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

Farong Wang; Sai Swaminathan; Fei Liu

cs.ROMar 17, 2026

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

Authors: Farong Wang, Sai Swaminathan, Fei Liu

Organizations: All authors are with the Min H. Kao Department of Electrical Engineering and Computer Science (EECS), University of Tennessee, Knoxville (UTK), Knoxville, TN 37996, USA.

Abstract

Robotic manipulation tasks that require repeated tool motion along curved surfaces frequently arise in surface finishing, inspection, and guided interaction. In practice, nominal motion primitives are often designed independently of the deployment surface and later reused across varying geometries. Directly tiling such primitives onto nonplanar surfaces introduces geometric inconsistencies, leading to interpenetration, orientation discontinuities, and cumulative drift over repeated cycles. We present a two-stage framework that separates geometric embedding from execution-level regulation. An offline surface-constrained warping operator embeds a nominal periodic primitive onto curved surfaces through asymmetric diffeomorphic deformation of dual-track waypoints and axis-consistent orientation completion, producing a surface-adapted reference trajectory. An online contact-aware projection operator then enforces bounded deviation relative to this reference using FSR-driven disturbance adaptation and a conic orientation safety constraint. Experiments across multiple analytic surface families and real-robot validation on a sinusoidal surface demonstrate improved geometric continuity, reduced large orientation jumps, and robust contact maintenance compared with direct tiling. These results show that decoupling offline geometric remapping from lightweight online projection enables stable and repeatable surface-embedded trajectory execution under sensor-lite feedbacks.

Figures & tables

Fig. 1 : Surface-constrained robotic trajectory execution with stable contact. A robotic end-effector follows a warped periodic trajectory over a curved surface using offline geometric warping and online contact-aware projection for stable and drift-free interaction, with applications in polishing, coating, inspection, and surgical assistance.

Fig. 2 : Problem formulation and execution pipeline. A nominal periodic trajectory

\mathbf{T}^{\mathrm{nom}}

is first adapted to a surface-embedded guide curve

\gamma(s)

through the offline warping operator

\mathcal{W}_{\Phi}

, producing a surface-consistent warped trajectory

\mathbf{T}^{\mathrm{warp}}

(orange). During execution, an online projection operator

\mathcal{E}

constrains the executed pose

\mathbf{T}^{\mathrm{proj}}

within a conic feasible set around the warped orientation while regulating position along gravity using contact-feedback measurements. This two-stage formulation separates offline geometric embedding from online safety-constrained execution.

Fig. 3 : Offline surface-constrained warping pipeline. Step 1 extracts a single-period primitive and tiles its waypoints along a surface guide curve, separating contact (

\mathcal{I}_{c}

, green waypoints) and free-space (

\mathcal{I}_{f}

, orange waypoints) samples. Step 2 constructs a dual-track tool-axis parameterization using coupled base and tip waypoints. Step 3 applies a surface-constrained diffeomorphic deformation driven by local surface geometry. Step 4 constructs the final warped pose sequence

\mathbf{T}_{k}^{\mathrm{warp}}

by combining the deformed waypoints (with contact-critical waypoints anchored) with axis-consistent orientation completion.

Fig. 4 : Contact-aware online projection under FSR-driven disturbances. Force feedback perturbs the warped pose

\mathbf{T}_{k}^{\mathrm{warp}}

: low force drives downward motion, while high force drives upward motion. The disturbed pose is then projected into the conic feasible set, yielding

\mathbf{T}_{k}^{\mathrm{proj}}

with bounded orientation deviation and stable contact.

Fig. 5 : Collision-prone configurations under direct tiling. First row: tiled ( $\mathbf{T}^{\mathrm{tile}}$ ). Second row: warped ( $\mathbf{T}^{\mathrm{warp}}$ ). Direct tiling remains feasible on the convex surface but becomes collision-prone on the concave surface due to an unsafe local attitude. Offline warping produces a surface-consistent trajectory that avoids this failure mode.

Fig. 6 : Continuity correction on a convex surface. First row: tiled . Second row: warped . Compared with direct tiling, the warped trajectory yields smoother and more monotone local pose evolution along the same guide neighborhood.

Fig. 7 : Real-robot validation under disturbances and abrupt height reduction. The proposed FSR-conic Projection improves contact consistency during disturbed execution and recovers from sudden surface-height reduction through translational adaptation, while conic filtering maintains bounded orientation deviation throughout the motion.

Surf.	#Pair	#Step	Med. $\Delta(\mathrm{d}\theta_{p95})$	BadRot t	BadRot w	$\Delta$
cos	4	463	-14.98	0.093	0.000	0.093
cubic	1	98	-0.05	0.000	0.000	0.000
exp	3	1121	-0.99	0.005	0.000	0.005
parabolic	4	436	-6.77	0.037	0.000	0.037
sin	4	471	-16.59	0.125	0.016	0.109

TABLE I : Surface-family continuity summary (warped vs. tiled). #Pair denotes the number of paired tiled/warped trajectories, and #Step denotes the total number of evaluated pose transitions from the tiled trajectories. Median

\Delta(\mathrm{d}\theta_{p95})

(deg) is warped minus tiled (negative is better). BadRot t / BadRot w are the average fractions of steps with

\Delta\theta_{k}>10^{\circ}

for tiled / warped .

Fig. 8 : Representative simulation results of offline warping. Examples compare tiled ( $T^{\mathrm{tile}}$ ) and warped ( $T^{\mathrm{warp}}$ ) trajectories. Direct tiling may produce collision-prone or geometrically inconsistent poses near complex surface regions, whereas offline warping yields surface-consistent and smoother motion.

Robot Motion Generation

Robot motion generation creates feasible, task-directed trajectories for robots to move, manipulate objects, and interact with people and environments.

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Mobile Robotics Ergodic Control

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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.

Abstract

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