Unsupervised Segmentation and Alignment of Multi-Demonstration Trajectories via Multi-Feature Saliency and Duration-Explicit HSMMs

Tianci Gao (), Konstantin A. Neusypin, Dmitry D. Dmitriev, Bo Yang and Shengren Rao
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Tianci Gao: Department IU-1 “Automatic Control Systems”, Bauman Moscow State Technical University, Moscow 105005, Russia
Konstantin A. Neusypin: Department IU-1 “Automatic Control Systems”, Bauman Moscow State Technical University, Moscow 105005, Russia
Dmitry D. Dmitriev: Department IU-1 “Automatic Control Systems”, Bauman Moscow State Technical University, Moscow 105005, Russia
Bo Yang: Department IU-1 “Automatic Control Systems”, Bauman Moscow State Technical University, Moscow 105005, Russia
Shengren Rao: Department IU-1 “Automatic Control Systems”, Bauman Moscow State Technical University, Moscow 105005, Russia

Mathematics, 2025, vol. 13, issue 19, 1-29

Abstract: Learning from demonstration with multiple executions must contend with time warping, sensor noise, and alternating quasi-stationary and transition phases. We propose a label-free pipeline that couples unsupervised segmentation, duration-explicit alignment, and probabilistic encoding. A dimensionless multi-feature saliency (velocity, acceleration, curvature, direction-change rate) yields scale-robust keyframes via persistent peak–valley pairs and non-maximum suppression. A hidden semi-Markov model (HSMM) with explicit duration distributions is jointly trained across demonstrations to align trajectories on a shared semantic time base. Segment-level probabilistic motion models (GMM/GMR or ProMP, optionally combined with DMP) produce mean trajectories with calibrated covariances, directly interfacing with constrained planners. Feature weights are tuned without labels by minimizing cross-demonstration structural dispersion on the simplex via CMA-ES. Across UAV flight, autonomous driving, and robotic manipulation, the method reduces phase-boundary dispersion by 31% on UAV-Sim and by 30–36% under monotone time warps, noise, and missing data (vs. HMM); improves the sparsity–fidelity trade-off (higher time compression at comparable reconstruction error) with lower jerk; and attains nominal 2σ coverage (94–96%), indicating well-calibrated uncertainty. Ablations attribute the gains to persistence plus NMS, weight self-calibration, and duration-explicit alignment. The framework is scale-aware and computationally practical, and its uncertainty outputs feed directly into MPC/OMPL for risk-aware execution.

Keywords: hidden semi-Markov model; learning from demonstration; unsupervised segmentation; feature fusion; topological persistence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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