SRIBO: An Efficient and Resilient Single-Range and Inertia Based Odometry for Flying Robots

Positioning with one inertial measurement unit and one ranging sensor is commonly thought to be feasible only when trajectories are in certain patterns ensuring observability. For this reason, to pursue observable patterns, it is required either exciting the trajectory or searching key nodes in a long interval, which is commonly highly nonlinear and may also lack resilience. Therefore, such a positioning approach is still not widely accepted in real-world applications. To address this issue, this work first investigates the dissipative nature of flying robots considering aerial drag effects and re-formulates the corresponding positioning problem, which guarantees observability almost surely. On this basis, a dimension-reduced wriggling estimator is proposed accordingly. This estimator slides the estimation horizon in a stepping manner, and output matrices can be approximately evaluated based on the historical estimation sequence. The computational complexity is then further reduced via a dimension-reduction approach using polynomial fittings. In this way, the states of robots can be estimated via linear programming in a sufficiently long interval, and the degree of observability is thereby further enhanced because an adequate redundancy of measurements is available for each estimation. Subsequently, the estimator's convergence and numerical stability are proven theoretically. Finally, both indoor and outdoor experiments verify that the proposed estimator can achieve decimeter-level precision at hundreds of hertz per second, and it is resilient to sensors' failures. Hopefully, this study can provide a new practical approach for self-localization as well as relative positioning of cooperative agents with low-cost and lightweight sensors