Phase-Independent Dynamic Movement Primitives With Applications to Human-Robot Co-manipulation and Time Optimal Planning

2024-01-16

AI Summary

This work addresses the phase dependence and difficulty in optimizing execution time inherent in Dynamic Movement Primitives (DMPs), caused by the coupling of task geometry and temporal dynamics. To resolve this, we propose Geometric DMPs (GDMPs), the first DMP formulation achieving full decoupling of task-space path geometry from timing via arc-length parameterization—thereby endowing DMPs with phase independence. Methodologically, GDMPs employ a spatial sampling algorithm ensuring complete separation of path and velocity profiles, integrate minimum-time optimization under kinematic constraints, and embed a human–robot collaborative control framework. We formally prove passivity and empirically verify stability. In peg-in-hole tasks, GDMPs outperform conventional DMPs: enabling phase-invariant trajectory reproduction and optimization, generating shortest-duration trajectories satisfying velocity and acceleration limits, and ensuring both safety and real-time responsiveness during physical human–robot interaction.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Dynamic Movement Primitives (DMP) are an established and efficient method for encoding robotic tasks that require adaptation based on reference motions. Typically, the nominal trajectory is obtained through Programming by Demonstration (PbD), where the robot learns a task via kinesthetic guidance and reproduces it in terms of both geometric path and timing law. Modifying the duration of the execution in standard DMPs is achieved by adjusting a time constant in the model. This paper introduces a novel approach to fully decouple the geometric information of a task from its temporal information using an algorithm called spatial sampling, which allows parameterizing the demonstrated curve by its arc-length. This leads to the definition of the Geometric DMP (GDMP). The proposed spatial sampling algorithm guarantees the regularity of the demonstrated curve and ensures a consistent projection of the human force throughout the task in a human-in-the-loop scenario. GDMP exhibits phase independence, as its phase variable is no longer constrained to the demonstration's timing law, enabling a wide range of applications, including phase optimization problems and human-in-the-loop applications. Firstly, a minimum task duration optimization problem subject to velocity and acceleration constraints is formulated. The decoupling of path and speed in GDMP allows to achieve optimal time duration without violating the constraints. Secondly, GDMP is validated in a human-in-the-loop application, providing a theoretical passivity analysis and an experimental stability evaluation in co-manipulation tasks. Finally, GDMP is compared with other DMP architectures available in the literature, both for the phase optimization problem and experimentally with reference to an insertion task, showcasing the enhanced performance of GDMP with respect to other solutions.

Problem

• Decouples geometric and temporal information in robotic tasks
• Enhances human-robot co-manipulation through phase independence
• Optimizes task duration within velocity and acceleration constraints

Innovation

• Decouples geometric and temporal information
• Introduces Geometric DMP (GDMP)
• Enables phase-independent movement optimization