MultivariateSystem Identification of Differential Drive Robot: Comparison Between State-Space and LSTM-Based Models

Modeling mobile robots is crucial to odometry estimation, control design, and navigation. Classical state-space models (SSMs) have traditionally been used for system identification, while recent advances in deep learning, such as Long Short-Term Memory (LSTM) networks, capture complex nonlinear dependencies. However, few direct comparisons exist between these paradigms. This paper compares two multivariate modeling approaches for a differential drive robot: a classical SSM and an LSTM-based recurrent neural network. Both models predict the robot's linear (v) and angular (ω) velocities using experimental data from a five-minute navigation sequence. Performance is evaluated in terms of prediction accuracy, odometry estimation, and computational efficiency, with ground-truth odometry obtained via a SLAM-based method in ROS2. Each model was tuned for fair comparison: order selection for the SSM and hyperparameter search for the LSTM. Results show that the best SSM is a second-order model, while the LSTM used seven layers, 30 neurons, and 20-sample sliding windows. The LSTM achieved a FIT of 93.10% for v and 90.95% for ω, with an odometry RMSE of 1.09 m and 0.23 rad, whereas the SSM outperformed it with FIT values of 94.70% and 91.71% and lower RMSE (0.85 m, 0.17 rad). The SSM was also more resource-efficient (0.00257 ms and 1.03 bytes per step) compared to the LSTM (0.0342 ms and 20.49 bytes). The results suggest that SSMs remain a strong option for accurate odometry with low computational demand while encouraging the exploration of hybrid models to improve robustness in complex environments. At the same time, LSTM models demonstrated flexibility through hyperparameter tuning, highlighting their potential for further accuracy improvements with refined configurations.