Optimization of Motion Planning and Navigation for Aerial Vehicles with Differential Constraints through Analysis and Control of its Observability
Final Report Abstract
During the first funding period, different approaches for “integrated trajectory planning under consideration of uncertainties and computation time limitations” were investigated. A favorable solution was found in the combination of optimization- based guidance laws and visual-inertial navigation without estimating feature positions. One benefit of this approach is that it requires less computational power than SLAM (simultane- ous localization and mapping) algorithms. In addition, only the vehicle’s attitude, position, and velocity are estimated, which allows an analytical investigation of the estimation problem’s observability properties. Based on these outcomes, the objectives of the second funding period were formulated as collected in Table 1 along with the results achieved. During the second funding period, the objectives Z1, Z2, and Z3 were met. As a navigation solution (Z1), an extended Kalman filter based algorithm was found suitable. For this filter, a minimal measurement model was derived, whose five-dimensional residual corresponds to three pieces of attitude information and two pieces of translatorial information. The observability analysis of this “loosely-coupled” formulation yielded first relevant insights for trajectory planning. The central challenge turned out to be the “derivation of a directional observability measure” (Z2) for the estimation problem. To solve this, the existing approach to compute Cramér- Rao bounds for dynamic filtering problems was fundamentally extended to include state con- straints. Furthermore, it was shown that established models to describe noisy directional measurements were flawed and a globally valid model was proposed. Using these central scientific contributions, the Cramér-Rao bound for loosely-coupled visual inertial odometry was formulated. These results allowed first analyses of the achievable estimation accuracy for given trajectories (Z3). Using the information matrix, every state of a given trajectory can be mapped to its information content in magnitude and direction. It is therefore now possible to predict when and where the expected estimation accuracy falls below a critical threshold and which state is affected. Furthermore, the stored information can be used to target specific previously visited points for loop closures to improve the accuracy again. Due to the theoretical complexity and thus high effort to solve this central challenge, the “analysis of the coupled system” (Z4) could not be conducted to the originally planned extent. However, the approach to maximize observability via trajectory planning was applied to the task of localizing thermal updrafts.
Publications
- Cramer-Rao Lower Bound for State-Constrained Nonlinear Filtering. In: IEEE signal processing letters 24 (2017), Nr. 12, S. 1882–1885
Schmitt, Lorenz ; Fichter, Walter
(See online at https://doi.org/10.1109/LSP.2017.2764540) - Globally Valid Posterior Cramér–Rao Bound for Three-Dimensional Bearings-Only Filtering. In: IEEE Transactions on Aerospace and Electronic Systems 55 (2019), S. 2036–2044
Schmitt, Lorenz ; Fichter, Walter
(See online at https://doi.org/10.1109/TAES.2018.2881352) - Multiple Thermal Updraft Estimation and Observability Analysis. In: Journal of Guidance, Control, and Dynamics 43 (2020), March, Nr. 3, S. 490–503
Notter, Stefan ; Groß, Pascal ; Schrapel, Philipp ; Fichter, Walter
(See online at https://doi.org/10.2514/1.G004205)
