This work presents a finite-time stable pose estimator (FTS-PE) for rigid bodies undergoing rotational and translational motion in three dimensions, using measurements from onboard sensors that provide position vectors to inertially-fixed points and body velocities. The FTS-PE is a full-state observer for the pose (position and orientation) and velocities and is obtained through a Lyapunov analysis that shows its stability in finite time and its robustness to bounded measurement noise. Further, this observer is designed directly on the state space, the tangent bundle of the Lie group of rigid body motions, SE(3), without using local coordinates or (dual) quaternion representations. Therefore, it can estimate arbitrary rigid body motions without encountering singularities or the unwinding phenomenon and be readily applied to autonomous vehicles. A version of this observer that does not need translational velocity measurements and uses only point clouds and angular velocity measurements from rate gyros, is also obtained. It is discretized using the framework of geometric mechanics for numerical and experimental implementations. The numerical simulations compare the FTS-PE with a dual-quaternion extended Kalman filter and our previously developed variational pose estimator (VPE). The experimental results are obtained using point cloud images and rate gyro measurements obtained from a Zed 2i stereo depth camera sensor. These results validate the stability and robustness of the FTS-PE.

翻译：本文提出一种有限时间稳定位姿估计器（FTS-PE），用于估计三维空间中经历旋转与平移运动的刚体。该估计器利用机载传感器提供的惯性系固定点位置矢量与本体速度测量值。FTS-PE是一种针对位姿（位置与姿态）及速度的全状态观测器，通过李雅普诺夫分析证明其具有有限时间稳定性，并对有界测量噪声具有鲁棒性。该观测器直接在设计状态空间——刚体运动李群SE(3)的切丛上构建，无需使用局部坐标或（对偶）四元数表示。因此，它能估计任意刚体运动而不会遇到奇异性或解卷绕现象，并可直接应用于自主载具系统。本文还推导了该观测器的一个变体版本，该版本无需平移速度测量，仅需使用点云数据与速率陀螺提供的角速度测量。通过几何力学框架对观测器进行离散化处理，以支持数值仿真与实验实现。数值仿真将FTS-PE与对偶四元数扩展卡尔曼滤波器及我们先前开发的变分位姿估计器（VPE）进行对比。实验结果采用Zed 2i立体深度相机传感器获取的点云图像与速率陀螺测量数据。实验结果验证了FTS-PE的稳定性与鲁棒性。