Noise-Resistant and Highly Generalizable Trajectory Learning for Robots with the NGGD Framework

Imitation learning provides an effective means for robot skill acquisition; however, conventional single-demonstration approaches are often susceptible to teaching noise and offer limited generalization. To overcome these limitations, this paper proposes a noise-resistant imitation learning framework named NGGD (New-GMM-GMR-DMP), which integrates Gaussian Mixture Models (GMM), Gaussian Mixture Regression (GMR), and an enhanced Dynamic Movement Primitives (DMP) algorithm for robust trajectory modeling and generalization from multiple demonstrations. The proposed framework first augments the data with Gaussian noise to improve robustness, employs GMM for probabilistic trajectory encoding, and then utilizes GMR to reconstruct an optimal smooth trajectory, effectively mitigating uncertainty and noise from individual demonstrations. Furthermore, we enhance the nonlinear function in the DMP formulation to improve stability and convergence accuracy during trajectory generalization. Evaluations on the LASA handwriting dataset and real-world robot drag-teaching tasks demonstrate that the NGGD algorithm significantly reduces the reproduction error (RMSE decreased from 5.219 to 0.547), completely eliminates anomalous trajectories, and maintains high accuracy and smoothness across varying target conditions. This work offers a highly robust and generalizable trajectory learning approach suitable for intelligent manufacturing and human–robot collaboration.