ROLA-GS: Link-Canonical 3D Gaussian Splatting for Differentiable Robot Self-Modeling

Differentiable robot rendering synthesizes robot images from joint configurations and enables joint-state optimization through image gradients. Although robot kinematics specifies rigid link motion, learned deformation can couple this motion with appearance variation. We introduce \method, a Gaussian visual self-model that separates rigid articulation from appearance modeling through fixed link assignments, exact relative forward kinematics, and pose-dependent appearance correction. Specifically, each Gaussian retains a fixed link assignment, allowing its center and covariance to move rigidly with the assigned link. A bounded appearance correction accounts for radiance variation without altering the transported geometry. This construction restricts each joint's spatial influence to its descendant links and provides differentiable rendering for visual inverse kinematics and selective control. Experiments demonstrate improved reconstruction across diverse robots and lower average errors in visual inverse kinematics and selective control. The results further show that rigid transport and appearance correction improve reconstruction, with rigid transport also improving forward-query efficiency.