Trajectory Estimation of a Flying Robot With a Single Ranging Beacon and Derived Velocity Constraints

Abstract

The performance of the trajectory estimation with a single beacon highly depends on the observability of the system, which is further determined by the excitation patterns of the robot. Because the desired excitation patterns regarding specific observability conditions cannot always be guaranteed in real-time, the trajectory estimation may casually fail with divergence. To tackle this issue, indirectly derived velocity constraints are first introduced in this work, and their effects on improving the performance of trajectory estimation are comparatively investigated. Considering the geometric evolution equation and using the state augmentation technique, seven different velocity constraints are evaluated. The comparative results indicate that the trajectory estimation divergence can be most effectively avoided with a pure velocity magnitude constraint. On this basis, a velocity-constrained moving horizon estimation algorithm is implemented and verified in an indoor experimental testbed to accurately estimate the trajectory of the flying robot with a single ultra-wideband beacon in a long time interval. The results also quantitatively illustrate that the overall performance of the proposed approach outperforms that of the latest benchmark approach in both estimation precision and computational efficiency. In particular, with approximately the same estimation precision, the computational time cost of the proposed approach is less than 1/10 of that of existing approaches.