From Movement Primitives to Distance Fields to Dynamical Systems
Yiming Li, Sylvain Calinon
AI summary
Problem
Conventional movement primitives struggle with robust perturbation handling due to their explicit time-dependent representation, while existing autonomous systems often require complex modeling or learning-based estimation.
Approach
MPDS encodes trajectories as concatenated quadratic Bézier curves to analytically compute distance fields, then directly derives stable dynamical systems from spatial gradients without system identification or learning.
Key results
- Analytical distance field computation for quadratic spline trajectories
- Provable asymptotic stability for the derived autonomous dynamical systems
- Low reconstruction error matching or exceeding standard basis functions
- Successful real-world robotic experiments demonstrating perturbation robustness
Why it matters
Offers a simple, model-free alternative for robust motion reproduction and adaptive control, benefiting robot learning and autonomous manipulation research.
Abstract
Developing autonomous robots capable of learning complex motions from demonstrations remains a fundamental challenge in robotics. On the one hand, movement primitives (MP) provide a compact and modular representation of continu- ous trajectories. On the other hand, dynamical systems (DS) pro- vide control policies that are time-independent. In this paper, we propose a simple and flexible approach called MPDS that gathers the advantages of both representations by transforming MPs into autonomous systems. The key idea is to transform the explicit representation of a trajectory to an implicit shape encoded as a distance field. This conversion from a time-dependent motion to a spatial representation enables the construction of an autonomous dynamical system with modular reactions to perturbation. This approach bridges conventional MPs with distance fields, ensuring smooth and precise motion encoding, while maintaining a con- tinuous spatial representation. We use Bernstein basis functions in the MPs to represent trajectories as concatenated quadratic B ́ezier curves, which provide an analytical method for computing distance fields. By simply leveraging the analytic gradients of the curve and its distance field, a stable dynamical system can be computed to reproduce the demonstrated trajectories while handling perturbations, without requiring a model of the dynamical system to be estimated. Numerical simulations and real-world robotic experiments validate our method’s ability to encode complex motion patterns while ensuring trajectory stabil- ity, together with the flexibility of designing the desired reaction to perturbations. An interactive project page demonstrating our approach is available at https://idiap.github.io/mp-df-ds/.