Model-Free Co-Optimization of Manufacturable Sensor Layouts and Deformation Proprioception

TL;DR

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 is introduced.

Abstract

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.

Figures (20)

• Figure 1: For a pneumatic actuated deformable mannequin (a), the body shapes of different individuals, as shown in (b), can be realized and controlled with the help of stretchable sensors. When the sensor layout is determined by the intuitive design of experts in the garment industry -- i.e., heuristic consideration as the dimensions of girth measurement as shown in (c), large errors are observed in the shape predicted by these sensors (10 sensors with a total length of 1,204 mm). After applying the optimization approach presented in this paper, the error of shape prediction can be effectively reduced when using the same number of sensors but different layout as shown in (d) -- the total length reduced to 609 mm. The color map for shape approximation error on the models with maximal error are shown on the right of (c) and (d). The statistical comparisons of the shape prediction errors by using different sensor layouts can be found in (e) and (f) for the maximal errors and the average errors on 3,000 different shapes.
• Figure 2: The deformable freeform surface is parameterized by fitting a B-spline surface, defining a $u,v$-domain used as the design space for sensor layout optimization. Given the start point $(u_s,v_s)$ and the end point $(u_e,v_e)$, each sensor is represented as a line subdivided into $(K-1)$ segments, which are mapped onto the deformed 3D surface to compute its current length under deformation.
• Figure 3: Overview of our computational pipeline for co-optimizing (i) the sensor layout, parameterized by sensor locations $\mathbf{L}$ in the $u,v$-domain and the occupancy variable $\mathbf{b}$(see (a) for the sensor layout module), and (ii) the shape prediction neural network $\mathcal{N}_p$, parameterized by its coefficients $\mathbf{\theta}_p$. Co-optimization is performed using a learning routine based on backpropagation over a training dataset of models with varying shapes $\Theta=\{\mathcal{S}^c\}$. The optimization is guided by loss functions that account for both shape prediction error and constraints related to design and manufacturability (see (b) for the shape estimation module). In the context of wearable applications, the input shapes are selected from regions-of-interest (RoI) on the human body.
• Figure 4: Possible intersection scenarios between Sensor $s_1$ (AB) and Sensor $s_2$ (CD), represented as straight line segments, include: (a, b) one sensor lies entirely on the same side of the other -- no intersection occurs; and (c) the endpoints of each sensor lie on opposite sides of the other, indicating a potential intersection.
• Figure 5: Illustration of computing the minimum distance between two sensors: (a) each sensor is first uniformly subdivided into $K$ points, denoted as $\{(u_\eta,v_\eta)\}$ and $\{(u_\xi,v_\xi)\}$, with $\eta$ and $\xi$ as the respective indices, and (b) the minimum Euclidean distance between the two sensors is obtained by exhaustively computing the pairwise distances between all points from the two sets mapped onto the surface.