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.

Five-axis toolpaths are typically formatted as G01 commands by breaking curves into linear segments before being inputted into the computer numerical control systems. Despite the availability of various trajectory generation methods, real-time generation of smooth trajectories with limited smoothing error and constrained high-order kinematics remains a challenge. This paper proposes a velocity profile blending-based interpolation method for G01 paths of five-axis hybrid robots to obtain jerk-limited trajectories with constrained smoothing error. Each linear segment is represented by a 13-phase velocity profile instead of the widely adopted S-shape curve. The velocity profiles are locally blended to construct a smooth trajectory. For adjacent velocity profiles, the first three phases of the following profile strictly align with the last three phases of the preceding one. In the implementation, a bidirectional scanning algorithm is adopted to generate the velocity profile of each linear segment with the time constants of the overlapping phases pre-optimized. In the simulations and experiments, the effectiveness and benefits of the proposed method on G01 paths comprised of both long segments and short segments are validated through a comparative analysis with several representative trajectory generation methods. Note to Practitioners—This work aims to generate error-constrained and jerk-limited trajectories with high machining efficiency from G01 commands in real time for five-axis hybrid robots. Computer-aided manufacturing software typically exports five-axis toolpaths as G01 commands. Next, computer numerical control systems read the G01 commands and produce trajectories with limited error and constrained kinematics as reference commands to the drivers. To obtain smooth trajectories from G01 commands for five-axis mechanisms more efficiently, one-step trajectory generation methods based on finite impulse response (FIR) filtering are increasingly studied. Nevertheless, due to their simplistic velocity profiles, existing FIR filtering-based one-step trajectory generation approaches struggle to simultaneously enhance machining efficiency, limit blending errors, and constrain the mechanism’s high-order kinematics. Thus, we propose a more general velocity profile blending-based interpolation method that expresses the movements along linear segments as 13-phase velocity profiles rather than the S-shape velocity profiles generated by the FIR filters. Accordingly, a novel strategy is developed to efficiently determine the velocity profiles. The proposed method, implemented on a specific hybrid machining robot, was compared with a spline-based trajectory generation approach and three representative FIR filtering-based approaches. Simulations and experiments were performed, in which G01 paths constituted by both long and short segments were used to validate our method. The results suggest that our method offers several advantages at the same time: low computational cost, significant improvements in machining efficiency, strictly constrained blending error, and precisely limited robot kinematics. Furthermore, this method does not make any assumptions about the structure of the five-axis mechanism, allowing for its application to general five-axis mechanisms. In industrial applications, the proposed method can be embedded in the computer numerical control system for real-time implementation.

This paper presents a method for computing interleaved additive and subtractive manufacturing operations to fabricate models of arbitrary shapes. We solve the manufacturing planning problem by searching a sequence of inverse operations that progressively transform a target model into a null shape. Each inverse operation corresponds to either an additive or a subtractive step, ensuring both manufacturability and structural stability of intermediate shapes throughout the process. We theoretically prove that any model can be fabricated exactly using a sequence generated by our approach. To demonstrate the effectiveness of this method, we adopt a voxel-based implementation and develop a scalable algorithm that works on models represented by a large number of voxels. Our approach has been tested across a range of digital models and further validated through physical fabrication on a hybrid manufacturing system with automatic tool switching.