Assignment Algorithms for Multi-Robot Multi-Target Tracking with Sufficient and Limited Sensing Capability

TL;DR

This paper tackles the problem of assigning robot-actions to track multiple moving targets under two sensing regimes: sufficient sensing (one robot per target) and limited sensing (two robots per target). It introduces two greedy algorithms with $1/2$ and $1/3$ approximation guarantees for the respective problems and proves these bounds with mapping arguments, while ensuring polynomial-time execution. Empirical validation in ROS-Gazebo and quantitative comparisons against exhaustive and Hungarian-relaxation baselines demonstrate that the greedy methods perform close to optimal and significantly better than their theoretical limits. The work provides actionable centralized strategies for multi-robot target tracking and motivates future research into decentralized and resilient extensions.

Abstract

We study the problem of assigning robots with actions to track targets. The objective is to optimize the robot team's tracking quality which can be defined as the reduction in the uncertainty of the targets' states. Specifically, we consider two assignment problems given the different sensing capabilities of the robots. In the first assignment problem, a single robot is sufficient to track a target. To this end, we present a greedy algorithm (Algorithm 1) that assigns a robot with its action to each target. We prove that the greedy algorithm has a 1/2 approximation bound and runs in polynomial time. Then, we study the second assignment problem where two robots are necessary to track a target. We design another greedy algorithm (Algorithm 2) that assigns a pair of robots with their actions to each target. We prove that the greedy algorithm achieves a 1/3 approximation bound and has a polynomial running time. Moreover, we illustrate the performance of the two greedy algorithms in the ROS-Gazebo environment where the tracking patterns of one robot following one target using Algorithm 1 and two robots following one target using Algorithm 2 are clearly observed. Further, we conduct extensive comparisons to demonstrate that the two greedy algorithms perform close to their optimal counterparts and much better than their respective (1/2 and 1/3) approximation bounds.

Figures (8)

• Figure 1: Assigning robots (drones) with actions to track targets (rovers). Each robot has four candidate actions (represented by the arrows), and it chooses one action (the blue arrow) to execute at a step. The solid blue line represents the robot-action to target assignment. (a): Assigning one robot with action to one target. (b): Assigning a pair of robots with actions to one target.
• Figure 2: The optimal solution in two cases. In all cases, GREEDY selects pair $(\phi_i,j)$. Case 1: OPT charges $q(\phi_i,j)$ to the same pair $(\phi_i,j)$ selected by the GREEDY. Case 2: OPT charges $q(\phi_i,j)$ to at most two pairs --- $(\phi_i,j')$ and $(\phi_{i'},j)$.
• Figure 3: A top view of target tracking in action using Algorithm \ref{['algorithm:complete_assignment']} for the assignment with sufficient sensing in Gazebo environment. The Hummingbird drones are the robots and the Scarab cars (solid dots) are the targets. A robot can sufficiently track a target.
• Figure 4: The trace of the covariance matrix (top) and the mean squared estimation error (bottom) of three targets during 100 time steps using Algorithm \ref{['algorithm:complete_assignment']}. Each robot is equipped with a range-and-bearing sensor.
• Figure 5: A top view of target tracking in action using Algorithm \ref{['algorithm:limited_assignment']} for the assignment with limited sensing in Gazebo environment. The Hummingbird drones are the robots, and the Scarab cars (solid dots) are the targets. Two robots are necessary to track a target.

Theorems & Definitions (7)

• Theorem 1
• proof
• Theorem 2
• proof
• Remark 1
• proof
• Remark 2