This paper addresses the problem of estimating the attitude of a robotic platform using biased measurements of: (i) the direction of the gravitational field and (ii) angular velocity obtained from a set of high-grade gyroscopes sensitive to the Earth’s rotation. A cascade solution is proposed that features a Kalman filter (KF) tied to a rotation matrix observer built on the special orthogonal group of order 3. The KF, whose model stems from a uniformly observable linear time-varying system, yields estimates of: (i) the Earth’s total rotational rate; (ii) two sensor biases associated with the aforementioned measurements; and, (iii) noise-filtered and bias-corrected accelerometer data. All estimates are expressed in the platform’s body-fixed frame. In turn, the attitude observer put forward is shown to be almost globally asymptotically stable, in particular locally input-to-state stable with respect to the KF errors. Experimental results are showcased that successfully demonstrate the efficiency of the proposed attitude estimation solution.

本文解决了使用以下偏差测量来估计机器人平台姿态的问题：（i）重力场的方向和（ii）从一组对地球旋转敏感的高级陀螺仪获得的角速度。提出了一种级联解决方案，其特征是将卡尔曼滤波器（KF）绑定到建立在3阶特殊正交组上的旋转矩阵观察器上。该KF模型的模型来自一致可观察的线性时变系统，其得出的估计为：（ i）地球的总自转率；（ii）与上述测量相关的两个传感器偏置；（iii）经过噪声过滤和偏置校正的加速度计数据。所有估算值均以平台的固定框架表示。反过来，事实证明观察者提出的态度在全球范围内几乎是渐近稳定的，特别是对于KF误差在本地输入到状态稳定。实验结果表明，可以成功地证明所提出的姿态估计解决方案的效率。