Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems

Abstract

Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work presents a novel approach to learn workspace constraints from human demonstrations and to generate motion trajectories for the robot that lie in the constrained workspace. Training data are incrementally clustered into different linear subspaces and used to fit a low dimensional representation of each subspace. By considering the learned constraint subspaces as zeroing barrier functions, we are able to design a control input that keeps the system trajectory within the learned bounds. This control input is effectively combined with the original system dynamics preserving eventual asymptotic properties of the unconstrained system. Simulations and experiments on a real robot show the effectiveness of the proposed approach.

References in corpus (3)

• Control Barrier Function Based Quadratic Programs for Safety Critical Systems
• Merging Position and Orientation Motion Primitives
• Incremental Skill Learning of Stable Dynamical Systems

Cited by in corpus (9)

• Learning for Safety-Critical Control with Control Barrier Functions
• Constrained Probabilistic Movement Primitives for Robot Trajectory Adaptation
• Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates
• Learning Stable Robotic Skills on Riemannian Manifolds
• Learning Hybrid Control Barrier Functions from Data
• Safety on the Fly: Constructing Robust Safety Filters via Policy Control Barrier Functions at Runtime
• EKMP: Generalized Imitation Learning with Adaptation, Nonlinear Hard Constraints and Obstacle Avoidance
• Safe Feedback Motion Planning in Unknown Environments: An Instantaneous Local Control Barrier Function Approach
• ADMM-MCBF-LCA: A Layered Control Architecture for Safe Real-Time Navigation