Surface-Constrained Offline Warping with Contact-Aware Online Pose Projection for Safe Robotic Trajectory Execution

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.

Robotic surface-interaction tasks, such as spray painting or welding, require both accurate geometric planning and precise motion execution. While modern motion planners generate valid geometric paths, they often lack the expert motor patterns observed in human operators. Conversely, learning from demonstration often tightly couples task execution to the specific training geometry, limiting transferability. We propose a modular framework that decouples geometric motion planning from execution-level expertise. Expert behavior is represented as a vocabulary of interpretable, atomic motor rules, such as velocity scaling and orientation offsets, that systematically modify a geometrically planned reference path. We train a multimodal neural network to infer rule parameters jointly from kinematic trajectory data and CAD model geometry. We evaluate our approach through dynamic simulation on L-shaped and window-shaped objects, demonstrating on simulated data that the model successfully extracts velocity and orientation rules across both topologies.

Diffusion-based imitation learning methods have driven rapid progress in robot dexterous manipulation tasks. However, they have limitations when applied to tasks that involve complex free-form surface constraints because of their lack of explicit surface geometry constraint modeling and the dynamic feasibility issue, resulting in stochastic action generation that fails to achieve reliable surface alignment and maintain stable contact. To address these limitations, we propose a novel surface constraint policy (SCP) for generating robot actions that satisfy free-form surface constraints on the basis of human demonstrations and real-time visual observations. First, the surface geometry constraint is encoded using a two-dimensional weighted Gaussian kernel function that is derived from demonstrations. Building on the encoded surface geometry constraints, the diffusion-based policy is used to infer task-level action intentions from multimodal sensory inputs, including visual observations and robot state feedback. These intentions are further transformed into surface-constrained dynamic movement primitives (DMPs) through a similarity-based action mapping method, thereby enabling smooth and compliant motion execution. The SCP achieves generation of structured surface geometric intent and dynamically admissible actions. The proposed method is validated on multiple surface manipulation tasks and compared with existing techniques. The experimental results demonstrate superior task success rates and contact stability under surface constraints.