Perception-latency aware distributed target tracking

TL;DR

This work tackles distributed target tracking under perception-latency by introducing a smooth-output estimator that generates differentiable target estimates, avoiding the discontinuities that plague traditional filters. It combines this with a distributed estimation fusion stage based on exact dynamic consensus (REDCHO) to produce a global target trajectory and its derivatives, which serves as a smooth reference for formation control. The proposed approach decouples formation control from perception-latency decisions and demonstrates, through simulations, that SOE plus fusion significantly reduces estimation error (up to about 3.5x) and achieves asymptotic formation convergence around the fused target center. The results highlight the practical impact of robust, latency-aware estimation and fusion for multi-robot formation control, with future real-world validation identified as a natural next step.

Abstract

This work is devoted to the problem of distributed target tracking when a team of robots detect the target through a variable perception-latency mechanism. A reference for the robots to track is constructed in terms of a desired formation around the estimation of the target position. However, it is noted that due to the perception-latency, classical estimation techniques have smoothness issues which prevent asymptotic stability for the formation control. We propose a near-optimal smooth-output estimator which circumvents this issue. Moreover, local estimations are fused using novel dynamic consensus techniques. The advantages of the proposal as well as a comparison with a non-smooth optimal alternative are discussed through simulation examples.

Figures (6)

• Figure 1: High-level of the processing flow for our proposal as described in Section \ref{['sec:outline']}.
• Figure 2: A realization of the target position $\mathbf{C}\mathbf{x}(t)$ as well as its corresponding estimations $\mathbf{C}\hat{\mathbf{x}}(t)$ and $\mathbf{C}\hat{\mathbf{x}}^*(t)$ for the SOE and the DOE respectively. Note that the SOE is always a smooth estimation whereas the DOE is discontinuous at the sampling instants.
• Figure 3: Trajectory tracking performance of a single robot \ref{['eq:agents']} under the control input \ref{['eq:local_control']}. Note that the reference is always smooth when using the SOE, resulting in asymptotic convergence for the tracking error. However, the reference is discontinuous when using the DOE, which leads to persistent transients in the robot performance, preventing asymptotic convergence of the tracking error.
• Figure 4: Trajectories for the first components of $\mathbf{y}_{i,0}(t), \mathbf{y}_{i,1}(t), \mathbf{y}_{i,2}(t)$ denoted as $[\mathbf{y}_{i,0}(t)]_1, [\mathbf{y}_{i,1}(t)]_1, [\mathbf{y}_{i,2}(t)]_1$, shown to converge to $[\bar{\mathbf{y}}_{{\normalfont\textsf{G}}}(t)]_1,[\dot{\bar{\mathbf{y}}}_{{\normalfont\textsf{G}}}(t)]_1,[\ddot{\bar{\mathbf{y}}}_{{\normalfont\textsf{G}}}(t)]_1$ which appear in solid red color. Figures on the left show trajectories in the interval $t\in[0,10]$ to depict the asymptotic convergence behavior of the algorithm towards the global signals. On the other hand, figures on the right show convergence towards consensus which occurs in the interval $t\in[0,0.2]$.
• Figure 5: Error comparison between the actual realization of the target position $\mathbf{p}(t)$, local SOE estimates $\hat{\mathbf{p}}_i(t)$ (grey) and the collaborative estimation $\bar{\mathbf{p}}_{{\normalfont\textsf{G}}}(t)$ (blue). Moreover, average Root Mean Squared (RMS) values are shown in each case, where an improvement of a factor of $3.5$ is observed when comparing the collaborative estimate with respect to the local ones.

Theorems & Definitions (6)

• Theorem 1
• Lemma 1
• Theorem 2
• Proposition 1
• Proposition 2
• Proposition 3