Infinite-Horizon Ergodic Control via Kernel Mean Embeddings
This work addresses a computational bottleneck for researchers and practitioners in robotics and control systems, enabling long-duration coverage applications, though it is incremental as it builds on existing kernel-based methods.
The paper tackles the computational scaling issue of kernel-based ergodic control for long-duration coverage tasks by deriving an infinite-horizon controller with an extended kernel mean embedding error state, enabling asymptotic convergence and preserving coverage guarantees in 2D and 3D problems.
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.