Infinite-Horizon Ergodic Control via Kernel Mean Embeddings

TL;DR

This paper introduces an infinite-horizon ergodic control method using kernel mean embeddings, enabling long-duration coverage tasks with scalable computation and proven convergence.

Contribution

It extends kernel-based ergodic control to infinite time horizons by developing a recursive extended state, allowing scalable long-duration coverage.

Findings

The controller guarantees asymptotic convergence.

It preserves ergodic coverage in 2D and 3D tasks.

The method is applicable to general domains.

Abstract

This paper derives an infinite-horizon ergodic controller based on kernel mean embeddings for long-duration coverage tasks on general domains. While existing kernel-based ergodic control methods provide strong coverage guarantees on general coverage domains, their practical use has been limited to sub-ergodic, finite-time horizons due to intractable computational scaling, prohibiting its use for long-duration coverage. We resolve this scaling by deriving an infinite-horizon ergodic controller equipped with an extended kernel mean embedding error visitation state that recursively records state visitation. This extended state decouples past visitation from future control synthesis and expands ergodic control to infinite-time settings. In addition, we present a variation of the controller that operates on a receding-horizon control formulation with the extended error state. We demonstrate theoretical proof of asymptotic convergence of the derived controller and show preservation of ergodic coverage guarantees for a class of 2D and 3D coverage problems.