AI 中文总结
研究基于扳手的姿态估计问题，提出残差保障的局部矩阵费舍尔 - 高斯推理方法，通过线性化简化扳手残差等构建局部贝叶斯更新，在测试中降低了残差优点和姿态误差，为相关研究提供了新方法及验证。
AI 中文摘要
本文针对\(\mathrm{SO}(3)\times\mathbb{R}^3\)上基于扳手的姿态估计，开发了一种残差保障的局部矩阵费舍尔 - 高斯（MFG）推理方法。力/扭矩测量由准静态接触系统建模，其中预测扳手通过隐式平衡状态依赖于未知物体姿态。由于所得非线性似然与耦合MFG族不全局共轭，通过线性化简化扳手残差并将诱导的高斯 - 牛顿后验模型与耦合MFG分布匹配来构建局部贝叶斯更新。结果表明简化残差雅可比具有舒尔补形式，局部二次后验允许与规定的局部一阶和二阶后验系数匹配的闭式MFG近似。相同的灵敏度模型产生补偿旋转信息得分，表征平移补偿后最弱的局部信息姿态方向。还引入了残差保障的重新居中算法，仅通过降低重新计算的白化扳手残差的候选值来更新线性化点。在测试的稀疏先验不匹配情况下，所得估计器相对于单通道和局部基线变体降低了残差优点和姿态误差，并且受控机器人实验在校准的准静态条件下提供了概念验证。
英文摘要
In this paper, a residual-safeguarded local Matrix Fisher--Gaussian (MFG) inference method is developed for wrench-based pose estimation on $\mathrm{SO}(3)\times\mathbb{R}^3$. The force/torque measurements are modeled by a quasi-static contact system in which the predicted wrench depends on the unknown object pose through an implicit equilibrium state. Since the resulting nonlinear likelihood is not globally conjugate to the coupled MFG family, a local Bayesian update is constructed by linearizing the reduced wrench residual and matching the induced Gauss--Newton posterior model to a coupled MFG distribution. It is shown that the reduced residual Jacobian has a Schur-complement form, and that the local quadratic posterior admits a closed-form MFG approximation matching the prescribed local first- and second-order posterior coefficients. The same sensitivity model yields a compensated rotational information score, which characterizes the weakest locally informative attitude direction after translational compensation. A residual-safeguarded recentering algorithm is further introduced to update the linearization point only through candidates that decrease the recomputed whitened wrench residual. In the tested sparse prior-mismatch regimes, the resulting estimator reduces residual merit and pose error relative to single-pass and local baseline variants, and controlled robot experiments provide a proof of concept under calibrated quasi-static conditions.
CommentsThe main text contains 13 pages; supplementary materials can be found in Ancillary files: SM.pdf
