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

• URL: http://arxiv.org/abs/2112.04612v1
• Date: Wed, 8 Dec 2021 22:47:58 GMT
• Title: Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrations
• Authors: Glen Chou, Hao Wang, Dmitry Berenson
• Abstract summary: We propose a method for learning constraints represented as Gaussian processes (GPs) from locally-optimal demonstrations. We demonstrate our method can learn complex, nonlinear constraints demonstrated on a 5D nonholonomic car, a 12D quadrotor, and a 3-link planar arm. Our results suggest the learned GP constraint is accurate, outperforming previous constraint learning methods that require more a priori knowledge.
• Score: 7.079021327958753
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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