Invariant Stochastic Filtering on SE(3) for Inertial-Encoder State Estimation of Serial Rigid Manipulators

• URL: http://arxiv.org/abs/2607.00026v1
• Date: Sun, 21 Jun 2026 08:11:39 GMT
• Title: Invariant Stochastic Filtering on SE(3) for Inertial-Encoder State Estimation of Serial Rigid Manipulators
• Abstract summary: An invariant extended Kalman filter (IEKF) is developed for state estimation of serial rigid manipulators.<n>The Riccati equation governs the true error covariance rather than a local approximation.<n>A physically separated noise model treats gyroscope and accelerometer channels independently.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An invariant extended Kalman filter (IEKF) is developed for state estimation of serial rigid manipulators with an arbitrary number of links, formulated entirely within the Lie group SE(3). The group-affine property of the kinematic equations makes the linearised error dynamics autonomous, so the Riccati equation governs the true error covariance rather than a local approximation. A physically separated noise model treats gyroscope and accelerometer channels independently: the accelerometer provides translational twist via gravity-compensated integration, yielding a measurement covariance that scales with the sample interval in exact analogy with process noise discretisation; a state-dependent Coriolis noise term captures gyroscope noise propagating through the nonlinear dynamics, vanishing at rest and growing with twist magnitude. The filter is structured as a modular chain of per-link IEKFs in which the predicted covariance of each link depends on its predecessor only through the Adjoint-transformed posterior, giving linear computational cost in link count. Exponential ultimate boundedness in mean square is established via a Lie algebra Lyapunov function, with per-link bounds chained through the Adjoint operator norm to yield a stability certificate that is modular and scalable to arbitrary chain length. Numerical results validate the design.

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