Navigation and Control of Unconventional VTOL UAVs in Forward-Flight With Explicit Wind Velocity Estimation

Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$

“…To ensure robustness to state-estimation error, an IEKF based on [26] is used to provide an estimate of the quadrotor states, which are an element of SE 2 (3), and sensor biases. Biased rate gyro and accelerometer measurements are used as interoceptive prediction sensors, and GPS position and velocity measurements, as well as magnetometer measurements, are used as correction sensors.…”

The Geometry of Navigation Problems

“…In various implementations related to the IEKF, researchers -including the authors -have proposed to treat IMU biases in the state linearly, that is, complete SE 2 (3) group law with x 1 + x 2 regarding body variables (biases). This is advocated notably in [10][11][12]14,16,[20][21][22]24] and the term "imperfect IEKF" that refers to it, as well as the technique itself, was coined in [17]. We demonstrate in this paper that the proposed group law (10) is a far better option, both theoretically and in practice.…”

“…The definition encompasses recently introduced Lie groups: SO(d) + k,0 coincides with SE k (d) introduced for SLAM in [30], named SE k (d) in [18], and exploited in [20][21][22][23][24], see also [35]. Similarly SO(3) + 2,0 coincides with SE 2 (3), introduced in [9,17] for navigation and exploited in [11][12][13][14]22]. In various implementations related to the IEKF, researchers -including the authors -have proposed to treat IMU biases in the state linearly, that is, complete SE 2 (3) group law with x 1 + x 2 regarding body variables (biases).…”

“…The discovery that dynamics associated with (unbiased) inertial measurement units (IMU) are group affine in [9] has led to various recent experimental and theoretical successes, e.g. [11][12][13][14][15][16]. 2-IEKF possesses consistency properties when the system is not fully observable as in the problem of Simultaneous Localization and Mapping (SLAM) [17][18][19], as exploited in [20][21][22][23][24][25].…”

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation With Online Calibration

“…A key observation [5] is that the group-affine property only holds for the model of the navigation states and is lost for the combined system when bias is added in this manner. The practical applicability of this approach, named "Imperfect-IEKF" by Barrau [5], has been confirmed by several authors [5], [6], [7]. Recent work [8] on second order systems on Lie-groups has demonstrated that there is a natural symmetry that can be used to model both configuration and velocity states in a single geometry.…”