Martin Barczyk

Integration of a Triaxial Magnetometer into a Helicopter UAV GPS-Aided INS

The University of Albertas Applied Nonlinear Controls Lab (ANCL) helicopter unmanned aerial vehicles (UAVs) existing GPS-aided inertial navigation system (INS) does not provide observability of heading angle during hover. This motivates the integration of a triaxial magnetometer aiding sensor into the extended Kalman filter (EKF)-based navigation algorithm. A novel magnetometer calibration procedure is implemented and compared with conventional approaches. Experimental results in ground and flight testing confirm that the observability issue is resolved and demonstrate improvements in attitude estimation.

Invariant Observer Design for a Helicopter UAV Aided Inertial Navigation System

The invariant observer is a recently introduced constructive nonlinear design method for symmetry-possessing systems such as the magnetometer-plus-global positioning system (GPS)-aided inertial navigation system (INS) example considered in this paper. The resulting observer guarantees a simplified form of the nonlinear estimation error dynamics, which can be stabilized by a proper choice of observer gains using a nonlinear analysis. A systematic approach to this step is the invariant Extended Kalman Filter (EKF), which is modified from its originally proposed form and applied to the aided INS example to obtain the observer gains. The resulting invariant observer is implemented onboard an outdoor helicopter unmanned aerial vehicle platform and successfully validated in experiment and demonstrates an improvement in performance over a conventional (non-invariant) EKF design.

Invariant EKF Design for Scan Matching-Aided Localization

Localization in indoor environments is a technique that estimates the robots pose by fusing data from onboard motion sensors with readings of the environment, in our case obtained by scan matching point clouds captured by a low-cost Kinect depth camera. We develop both an invariant extended Kalman filter (IEKF)-based and a multiplicative extended Kalman filter-based solution to this problem. The two designs are successfully validated in experiments and demonstrate the advantage of the IEKF design.

Control-oriented modeling of a helicopter UAV with a Bell-Hiller stabilizer mechanism

We derive a control-oriented model for a helicopter UAV whose complexity is sufficiently low to be usable for model-based control design yet which accurately reflects the dominant physics. The model consists of rigid-body dynamics coupled with simplified models of its subsystems: main rotor, Bell-Hiller system and tail rotor. The Bell-Hiller system is shown to provide a derivative feedback action in flight. The physical parameters of the resulting model are directly identified through a series of measurements explained throughout.

Invariant Extended Kalman Filter design for a magnetometer-plus-GPS aided inertial navigation system

We introduce a magnetometer-plus-GPS aided inertial navigation system for a helicopter UAV. A nonlinear observer is required to estimate the navigation states, typically an Extended Kalman Filter (EKF). A novel approach is the invariant observer, a constructive design method applicable to systems possessing symmetries. We review the theory and design an invariant observer for our example. Using an invariant observer guarantees a simplified form of the nonlinear estimation error dynamics. These are stabilized using an adaptation of the Invariant EKF, a systematic approach to compute the gains of an invariant observer. The resulting design is successfully implemented and validated in experiment and shows an improvement in performance over a conventional EKF.

On the covariance of ICP-based scan-matching techniques

This paper considers the problem of estimating the covariance of roto-translations computed by the Iterative Closest Point (ICP) algorithm. The problem is relevant for localization of mobile robots and vehicles equipped with depth-sensing cameras (e.g., Kinect) or Lidar (e.g., Velodyne). The closed-form formulas for covariance proposed in previous literature generally build upon the fact that the solution to ICP is obtained by minimizing a linear least-squares problem. In this paper, we show this approach needs caution because the rematching step of the algorithm is not explicitly accounted for, and applying it to the point-to-point version of ICP leads to completely erroneous covariances. We then provide a formal mathematical proof why the approach is valid in the point-to-plane version of ICP, which validates the intuition and experimental results of practitioners.

Experimental implementation of an Invariant Extended Kalman Filter-based scan matching SLAM

We describe an application of the Invariant Extended Kalman Filter (IEKF) design methodology to the scan matching SLAM problem. We review the theoretical foundations of the IEKF and its practical interest of guaranteeing robustness to poor state estimates, then implement the filter on a wheeled robot hardware platform. The proposed design is successfully validated in experimental testing.

Towards realistic covariance estimation of ICP-based Kinect V1 scan matching: The 1D case

The Iterative Closest Point (ICP) algorithm is a classical approach to obtaining relative pose estimates of a robot by scan matching successive point clouds captured by an onboard depth camera such as the Kinect V1, which has enjoyed tremendous popularity for indoor robotics due to its low cost and good performance. Because the sensed 3D point clouds are noticeably corrupted by noise, it is useful to associate a covariance matrix to the relative pose estimates, either for diagnostics or for fusing them with other onboard sensors by means of a probabilistic sensor fusion method such as the Extended Kalman Filter (EKF). In this paper, we review the sensing characteristics of the Kinect camera, then present a novel approach to estimating the covariance of pose estimates obtained from ICP-based scan matching of point clouds from this sensor. Our key observation is that the prevailing source of error for ICP registration of Kinect-measured point clouds is quantization noise rather than white noise. We then derive a closed-form formula which can be computed in real time onboard the robots hardware, for the case where only 1D translations are considered. Experimental testing against a ground truth provided by an optical motion capture system validates the effectiveness of our proposed method.