Data-Driven Chance Constrained Control using Kernel Distribution Embeddings

TL;DR

This paper introduces a data-driven method using kernel distribution embeddings to efficiently solve stochastic control problems with chance constraints, without assuming specific system models, demonstrated on nonlinear dynamics in cluttered environments.

Contribution

The paper proposes a novel kernel embedding-based framework for chance constrained control that avoids prior system assumptions and simplifies the problem to a convex optimization task.

Findings

Effective in simulation with nonlinear, non-Markovian dynamics

Handles complex environments with cluttered obstacles

Provides a scalable, data-driven control solution

Abstract

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment.