Neural-Augmented Hybrid Dynamic Modeling of a Series-Parallel Elastic Actuator

This paper proposes a neural network-based model of a novel hybrid Series-Parallel Elastic Actuator (SEA-PEA) architecture for high-performance robotic applications. The system combines a Brushless DC (BLDC) motor, a planetary gearbox, and a rotary pneumatic actuator serving as an elastic element. While the gearbox offers advantages such as low cost and back-drivability, it suffers from significant backlash due to manufacturing tolerances. To address this, the actuator connects the gearbox output shaft directly to that of the pneumatic actuator. For a parallel configuration, both stators are mounted on an aluminum holder supporting the entire assembly. Within the backlash region, the system behaves as a Series Elastic Actuator (SEA), with the pneumatic actuator’s elasticity influencing stiffness, damping, and inertia. Outside this region, the system transitions to a Parallel Elastic Actuator (PEA), rigidly coupling the motor and gearbox shafts. A hybrid modeling approach is introduced to capture the actuator’s dynamic response. The SEA behavior is modeled using a black-box Artificial Neural Network (ANN), specifically an Echo State Network (ESN), which showed the lowest mean squared error (MSE) among the tested architectures. The PEA behavior is modeled using a gray-box approach, combining a linear dynamic block with a nonlinear static block represented by an ANN (Wiener model). This hybrid framework, integrating an ESN, achieved lower prediction error and better performance than other ANN architectures, as confirmed by experimental results.