ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations. We prove the Lyapunov stability for a class of Stochastic Differential Equations and we propose a learning algorithm to learn them from a set of demonstrated trajectories. Our model extends the set of stable dynamical systems that can be represented by state-of-the-art approaches, eliminates the Gaussian assumption on the demonstrations, and outperforms the previous algorithms in terms of representation accuracy. We show the effectiveness of our method with both standard datasets and a real robot experiment.

Authors

• Julen Urain
• Michele Ginesi
• Davide Tateo
• Jan Peters 0001

Keywords

• Heuristic algorithms
• Stochastic processes
• Differential equations
• Trajectory
• Nonlinear dynamical systems
• Mathematical model
• Standards
• System Dynamics
• Stability Of System
• Stochastic Dynamical Systems
• Learning Algorithms
• Asymptotically Stable
• Stochastic Differential Equations
• Real Robot
• Deep Generative Models
• Dynamic Model
• Deep Models
• Quadratic Function
• Conditional Probability
• Stationary Distribution
• Latent Space
• Lyapunov Function
• Dynamic Stability
• Orthogonal Matrix
• Rule Changes
• Polar Coordinates
• Linear Dynamics
• Limit Cycle
• Inverse Reinforcement Learning
• Lyapunov Candidate
• Global Stability
• Motion Primitives
• Quadratic Lyapunov Function
• Imitation Learning
• Reproducing Kernel Hilbert Space
• Contractive