Flexible sensors are increasingly employed in soft robotics and wearable devices to provide proprioception of freeform deformations. Although supervised learning can train shape predictors from sensor signals, prediction accuracy strongly depends on sensor layout, which is typically determined heuristically or through trial-and-error. This work introduces a model-free, data-driven computational pipeline that jointly optimizes the number, length, and placement of flexible length-measurement sensors together with the parameters of a shape prediction network for large freeform deformations. Unlike model-based approaches, the proposed method relies solely on datasets of deformed shapes, without requiring physical simulation models, and is therefore broadly applicable to diverse robotic sensing tasks. The pipeline incorporates differentiable loss functions that account for both prediction accuracy and manufacturability constraints. By co-optimizing sensor layouts and network parameters, the method significantly improves deformation prediction accuracy over unoptimized layouts while ensuring practical feasibility. The effectiveness and generality of the approach are validated through numerical and physical experiments on multiple soft robotic and wearable systems.

This paper presents a correspondence-free, function-based sim-to-real learning method for controlling deformable freeform surfaces. Unlike traditional sim-to-real transfer methods that strongly rely on marker points with full correspondences, our approach simultaneously learns a deformation function space and a confidence map – both parameterized by a neural network – to map simulated shapes to their real-world counterparts. As a result, the sim-to-real learning can be conducted by input from either a 3D scanner as point clouds (without correspondences) or a motion capture system as marker points (tolerating missed markers). The resultant sim-to-real transfer can be seamlessly integrated into a neural network-based computational pipeline for inverse kinematics and shape control. We demonstrate the versatility and adaptability of our method on two vision devices and across four pneumatically actuated soft robots: a deformable membrane, a robotic mannequin, and two soft manipulators.

This paper introduces a novel curve-based slicing method for generating planar layers with dynamically varying orientations in digital light processing (DLP) 3D printing. Our approach effectively addresses key challenges in DLP printing, such as regions with large overhangs and staircase artifacts, while preserving its intrinsic advantages of high resolution and fast printing speeds. We formulate the slicing problem as an optimization task, in which parametric curves are computed to define both the slicing layers and the model partitioning through their tangent planes. These curves inherently define motion trajectories for the build platform and can be optimized to meet critical manufacturing objectives, including collision-free motion and floating-free deposition. We validate our method through physical experiments on a robotic multi-axis DLP printing setup, demonstrating that the optimized curves can robustly guide smooth, high-quality fabrication of complex geometries.

We introduce a general, scalable computational framework for multi-axis 3D printing based on implicit neural fields (INFs) that unifies all stages of tool-path generation and global collision-free motion planning. In our pipeline, input models are represented as signed distance fields, with fabrication objectives—such as support-free printing, surface finish quality, and extrusion control—directly encoded in the optimization of an implicit guidance field. This unified approach enables toolpath optimization across both surface and interior domains, allowing shell and infill paths to be generated via implicit field interpolation. The printing sequence and multi-axis motion are then jointly optimized over a continuous quaternion field. Our continuous formulation constructs the evolving printing object as a time-varying SDF, supporting differentiable global collision handling throughout INF-based motion planning. Compared to explicit-representation-based methods, INF-3DP achieves up to two orders of magnitude speedup and significantly reduces waypoint-to-surface error. We validate our framework on diverse, complex models and demonstrate its efficiency with physical fabrication experiments using a robot-assisted multi-axis system.

Joint injuries, and their long-term consequences, present a substantial global health burden. Wearable prophylactic braces are an attractive potential solution to reduce the incidence of joint injuries by limiting joint movements that are related to injury risk. Given human motion and ground reaction forces, we present a computational framework that enables the design of personalized braces by optimizing the distribution of microstructures and elasticity. As varied brace designs yield different reaction forces that influence kinematics and kinetics analysis outcomes, the optimization process is formulated as a differentiable end-to-end pipeline in which the design domain of microstructure distribution is parameterized onto a neural network. The optimized distribution of microstructures is obtained via a self-learning process to determine the network coefficients according to a carefully designed set of losses and the integrated biomechanical and physical analyses. Since knees and ankles are the most commonly injured joints, we demonstrate the effectiveness of our pipeline by designing, fabricating, and testing prophylactic braces for the knee and ankle to prevent potentially harmful joint movements.

This paper presents a learning based planner for computing optimized 3D printing toolpaths on prescribed graphs, the challenges of which include the varying graph structures on different models and the large scale of nodes & edges on a graph. We adopt an on-the-fly strategy to tackle these challenges, formulating the planner as a Deep Q-Network (DQN) based optimizer to decide the next 'best' node to visit. We construct the state spaces by the Local Search Graph (LSG) centered at different nodes on a graph, which is encoded by a carefully designed algorithm so that LSGs in similar configurations can be identified to re-use the earlier learned DQN priors for accelerating the computation of toolpath planning. Our method can cover different 3D printing applications by defining their corresponding reward functions. Toolpath planning problems in wire-frame printing, continuous fiber printing, and metallic printing are selected to demonstrate its generality. The performance of our planner has been verified by testing the resultant toolpaths in physical experiments. By using our planner, wire-frame models with up to 4.2k struts can be successfully printed, up to 93.3% of sharp turns on continuous fiber toolpaths can be avoided, and the thermal distortion in metallic printing can be reduced by 24.9%.

Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more concise subspaces can be detected. However, the complexity and landscape of simulation objectives within the subspace have not been optimized, which leaves room for enhancement of the convergence speed. This work focuses on this point by proposing a general method for finding optimized subspace mappings, enabling further acceleration of neural reduced-order simulations while capturing comprehensive representations of the configuration manifolds. We achieve this by optimizing the Lipschitz energy of the elasticity term in the simulation objective, and incorporating the cubature approximation into the training process to manage the high memory and time demands associated with optimizing the newly introduced energy. Our method is versatile and applicable to both supervised and unsupervised settings for optimizing the parameterizations of the configuration manifolds. We demonstrate the effectiveness of our approach through general cases in both quasi-static and dynamics simulations. Our method achieves acceleration factors of up to 6.83 while consistently preserving comparable simulation accuracy in various cases, including large twisting, bending, and rotational deformations with collision handling. This novel approach offers significant potential for accelerating physical simulations, and can be a good add-on to existing neural-network-based solutions in modeling complex deformable objects.

Robot-assisted 3D printing has drawn a lot of attention by its capability to fabricate curved layers that are optimized according to different objectives. However, the support generation algorithm based on a fixed printing direction for planar layers cannot be directly applied for curved layers as the orientation of material accumulation is dynamically varied. In this paper, we propose a skeleton-based support generation method for robot-assisted 3D printing with curved layers. The support is represented as an implicit solid so that the problems of numerical robustness can be effectively avoided. The effectiveness of our algorithm is verified on a dual-material printing platform that consists of a robotic arm and a newly designed dual-material extruder. Experiments have been successfully conducted on our system to fabricate a variety of freeform models.

Soft robots can safely interact with environments because of their mechanical compliance. Self-collision is also employed in the modern design of soft robots to enhance their performance during different tasks. However, developing an efficient and reliable simulator that can handle the collision response well, is still a challenging task in the research of soft robotics. This paper presents a collision-aware simulator based on geometric optimization, in which we develop a highly efficient and realistic collision checking / response model incorporating a hyperelastic material property. Both actuated deformation and collision response for soft robots are formulated as geometry-based objectives. The collision-free body of a soft robot can be obtained by minimizing the geometry-based objective function. Unlike the FEA-based physical simulation, the proposed pipeline performs a much lower computational cost. Moreover, adaptive remeshing is applied to achieve the improvement of the convergence when dealing with soft robots that have large volume variations. Experimental tests are conducted on different soft robots to verify the performance of our approach.

Multi-axis motion introduces more degrees of freedom into the process of 3D printing to enable different objectives of fabrication by accumulating materials layers upon curved layers. An existing challenge is how to effectively generate the curved layers satisfying multiple objectives simultaneously. This paper presents a general slicing framework for achieving multiple fabrication objectives including support free, strength reinforcement and surface quality. These objectives are formulated as local printing directions varied in the volume of a solid, which are achieved by computing the rotation-driven deformation for the input model. The height field of a deformed model is mapped into a scalar field on its original shape, the isosurfaces of which give the curved layers of multi-axis 3D printing. The deformation can be effectively optimized with the help of quaternion fields to achieve the fabrication objectives. The effectiveness of our method has been verified on a variety of models.

We present a method for fabricating general models with multi-directional 3-D printing systems by printing different model regions along with different directions. The core of our method is a support-effective volume decomposition algorithm that minimizes the area of the regions with large overhangs. A beam-guided searching algorithm with manufacturing constraints determines the optimal volume decomposition, which is represented by a sequence of clipping planes. While current approaches require manually assembling separate components into a final model, our algorithm allows for directly printing the final model in a single pass. It can also be applied to models with loops and handles. A supplementary algorithm generates special supporting structures for models where supporting structures for large overhangs cannot be eliminated. We verify the effectiveness of our method using two hardware systems: a Cartesian-motion-based system and an angular-motion-based system. A variety of 3-D models have been successfully fabricated on these systems.

The anisotropy of mechanical strength on a 3D printed model can be controlled in a multi-axis 3D printing system as materials can be accumulated along dynamically varied directions. In this paper, we present a new computational framework to generate specially designed layers and toolpaths of multi-axis 3D printing for strengthening a model by aligning filaments along the directions with large stresses. The major challenge comes from how to effectively decompose a solid into a sequence of strength-aware and collision-free working surfaces. We formulate it as a problem to compute an optimized governing field together with a selected orientation of fabrication setup. Iso-surfaces of the governing field are extracted as working surface layers for filament alignment. Supporting structures in curved layers are constructed by extrapolating the governing field to enable the fabrication of overhangs. Compared with planar-layer based Fused Deposition Modeling (FDM) technology, models fabricated by our method can withstand up to 6 . 35× loads in experimental tests.

Robots fabricated with soft materials can provide higher flexibility and, thus, better safety while interacting in unpredictable situations. However, the usage of soft material makes it challenging to predict the deformation of a continuum body under actuation and, therefore, brings difficulty to the kinematic control of its movement. In this article, we present a geometry-based framework for computing the deformation of soft robots within the range of linear material elasticity. After formulating both manipulators and actuators as geometry elements, deformation can be efficiently computed by solving a constrained optimization problem. Because of its efficiency, forward and inverse kinematics for soft manipulators can be solved by an iterative algorithm with a low computational cost. Meanwhile, components with multiple materials can also be geometrically modeled in our framework with the help of a simple calibration. Numerical and physical experimental tests are conducted on soft manipulators driven by different actuators with large deformation to demonstrate the performance of our approach.

We present an inverse design tool for fabric formwork - a process where flat panels are sewn together to form a fabric container for casting a plaster sculpture. Compared to 3D printing techniques, the benefit of fabric formwork is its properties of low-cost and easy transport. The process of fabric formwork is akin to molding and casting but having a soft boundary. Deformation of the fabric container is governed by force equilibrium between the pressure forces from liquid fill and tension in the stretched fabric. The final result of fabrication depends on the shapes of the flat panels, the fabrication orientation and the placement of external supports. Our computational framework generates optimized flat panels and fabrication orientation with reference to a target shape, and determines effective locations for external supports. We demonstrate the function of this design tool on a variety of models with different shapes and topology. Physical fabrication is also demonstrated to validate our approach.

Robots fabricated by soft materials can provide higher flexibility and thus better safety while interacting with natural objects with low stiffness such as food and human beings. However, as many more degrees of freedom are introduced, the motion simulation of a soft robot becomes cumbersome, especially when large deformations are presented. Moreover, when the actuation is defined by geometry variation, it is not easy to obtain the exact loads and material properties to be used in the conventional methods of deformation simulation. In this paper, we present a direct approach to take the geometric actuation as input and compute the deformed shape of soft robots by numerical optimization using a geometry-based algorithm. By a simple calibration, the properties of multiple materials can be modeled geometrically in the framework. Numerical and experimental tests have been conducted to demonstrate the performance of our approach on both cable-driven and pneumatic actuators in soft robotics.

This paper presents a new method to fabricate 3D models on a robotic printing system equipped with multi-axis motion. Materials are accumulated inside the volume along curved tool-paths so that the need of supporting structures can be tremendously reduced - if not completely abandoned - on all models. Our strategy to tackle the challenge of tool-path planning for multi-axis 3D printing is to perform two successive decompositions, first volume-to-surfaces and then surfaces-to-curves. The volume-to-surfaces decomposition is achieved by optimizing a scalar field within the volume that represents the fabrication sequence. The field is constrained such that its iso-values represent curved layers that are supported from below, and present a convex surface affording for collision-free navigation of the printer head. After extracting all curved layers, the surfaces-to-curves decomposition covers them with tool-paths while taking into account constraints from the robotic printing system. Our method successfully generates tool-paths for 3D printing models with large overhangs and high-genus topology. We fabricated several challenging cases on our robotic platform to verify and demonstrate its capabilities.

This paper presents a robotic system - RoboFDM that targets at printing 3D models without support-structures, which is considered as the major restriction to the flexibility of 3D printing. The hardware of RoboFDM consists of a robotic arm providing 6-DOF motion to the platform of material accumulation and an extruder forming molten filaments of polylactic acid (PLA). The fabrication of 3D models in this system follows the principle of fused decomposition modeling (FDM). Different from conventional FDM, an input model fabricated by RoboFDM is printed along different directions at different places. A new algorithm is developed to decompose models into support-free parts that can be printed one by one in a collision-free sequence. The printing directions of all parts are also determined during the computation of model decomposition. Experiments have been successfully taken on our RoboFDM system to print general freeform objects in a support-free manner.

This paper introduces a novel method for designing personalized orthopedic casts which are aware of thermal-comfort while satisfying mechanical requirements. Our pipeline starts from thermal images taken by an infrared camera, by which the distribution of thermal-comfort sensitivity is generated on the surface of a 3D scanned model. We formulate a hollowed Voronoi tessellation pattern to represent the covered region for a web-like cast design. The pattern is further optimized according to the thermal-comfort sensitivity calculated from thermal images. Working together with a thickness variation method, we generate a solid model for a personalized cast maximizing both thermal comfort and mechanical stiffness. To demonstrate the effectiveness of our approach, 3D printed models of personalized casts are tested on body parts of different individuals.