Learning Complex Motion Plans using Neural ODEs with Safety and Stability Guarantees
accepted to ICRA 2024
Farhad Nawaz*, Tianyu Li, Nikolai Matni, Nadia Figueroa
*farhadn@seas.upenn.edu
Abstract: We propose a Dynamical System (DS) approach to learn complex, possibly periodic motion plans from kinesthetic demonstrations using Neural Ordinary Differential Equations (NODE). To ensure reactivity and robustness to disturbances, we propose a novel approach that selects a target point at each time step for the robot to follow, by combining tools from control theory and the target trajectory generated by the learned NODE. A correction term to the NODE model is computed online by solving a quadratic program that guarantees stability and safety using Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs), respectively. Our approach outperforms baseline DS learning techniques on the LASA handwriting dataset and complex periodic trajectories. It is also validated on the Franka Emika robot arm to produce stable motions for wiping and stirring tasks that do not have a single attractor, while being robust to perturbations and safe around humans and obstacles.
Abstract: We propose a Dynamical System (DS) approach to learn complex, possibly periodic motion plans from kinesthetic demonstrations using Neural Ordinary Differential Equations (NODE). To ensure reactivity and robustness to disturbances, we propose a novel approach that selects a target point at each time step for the robot to follow, by combining tools from control theory and the target trajectory generated by the learned NODE. A correction term to the NODE model is computed online by solving a quadratic program that guarantees stability and safety using Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs), respectively. Our approach outperforms baseline DS learning techniques on the LASA handwriting dataset and complex periodic trajectories. It is also validated on the Franka Emika robot arm to produce stable motions for wiping and stirring tasks that do not have a single attractor, while being robust to perturbations and safe around humans and obstacles.
Illustration of a spurious attractor in the presence of a disturbance
Illustration of a spurious attractor in the presence of a disturbance
Motion plan using NODE
Motion plan using the corrected CLF-NODE
Stirring a pan with disturbances
Stirring a pan with disturbances
Kinesthetic teaching
Task execution with human interaction
The blue arrow denotes a perturbation away from the nominal target trajectory
Wiping a mannequin with disturbances
Wiping a mannequin with disturbances
Kinesthetic teaching
Task execution with disturbances
The blue arrows denote perturbations away from the nominal target trajectory
Wiping a white board with dynamic obstacles
Wiping a white board with dynamic obstacles
Kinesthetic teaching
Nominal task execution
Dynamic obstacle avoidance
The purple spheres denote the moving obstacle at different time
Comparison of trajectory reproductions on periodic motions
Comparison of trajectory reproductions on periodic motions
I Shape
O Shape
S Shape
Wiping a white board
Wiping a mannequin
Disturbance rejection and obstacle avoidance on LASA data set
Disturbance rejection and obstacle avoidance on LASA data set
Performance comparison on some shapes from LASA data set
Performance comparison on some shapes from LASA data set
