Abstract
This paper presents an n-dimensional reduction algorithm for Learning from Demonstration (LfD) for robotic path planning, addressing the complexity of high-dimensional data. The method extends the Douglas-Peucker algorithm by incorporating velocity and orientation alongside position, enabling more precise trajectory simplification. A magnitude-based normalization process preserves proportional relationships across dimensions, and the reduced dataset is used to train Hidden Markov Models (HMMs), where continuous trajectories are discretized into identifier sequences. The algorithm is evaluated in 2D and 3D environments with datasets combining position and velocity. The results show that incorporating additional dimensions significantly enhances trajectory simplification while preserving key information. Additionally, the study highlights the importance of selecting appropriate encoding parameters to achieve optimal resolution. The HMM-based models generated new trajectories that retained the patterns of the original demonstrations, demonstrating the algorithm's capacity to generalize learned behaviors for trajectory learning in high-dimensional spaces.