Dual Quaternion-Based Dynamic Modeling and Adaptive Neural Identification for Load-Assist Exoskeletons

This article addresses the challenge of modeling and controlling load-assist exoskeletons operating under dynamic and uncertain conditions. Traditional approaches often rely solely on dual quaternions for kinematic modeling, limiting their applicability in scenarios that require dynamic interaction. Most existing works focus only on kinematic formulations, leaving the dynamic coupling effects underexplored. To overcome this limitation, we propose a novel adaptive identifier based on Dual Quaternion Neural Networks (ADQNN), integrated within a dynamic modeling framework that includes inertial, Coriolis, and gravitational forces using dual quaternion algebra. This formulation enables a compact, singularity-free representation of rigid-body dynamics, facilitating real-time estimation of unmodeled dynamics.Unlike conventional dual-quaternion formulations, the proposed model extends their use from purely kinematic to fully dynamic representations, thereby ensuring higher numerical stability and physical consistency in modeling exoskeletons under uncertain payloads.The ADQNN is embedded within a Proportional-Derivative (PD) controller to improve trajectory tracking accuracy under unknown payloads. The proposed methodology is validated through simulations of two exoskeleton subsystems—the upper and lower limbs—under varying external loads. Simulation results demonstrate that the proposed approach significantly enhances angular position estimation, adaptability, and robustness compared to traditional models. The main contributions of this paper can be summarized as follows: (1) development of a singularity-free dynamic model based on dual quaternion algebra that includes inertial, Coriolis, and gravitational terms; (2) design of an Adaptive Dual Quaternion Neural Network (ADQNN) for online identification of unmodeled dynamics; (3) integration of the ADQNN into a PD control law with Lyapunov-based stability analysis; and (4) validation through simulations on upper and lower limb subsystems demonstrating improved performance under variable loads.These findings demonstrate the effectiveness of the proposed approach for adaptive control of exoskeletons in changing environments, extending the applicability of dual quaternions beyond purely kinematic frameworks. This constitutes the first adaptive identification framework embedded in a full dual-quaternion dynamic model.