Machine Learning Approaches to Position Estimation in SMA-Actuated Soft Robotic Systems

Shape Memory Alloy (SMA) actuated soft robotic systems offer advantages in adaptability and compliance but present significant challenges for modeling and control due to nonlinear and time-dependent behavior. This work presents a data-driven approach for estimating the three-dimensional position of SMA-actuated soft robotic limbs using recurrent neural networks (RNNs). A multi-limbed soft robotic platform equipped with embedded temperature, current, and inertial measurement sensors was developed, with motion-capture data providing ground-truth position labels. A randomized actuation algorithm enabled varied and continuous data collection across independent and coupled limb activations. Advanced Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM) architectures with residual connections and layer normalization were trained and evaluated using synchronized multimodal sensor data across multiple lookback window configurations. The best-performing GRU model (240- timestep lookback) achieved a root mean squared error (RMSE) of 0.63 units, outperforming the best LSTM model (0.85 units RMSE). The GRU exhibited lower mean absolute error (0.19 vs. 0.35 units) and a reduced 95th percentile error (0.89 vs. 1.66 units), indicating improved robustness. Per-marker analysis indicated that the GRU more effectively modeled complex limb motion patterns, particularly for markers experiencing greater displacement and motion complexity. The results demonstrate the feasibility of applying RNN-based models for accurate, sensor-driven position estimation in SMA-actuated soft robots, providing a foundation for future closed-loop control and onboard state estimation implementations.