Distributed formation-enforcing control for UAVs robust to observation noise in relative pose measurements

TL;DR

This paper tackles the challenge of robustly enforcing UAV formations when relative localization onboard is noisy. It introduces a restraining framework that converts the gradient-descent FEC, derived from graph rigidity, into a noise-aware control law by decomposing each input term and applying per-term probabilistic setpoints conditioned on known noise distributions. The approach extends to full relative pose in $\mathbb{R}^3 \times \mathbf{S}^1$ by projecting high-dimensional terms to 1D components and applying restrained corrections ($\tau_{p_1}, \tau_{p_2}, \tau_{\psi_1}, \tau_{\psi_2}$), yielding a decentralized controller with reduced oscillations and improved convergence. The authors validate the method through extensive simulations and real-world outdoor flights using the UVDAR system, showing notably improved stability, reduced tilting, and better formation tracking compared to pure gradient-based FEC. The work provides theoretical analysis, simulation results, and publicly available code, with demonstrated potential to generalize to other sensing modalities and formation-types.

Abstract

A technique that allows a Formation-Enforcing Control (FEC) derived from graph rigidity theory to interface with a realistic relative localization system onboard lightweight Unmanned Aerial Vehicles (UAVs) is proposed in this paper. The proposed methodology enables reliable real-world deployment of UAVs in tight formations using relative localization systems burdened by non-negligible sensory noise, which is typically not fully taken into account in FEC algorithms. The proposed solution is based on decomposition of the gradient descent-based FEC command into interpretable elements, and then modifying these individually based on the estimated distribution of sensory noise, such that the resulting action limits the probability of the desired formation. The behavior of the system was analyzed and the practicality of the proposed solution was compared to pure gradient-descent in real-world experiments where it presented significantly better performance in terms of oscillations, deviation from the desired state and convergence time.

Figures (19)

• Figure 1: An example of our fully autonomous UAV MRS2022ICUAS_HW equipped with the mutual relative localization system UVDAR. The units depicted are based on the MRS F450 platforms. These devices can cooperate using a mutual relative localization and control scheme, such as the one proposed here. The output of the relative localization system is subject to observation noise expressed in terms of covariance of a multivariate Gaussian distribution that is taken into account in the presented method. An illustration of 3D ellipsoids representing the distribution of noise in relative position measurement is shown on the right.
• Figure 2: Symbols involved in the definition of a formation in this work. Lines marked with $/\!\!/$ or $/\!\!/\!\!/$ are parallel to those with the same marker.
• Figure 3: Illustration of the 1D control problem with an unknown true control error $\Delta_d$. Top: The probability distribution of $\Delta_d[k]$ is Gaussian with mean at the measured value $\Delta_m[k]$ and a standard deviation $\sigma_m[k]$. Bottom: The probability of overshooting the target $P_{\text{over}}(u[k])$ based on the selected action input $u[k]$ is equal to the CDF of the distribution of $\Delta_d[k]$.
• Figure 4: The velocity set with our proposed controller in 1D case. The region within $\Delta_m[k] \in \interval{s_{\mathrm{res}}}{-s_{\mathrm{res}}}$ represents a region where the agent remains purposefully passive.
• Figure 5: If the measured relative value of a target state is subject to observation noise, controlling the current state of the system towards the mean of that measurement at $s_\mathrm{ml}$ risks overshooting the target with probability $P_\mathrm{over} = 0.5$. This probability can be reduced to an arbitrary value $\ell < 0.5$ by choosing a restrained setpoint $s_\mathrm{res}$ that is closer to the current state than $s_\mathrm{ml}$ by $\abs{\sigma_m[k] \Phi^{-1}(\ell)}$. If $\ell < 0.5$, then $\sigma_m[k] \Phi^{-1}(\ell) < 0$.

Theorems & Definitions (1)

• Lemma 3.1