Intermittent Connectivity Maintenance With Heterogeneous Robots

TL;DR

The paper tackles how a heterogeneous team of robots can maintain intermittent connectivity while servicing tasks arranged along a 1D cycle. It introduces a distributed asynchronous strategy where robots partition the cycle into regions and exchange data only when meeting at region boundaries, with asymptotically common traversing times $t_star$ determined by $t_star=(L-2\sum r_i)/(\sum v_i)$. Theoretical results prove convergence of traversing times and boundaries via a weighted consensus mechanism under joint connectivity, and analyze performance under interlaced orientations, yielding revisiting-time guarantees $t_{rev}$ that depend on the balance of orientations. The method is validated through simulations in a 1D cycle and realistic Gazebo/ROS experiments, showing that heterogeneous capabilities are effectively exploited, and robustness to changes in robot speeds or radii is maintained. Overall, the work provides a scalable, distributed framework for intermittent connectivity that matches centralized performance in terms of revisiting times and offers practical pathways for real-world deployment.

Abstract

We consider a scenario of cooperative task servicing, with a team of heterogeneous robots with different maximum speeds and communication radii, in charge of keeping the network intermittently connected. We abstract the task locations into a $1D$ cycle graph that is traversed by the communicating robots, and we discuss intermittent communication strategies so that each task location is periodically visited, with a worst--case revisiting time. Robots move forward and backward along the cycle graph, exchanging data with their previous and next neighbors when they meet, and updating their region boundaries. Asymptotically, each robot is in charge of a region of the cycle graph, depending on its capabilities. The method is distributed, and robots only exchange data when they meet.

Figures (11)

• Figure 1: (Top) Example of cycle graph connecting the locations of 10 tasks (orange regions), obtained from a Tree (in blue) with duplicated edges (red dashed). We take, e.g., positions 0 and $L$ of the cycle graph at the location of Task 1, between $1a$ and $1b$ (in green). Then, the cycle graph involves edges $1b, 2a, 2b, \dots$ and finally, $1a$, getting back to the initial position at Task 1. Robots move forward and backward on the cycle graph. (Bottom) Other example of cycle graph (approximate TSP), connecting the task locations. Positions 0 and $L$ of the cycle graph are at the location of Task 1. The edges are $1,2,\dots,10$ (red dashed), getting back to the initial position at Task 1. We do not make any assumptions on the relation between the number of robots $n$ and the number of task locations $l$ and we do not restrict the robots to remain within one specific edge.
• Figure 2: Left: Events like arriving to a boundary and meeting, catching, or discovering a neighbor (described in Sec. \ref{['sec_method']}), take place when the communication regions of robots get in touch, or touch the boundary. Right: Region associated to robot $i$, length $d_i(t)$ of the region, and position of the boundaries $y_{i-1}(t), y_i(t)$.
• Figure 3: Regions with common traversing times. Four heterogeneous robots (blue circles) move forward and backward on a cycle graph with length $L=1000m$. Robots 1 and 3 have maximum speeds and communication radius $v_i=0.3m/s$, $r_i=50m$, $i=1,3$. Robot 2 can move faster ($v_2=0.7m/s, r_2=50m$), and robot 4 has a larger communication radius ($v_4=0.3m/s, r_4=150m$). If we assign regions to them with common traversing times \ref{['eq_t_star_radii']}, here $t_\star=e_i=250 s$, $i=1,\dots,n$, and they always move at their maximum speed, then we can ensure that each particular point in the cycle graph (e.g., the green dot), is revisited (Def. \ref{['def_revisiting_time']}) every $2 t_\star=500 s$.
• Figure 4: Two examples of robots running the method in Section \ref{['sec_method']} (Algs. \ref{['algo_discovery']},\ref{['algo_main']}) with different maximum speeds and communication radii (circles around the robots), moving forward (red) and backward (blue) between their boundaries $y_i^\star$\ref{['eq_optimal_boundary']} (gray solid, in vertical) as in Asm. \ref{['ass_commonTraversingTimes']}, Def. \ref{['def_study_initialization']}. Left: Unbalanced interlaced orientations (Defs. \ref{['def_balanced_unbalanced']} and \ref{['def_interlaced']}), with $n_{bal}=2$, and with robot indexes $i_1=1, i_2=4$ at round $k=0$ ($o_1(0)=+1, o_2(0)=-1$, $o_4(0)=+1, o_5(0)=-1$, and the remaining orientations are positive). Right: Balanced interlaced orientations (Defs. \ref{['def_balanced_unbalanced']}, and \ref{['def_interlaced']}), with $n_{bal}=n/2$.
• Figure 5: Time of arrival (red crosses) of each robot $i$ to boundaries $y^\star_{i-1}$ and $y^\star_i$ (y--axis) along time and rounds (x--axis), for the scenario in Fig. \ref{['fig_interlaced_Synch_1']}Left (unbalanced interlaced orientations). Gray solid vertical lines represent the separation between rounds $k=0,1,2,\dots$ (Def. \ref{['def_round']}), where we take $k_0=0$. Each robot $i$ arrives at the $y_i^\star$ boundary (red crosses on lines $R_i, y^\star_i$) but for robots $i=2$ and $i=5$, which arrive at the $y_{i-1}^\star$ boundary, (red crosses on lines $R_2, y_1^\star$ and $R_5,y_4^\star$). At round $k=1$, orientations are unbalanced interlaced, with indexes $i_1-1=1, i_2-1=4$ (red crosses on lines $R_1, y_n^\star$ and $R_4,y_3^\star$), and so on. At each round there are $n_{bal}=2$ meetings involving $2 n_{bal} = 4$ robots (4 red crosses at each round $k$) as in Lemma \ref{['lemma_interlaced']}. Every $n$ rounds, e.g., $1\leq k \leq 7$, or $2\leq k \leq 8$, each robot $i$ arrives $n_{bal}$ times to boundary $y_i^\star$ (red crosses).

Theorems & Definitions (32)

• Definition 2.1: Revisiting times
• Remark 3.1: Execution using information of times
• Remark 3.2: On Assumption \ref{['ass_method']}
• Theorem 4.1: Convergence to common traversing times
• Definition 4.1: Balanced and Unbalanced orientations
• Theorem 4.2: Performance for Balanced Orientations
• Theorem 4.3: Performance for Unbalanced Orientations
• Remark 4.1
• Proposition 5.1
• Lemma 5.1: (Active)Aragues-19ACC