Publication record · 18.cifr/2014.barfoot.se3-uncertainty

Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems

v1.0.0

Timothy D. Barfoot (University of Toronto), Paul T. Furgale (ETH Zurich)

RAI18.cifr/2014.barfoot.se3-uncertainty

IEEE Transactions on Robotics· 2014· doi:10.1109/TRO.2014.2298059

In this paper, we provide a mathematically rigorous framework for associating uncertainty with poses in SE(3). We use a perturbative approach based on the Lie algebra of SE(3) and derive expressions for propagating covariances through pose composition, inversion, and point transformation. The expressions are accurate to higher order than classical methods and avoid singularities inherent in Euler-angle parameterizations.

SE(3)Lie groupsuncertainty propagationpose estimationSLAMcovariance

✦ Research context

What this agent contributes to the literature.

Problem solved

Robotics estimation algorithms such as SLAM and visual odometry need accurate 3D pose uncertainty representations. Classical approaches linearize about the identity or use singular Euler parameterizations, losing accuracy for large uncertainties. This work provides consistent, singularity-free covariance propagation directly on SE(3).

Novelty

Derives closed-form fourth-order BCH expressions for propagating uncertainty on SE(3) entirely in the Lie algebra, avoiding Euler-angle singularities and first-order linearization errors. Introduces compound pose uncertainty formulas that respect the non-commutativity of SE(3).

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Canvas contract1-in / 1-out · unpacked into poses, params legacy ports

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sha256:1a4489371b4cef53dc6bc66d0da25448afc38167d86df18b2b3a027ff1f9dd4c

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python main.py

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input:application/json

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output:application/json

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Pre-filled with the paper's canonical scenario. Click Invoke agent to reproduce the original result, or edit the JSON below to run a counterfactual.

inputapplication/jsonoptional

Unified canvas input containing poses, covariances, and operation parameters

Leave empty to run the paper's canonical scenario.

{
  "poses": {
    "poses": [
      {
        "T": [
          [
            1,
            0,
            0,
            0.1
          ],
          [
            0,
            1,
            0,
            0
          ],
          [
            0,
            0,
            1,
            0
          ],
          [
            0,
            0,
            0,
            1
          ]
        ],
        "cov": [
          [
            0.01,
            0,
            0,
            0,
            0,
            0
          ],
          [
            0,
            0.01,
            0,
            0,
            0,
            0
          ],
          [
            0,
            0,
            0.01,
            0,
            0,
            0
          ],
          [
            0,
            0,
            0,
            0.001,
            0,
            0
          ],
          [
            0,
            0,
            0,
            0,
            0.001,
            0
          ],
          [
            0,
            0,
            0,
            0,
            0,
            0.001
          ]
        ]
      }
    ]
  },
  "params": {
    "operation": "compose",
    "order": 2
  }
}

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