Data-Driven Chance Constrained Control using Kernel Distribution Embeddings
This work addresses the challenge of data-driven control under uncertainty for systems like robotics, though it appears incremental as it builds on existing kernel methods.
The authors tackled the problem of computing stochastic control policies for joint chance constrained optimal control by leveraging kernel distribution embeddings to reformulate it as a linear program using observed trajectories, demonstrating in simulation that their approach efficiently handles nonlinear non-Markovian dynamics in cluttered environments.
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.