Learning Deep Dynamical Systems using Stable Neural ODEs

Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories; however, they have three shortcomings: a) the DS is assumed to have a single attractor, which limits the diversity of tasks it can achieve, b) state derivative information is assumed to be available in the learning process and c) the state of the DS is assumed to be measurable at inference time. We propose a class of provably stable latent DS with possibly multiple attractors, that inherit the training methods of Neural Ordinary Differential Equations, thus, dropping the dependency on state derivative information. A diffeomorphic mapping for the output and a loss that captures time-invariant trajectory similarity are proposed. We validate the efficacy of our approach through experiments conducted on a public dataset of handwritten shapes and within a simulated object manipulation task.

Authors

• Andreas Sochopoulos
• Michael Gienger
• Sethu Vijayakumar

Keywords

• Training
• Learning systems
• Shape
• Ordinary differential equations
• Stability analysis
• Time measurement
• Trajectory
• Dynamical systems
• Thermal stability
• Lyapunov methods
• System Dynamics
• Similar Trajectories
• Robotic Tasks
• Multiple Attractors
• Loss Function
• Energy Function
• Phase Space
• Radial Basis Function
• Feed-forward Network
• Latent Space
• Lyapunov Function
• Gaussian Mixture Model
• Training Loss
• Robot Control
• End-effector
• Robotic Applications
• Human Motion
• Human-robot Interaction
• Output Map
• Static Function
• Output Space
• Inverse Reinforcement Learning
• Stability Guarantees
• Actual Trajectory
• Vector Field
• Arbitrary Interval
• Mean Square Error Loss
• RGB Images
• Mean Square Error
• End-effector Position