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Dual Park-Ravani Interpolation of Rigid Motions: Acceleration-Field Continuity and Holonomic Hermite Repair

arXiv · AI, language, vision and robotics · article · Aug 28, 2026 · UTC

The Park-Ravani construction generates a twice continuously differentiable, frame-invariant spline on SO(3) by exponentiating cubic canonical-coordinate polynomials. We show that the construction transfers, without changing form, to the group of orthogonal dual tensors, a representation of rigid displacements. The transferred recurrence is stated compactly through the dual extension of the right Jacobian of the exponential map and its first Fréchet derivative. This yields interpolation of prescribed rigid poses and continuity of the body dual twist and its first derivative. Using the higher-or

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