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

arXiv: https://arxiv.org/abs/2112.04612 · HTML: https://mlsanity.com/paper/2112.04612/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 12 of 12)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [A survey of robot learning from demonstrations for Human-Robot Collaboration](https://mlsanity.com/paper/1710.08789/) (2017)
- [Explaining Multi-stage Tasks by Learning Temporal Logic Formulas from Suboptimal Demonstrations](https://mlsanity.com/paper/2006.02411/) (2020)
- [Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty](https://mlsanity.com/paper/2001.09336/) (2020)
- [Learning Parametric Constraints in High Dimensions from Demonstrations](https://mlsanity.com/paper/1910.03477/) (2019)
- [Uncertainty-Aware Constraint Learning for Adaptive Safe Motion Planning from Demonstrations](https://mlsanity.com/paper/2011.04141/) (2020)
- [Exploiting gradients and Hessians in Bayesian optimization and Bayesian quadrature](https://mlsanity.com/paper/1704.00060/) (2017)
- [Learning Constraints from Demonstrations](https://mlsanity.com/paper/1812.07084/) (2018)
- [Learning Equality Constraints for Motion Planning on Manifolds](https://mlsanity.com/paper/2009.11852/) (2020)
- [Inferring Obstacles and Path Validity from Visibility-Constrained Demonstrations](https://mlsanity.com/paper/2005.05421/) (2020)

## Built on by (most cited first, 6 of 6)

- [Data-Efficient Learning of Natural Language to Linear Temporal Logic Translators for Robot Task Specification](https://mlsanity.com/paper/2303.08006/) (2023)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [Maximum Causal Entropy Inverse Constrained Reinforcement Learning](https://mlsanity.com/paper/2305.02857/) (2023)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [DIAL: Distribution-Informed Adaptive Learning of Multi-Task Constraints for Safety-Critical Systems](https://mlsanity.com/paper/2501.18086/) (2025)
- [Active Constraint Learning in High Dimensions from Demonstrations](https://mlsanity.com/paper/2512.22757/) (2025)

## Abstract (arXiv)

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.