy's law with an added drainage term. A 2D soft arm unit is then optimized as a compliant mechanism under pneumatic loading. To ensure the design is robust and manufacturable, the problem is formulated as a min-max optimization, where output deformations of blueprint and eroded designs are considered. A volume constraint is imposed on the blueprint part, while a strain-energy constraint is enforced on the eroded part. The Method of Moving Asymptotes is employed to solve optimization problems. The optimized 2D part is extruded suitably to generate a 3D unit. Ten such 3D units are assembled to create a gripper arm. Both the optimized 2D unit and the corresponding gripper arm outperform their conventional rectangular designs under pneumatic loading, demonstrating the efficacy of the proposed approach. The arms are fabricated using the SLA printing technique. Numerical and experimental results are compared at different pneumatic loads. Four 3D-printed arms are integrated with a supporting structure to form the SPG. The gripping action of the SPG is demonstrated on objects with different weights, sizes, structures, stiffnesses, and shapes.

Effective physical interaction control in robotic manipulation requires not only kinematically feasible motion but also sufficient force-interaction capability. Existing redundancy resolution methods often ignore task-specific force demands or maximize the force capability indiscriminately, sacrificing dexterity when large force margins are unnecessary. We propose a task-oriented force capability optimization framework for redundant mobile manipulators. A Vision-Language Model (VLM) infers object physical properties from an RGB image and a task description, generating a desired task-force sequence that captures gravitational and inertial demands. We then define a task-oriented force capability metric as the signed distance between a task-force uncertainty ball and the dynamic residual force polytope (RFP), quantifying compatibility between task demands and the robot's remaining actuation capacity. This metric is incorporated, alongside manipulability, joint-limit avoidance, trajectory smoothness, and base-oscillation suppression, into a whole-body multi-objective trajectory-optimization problem. Experiments on a mobile manipulator performing lifting and single-point-holding tasks under varying payload conditions demonstrate that the proposed method provides sufficient force capability for heavy loads while preserving high manipulability for light loads. This yields a task-adaptive balance that fixed capability-maximizing baselines (RFP inscribed radius, RFP cone) and manipulability-only optimization fail to achieve. The core implementation is publicly available at https://github.com/yeying256/FORTE.