ErgoSurf: Ergodic Control for the Coverage of Unknown Surfaces

Contact-centric tasks on surfaces, ranging from inspection and cleaning to sanding and polishing, require robots to systematically cover the surface while maintaining stable contact. Ergodic control generates trajectories that spend time at a location proportional to a desired, task-specific spatial distribution, enabling efficient information gathering and coverage. However, traditional ergodic control methods rely on prior knowledge of surface geometry or require a vision sensory input to scan the geometry beforehand, limiting their applicability in real-world scenarios with unknown or dynamic environments. This paper introduces a novel online ergodic control framework that achieves systematic surface coverage while simultaneously reconstructing unknown surface geometry. We employ a Gaussian Process Implicit Surface (GPIS) model that learns global surface geometry from intrinsic tactile sensing during execution. For efficient online planning, we approximate the surface locally using point clouds sampled from tangent planes at observed contact points and iteratively fit them to the Gaussian Process. This approximation simultaneously serves as the sampling domain for both the target and the coverage distributions. We employ a heat-diffusion analogy to compute potential fields that guide ergodic exploration, translating spatial coverage objectives into smooth robot trajectories. We demonstrate our framework through simulation and real-robot experiments, validating simultaneous ergodic coverage and online surface geometry learning with reconstruction errors approaching the ground truth.