This work explores a spatial printing method to fabricate continuous fiber-reinforced thermoplastic composites (CFRTPCs), which can achieve exceptional mechanical performance. For models giving complex 3D stress distribution under loads, typical planar-layer based fiber placement usually fails to provide sufficient reinforcement due to their orientations being constrained to planes. The effectiveness of fiber reinforcement could be maximized by using multi-axis additive manufacturing (MAAM) to better control the orientation of continuous fibers in 3D-printed composites. Here, we propose a computational approach to generate 3D toolpaths that satisfy two major reinforcement objectives: (1) following the maximal stress directions in critical regions and (2) connecting multiple load-bearing regions by continuous fibers. Principal stress lines are first extracted in an input solid model to identify critical regions. Curved layers aligned with maximal stresses in these critical regions are generated by computing an optimized scalar field and extracting its iso-surfaces. Then, topological analysis and operations are applied to each curved layer to generate a computational domain that preserves fiber continuity between load-bearing regions. Lastly, continuous fiber toolpaths aligned with maximal stresses are generated on each surface layer by computing an optimized scalar field and extracting its iso-curves. A hardware system with dual robotic arms is employed to conduct the physical MAAM tasks depositing polymer or fiber reinforced polymer composite materials by applying a force normal to the extrusion plane to aid consolidation. When comparing to planar-layer based printing results in tension, up to 644% failure load and 240% stiffness are observed on shapes fabricated by our spatial printing method. We demonstrate the versatility of our approach through various complex load cases which demonstrate their successful implementation of continuous fiber printing in 3D.

This article presents an efficient learning-based method to solve the <italic>inverse kinematic</italic> (IK) problem on soft robots with highly nonlinear deformation. The major challenge of efficiently computing IK for such robots is due to the lack of analytical formulation for either forward or inverse kinematics. To address this challenge, we employ neural networks to learn both the mapping function of forward kinematics and also the Jacobian of this function. As a result, Jacobian-based iteration can be applied to solve the IK problem. A sim-to-real training transfer strategy is conducted to make this approach more practical. We first generate a large number of samples in a simulation environment for learning both the kinematic and the Jacobian networks of a soft robot design. Thereafter, a sim-to-real layer of differentiable neurons is employed to map the results of simulation to the physical hardware, where this sim-to-real layer can be learned from a very limited number of training samples generated on the hardware.

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.

Real-time proprioception is a challenging problem for soft robots, which have virtually infinite degrees of freedom in body deformation. When multiple actuators are used, it becomes more difficult as deformation can also occur on actuators caused by interaction between each other. To tackle this problem, we present a method in this article to sense and reconstruct 3-D deformation on pneumatic soft robots by first integrating multiple low-cost sensors inside the chambers of pneumatic actuators and then using machine learning to convert the captured signals into shape parameters of soft robots. An exterior motion capture system is employed to generate the datasets for both training and testing. With the help of good shape parameterization, the 3-D shape of a soft robot can be accurately reconstructed from signals obtained from multiple sensors. We demonstrate the effectiveness of this approach on two soft robot designs - a robotic joint and a deformable membrane. After parameterizing the deformation of these soft robots into compact shape parameters, we can effectively train the neural networks to reconstruct the 3-D deformation from the sensor signals. The sensing and shape prediction pipeline can run at 50 Hz in real time on a consumer-level device.

Multi-axis additive manufacturing enables high flexibility of material deposition along dynamically varied directions. The Cartesian motion platforms of these machines include three parallel axes and two rotational axes. Singularity on rotational axes is a critical issue to be tackled in motion planning for ensuring high quality of manufacturing results. The highly nonlinear mapping in the singular region can convert a smooth toolpath with uniformly sampled waypoints defined in the model coordinate system into a highly discontinuous motion in the machine coordinate system, which leads to over-extrusion/under-extrusion of materials in filament-based additive manufacturing. The problem is challenging as both the maximal and the minimal speeds at the tip of a printer head must be controlled in motion. Moreover, collision may occur when sampling-based collision avoidance is employed. In this letter, we present a motion planning method to support the manufacturing realization of designed toolpaths for multi-axis additive manufacturing. Problems of singularity and collision are considered in an integrated manner to improve the motion therefore the quality of fabrication.

We present a field-based method of toolpath generation for 3D printing continuous fibre reinforced thermoplastic composites. Our method employs the strong anisotropic material property of continuous fibres by generating toolpaths along the directions of tensile stresses in the critical regions. Moreover, the density of toolpath distribution is controlled in an adaptive way proportionally to the values of stresses. Specifically, a vector field is generated from the stress tensors under given loads and processed to have better compatibility between neighboring vectors. An optimal scalar field is computed later by making its gradients approximate the vector field. After that, isocurves of the scalar field are extracted to generate the toolpaths for continuous fibre reinforcement, which are also integrated with the boundary conformal toolpaths in user selected regions. The performance of our method has been verified on a variety of models in different loading conditions. Experimental tests are conducted on specimens by 3D printing continuous carbon fibres (CCF) in a polylactic acid (PLA) matrix. Compared to reinforcement by load-independent toolpaths, the specimens fabricated by our method show up to 71.4% improvement on the mechanical strength in physical tests when using the same (or even slightly smaller) amount of continuous fibres.

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. Note to Practitioners - In conventional planar-layer-based 3-D printing systems, supporting structures need to be added at the bottom of large overhanging regions to prevent material collapse. Supporting structures used in single-material 3-D printing technologies have three major problems: being difficult to remove, introducing surface damage, and wasting material. This article introduces a method to improve 3-D printing by adding rotation during the manufacturing process. To keep the hardware system relatively inexpensive, the hardware, called a multi-directional 3-D printing system, only needs to provide unsynchronized rotations. In this system, models are subdivided into different regions, and then, the regions are printed in different directions. We develop a general volume decomposition algorithm for effectively reducing the area that needs supporting structures. When supporting structures cannot be eliminated, we provide a supplementary algorithm for generating supports compatible with multi-directional 3-D printing. Our method can speed up the process of 3-D printing by saving time in producing and removing supports.

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.

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.

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.

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 isovalues 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.