Reactive Motion Generation via Phase-varying Neural Potential Functions

2026-04-29

AI Summary

This work addresses the challenges of motion direction ambiguity, sensitivity to external perturbations, and poor phase recovery inherent in learning from demonstrations involving intersecting trajectories—such as figure-eight paths—by proposing a Phase-variable Neural Potential Field (PNPF) framework. PNPF integrates a dynamically estimated phase variable with a neural potential field to generate a local vector field modulated by phase, enabling stable and reactive control for point-to-point, periodic, and 6D trajectory tasks. Compared to existing approaches, PNPF significantly enhances robustness and generalization on intersecting trajectories, supports real-time robotic execution, and achieves rapid phase recovery and accurate trajectory tracking under disturbances.

Abstract

Dynamical systems (DS) methods for Learning-from-Demonstration (LfD) provide stable, continuous policies from few demonstrations. First-order dynamical systems (DS) are effective for many point-to-point and periodic tasks, as long as a unique velocity is defined for each state. For tasks with intersections (e.g., drawing an "8"), extensions such as second-order dynamics or phase variables are often used. However, by incorporating velocity, second-order models become sensitive to disturbances near intersections, as velocity is used to disambiguate motion direction. Moreover, this disambiguation may fail when nearly identical position-velocity pairs correspond to different onward motions. In contrast, phase-based methods rely on open-loop time or phase variables, which limit their ability to recover after perturbations. We introduce Phase-varying Neural Potential Functions (PNPF), an LfD framework that conditions a potential function on a phase variable which is estimated directly from state progression, rather than on open-loop temporal inputs. This phase variable allows the system to handle state revisits, while the learned potential function generates local vector fields for reactive and stable control. PNPF generalizes effectively across point-to-point, periodic, and full 6D motion tasks, outperforms existing baselines on trajectories with intersections, and demonstrates robust performance in real-time robotic manipulation under external disturbances.

Problem

• Learning from Demonstration
• Dynamical Systems
• Motion Generation
• Phase Variables
• Trajectory Intersections

Innovation

• Phase-varying Neural Potential Functions
• Learning from Demonstration
• Reactive Motion Generation
• Dynamical Systems
• Robust Robotic Control