Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrations

TL;DR

This paper introduces a scalable method for learning complex constraints as Gaussian processes from demonstrations, enabling probabilistically-safe motion planning in high-dimensional systems with minimal prior knowledge.

Contribution

The authors develop a novel approach using KKT conditions to learn constraints as GPs from demonstrations, improving accuracy and scalability over previous methods.

Findings

Successfully learned nonlinear constraints for diverse systems

Achieved probabilistic safety guarantees in planning

Outperformed prior constraint learning methods

Abstract

We propose a method for learning constraints represented as Gaussian processes (GPs) from locally-optimal demonstrations. Our approach uses the Karush-Kuhn-Tucker (KKT) optimality conditions to determine where on the demonstrations the constraint is tight, and a scaling of the constraint gradient at those states. We then train a GP representation of the constraint which is consistent with and which generalizes this information. We further show that the GP uncertainty can be used within a kinodynamic RRT to plan probabilistically-safe trajectories, and that we can exploit the GP structure within the planner to exactly achieve a specified safety probability. We demonstrate our method can learn complex, nonlinear constraints demonstrated on a 5D nonholonomic car, a 12D quadrotor, and a 3-link planar arm, all while requiring minimal prior information on the constraint. Our results suggest the learned GP constraint is accurate, outperforming previous constraint learning methods that require more a priori knowledge.