Emerging soft robots, known for their flexible body deformations and agile movements, offer compliant, robust, and safe interactions for dynamic tasks in unstructured environments. To enhance the intelligence of soft robots, integrating compliant strain sensors into their structure is essential. These sensors provide real-time feedback on environmental stimuli, enabling kinematic estimation of the robot itself and mapping of surroundings for autonomous navigation. However, achieving this automation milestone is hampered by the high degree-of-freedom (DOF) body deformations and varied actuation behaviors of soft robots, which complicate robot kinematics and pose significant design challenges for integrated strain sensors. The diverse sensing requirements of soft robots with differing actuation behaviors or size scales necessitate strain sensors with user-specified characteristics (e.g., sensitivity, linear working window). Traditional methods often rely on trial-and-error experiments, which are time-consuming and inefficient, especially for custom sensor production. While sensor modeling tools using mathematical statistics or physical simulations offer an alternative, they struggle with the unpredictable material and structural changes in conventional soft strain sensors. Sensor stability is crucial for accurate closed-loop control in soft robotic automation but is often overlooked. This impacts the robot's ability to accurately self-estimate and adapt to environmental changes without recalibration or error correction. State-of-the-art soft strain sensors are mostly tested under simplistic conditions, failing to represent the complexities of real-world scenarios. Soft robots frequently encounter unexpected deformations and noisy environments, requiring intermittent operation to maintain performance and prevent premature failure. The variable operating speeds of soft robots also demand sensor stability across a wide range of frequencies. Existing sensors often fail under these conditions, leading to signal distortions and degraded feedback. Therefore, developing highly robust sensors capable of withstanding complex and dynamic environments is critical for bridging the gap between soft sensors and practical robot applications. This research addresses both sensor modeling and stability challenges to enable autonomous soft robot navigation.

The literature extensively covers the development of compliant strain sensors for soft robotics. Researchers have explored various materials and designs to achieve high sensitivity, wide linear ranges, and good durability. However, a significant gap exists in creating sensors that can accurately model their behavior under diverse operating conditions and maintain their functionality in the complex and often unpredictable environments encountered by soft robots. Existing methods often involve lengthy trial-and-error experimentation or rely on modeling techniques that struggle to capture the dynamic and complex material behavior of these sensors. Furthermore, the robustness of existing sensors is often evaluated under simplified conditions, failing to replicate real-world challenges such as intermittent operation, high-frequency actuation, and noisy environments. This study aims to bridge this gap by developing a computational design methodology and exploring the use of machine learning to enable robust and adaptable soft robotic systems.

This work introduces a computational strain sensor design using a "programmed crack array within micro-crumples" (PCAM) strategy. The methodology involves two key stages: **Stage 1: Programmed Crack Array:** Single-walled carbon nanotubes (SWNTs) are used to create piezoresistive strain sensors. A laser machine precisely creates user-defined interdigital crack patterns on a SWNT-coated polystyrene (PS) film. The laser power is carefully controlled to etch only the SWNT layer, leaving the PS substrate intact. The width of each crack is approximately 20 μm. **Stage 2: Micro-crumples:** The laser-processed crack array undergoes thermally induced shrinkage. The PS substrate contracts biaxially above its glass transition temperature, causing the SWNT layer to crumple isotropically, overlaying the laser-programmed cracks. The shrunken device is then top-coated with Ecoflex, and the PS substrate is removed, resulting in the PCAM sensor. **Finite Element Analysis (FEA):** A 3D FEA model of the PCAM sensor is created in COMSOL Multiphysics. This model simulates both the mechanical and electrical behavior of the sensor under strain, allowing for prediction of sensing curves before physical fabrication. The crack density (ρ) and shrinkage ratio (φ) are input as parameters. The FEA model simulates the growth of cracks under strain and the corresponding change in resistance. **Sensor Characterization:** The fabricated PCAM sensors are characterized under various conditions to evaluate their robustness: * Noise interruptions (dynamic mechanical loading including stretching, twisting, and bending) * Intermittent cyclic loadings (100,000 cycles with rest periods) * Dynamic frequencies (0–23 Hz) **Sensor Integration and Machine Learning:** PCAM sensors are integrated into different soft robots (origami, pneumatic, and micro-robots). Machine learning (ML) algorithms (Artificial Neural Networks - ANN) are used to predict robotic trajectories and terrain altitudes based on sensor data. Specifically, the crack density (ρ) is calculated as the cumulative length of surface cracks divided by the surface area of the SWNT layer. The shrinkage ratio (φ) is defined as the change in PS film dimensions before and after thermal contraction. The gauge factor (GF) and linear working window of the sensor are determined experimentally and compared with FEA predictions. Sensor stability is evaluated using metrics like signal deviation and hysteresis. The ML models are trained on datasets of sensor readings and robot movements, allowing for real-time trajectory prediction and terrain altitude awareness. The accuracy of these predictions is evaluated using various error metrics.

The research yielded several key findings: 1. **Tunable Sensor Characteristics:** The PCAM sensor design allows for programmable tuning of the gauge factor (GF) and linear working window by adjusting crack density (ρ) and shrinkage ratio (φ). Increasing ρ leads to higher GF, while increasing φ expands the linear working window. 2. **Accurate Sensor Modeling:** FEA simulations accurately predict the sensing curves of PCAM sensors, eliminating the need for extensive experimental iterations. The model captures the interplay between mechanical and electrical responses under strain. 3. **Ultra-Robust Sensing:** PCAM sensors exhibit exceptional mechanical stability under various demanding conditions, including: * Noise interruptions (up to 50% strain): The micro-crumple structure absorbs multiaxial impacts. * Intermittent cyclic loadings (100,000 cycles): Consistent signal baseline and peaks are observed. * Dynamic frequencies (0–23 Hz): Stable signals are maintained across a broad frequency range. 4. **Successful Integration into Soft Robots:** PCAM sensors are successfully integrated into origami, pneumatic, and micro-robots across different scales, providing reliable perception of robot motions and environmental interactions. The sensors maintain their integrity and functionality even under significant robot deformations. 5. **High-Accuracy Robotic Navigation with Machine Learning:** An ANN model trained on PCAM sensor data and robot actuation information enables high-accuracy trajectory prediction (<4% relative error) for an origami robot. Another ANN model successfully predicts terrain altitude (<10% mean relative error) during robot navigation over varying terrain, demonstrating surrounding awareness. 6. **Superior Performance compared to Existing Sensors:** The PCAM sensors outperform existing crack-based soft strain sensors in terms of tunability, modeling accuracy, and robustness across noisy, intermittent, and dynamic conditions.

This research addresses critical challenges in soft robotics by providing a design framework for ultra-robust and highly tunable strain sensors. The computational design approach using FEA eliminates the need for extensive empirical experiments, significantly streamlining sensor development. The PCAM sensors' exceptional stability in complex and dynamic environments demonstrates their suitability for real-world applications. The successful integration of the sensors into diverse soft robot platforms and the application of machine learning showcase their potential for enabling autonomous navigation and complex task performance. The combined hardware and software advancements enable reliable sensing, decision-making, and autonomous navigation in complex environments, paving the way for broader application of soft robots in exploration, rescue operations, and other challenging scenarios. The accuracy of the machine learning models demonstrates the potential for using sensor data to enhance soft robot autonomy and situational awareness.

This study presents a novel computational design for ultra-robust strain sensors based on a programmed crack array within micro-crumples strategy. These sensors, termed PCAM sensors, demonstrate high tunability, accurate FEA-based modeling, and exceptional mechanical robustness under demanding conditions. Successful integration into various soft robots and the application of machine learning demonstrate their potential for enabling autonomous robot navigation with high accuracy in trajectory prediction and terrain awareness. Future research directions include exploring advanced ML algorithms for improved swarm intelligence and investigating further applications of PCAM sensors in diverse soft robotic systems.

While the PCAM sensors demonstrate superior performance, some limitations remain. The current FEA model does not fully account for the spontaneous stress relaxation of the Ecoflex substrate during strain unloading, limiting the accuracy of the model during the release phase. The machine learning models were trained and tested on specific types of robots and terrains. Further research is needed to evaluate their generalizability to different robots, environments, and tasks. Additionally, the long-term durability of the sensors under extreme conditions may require further investigation.