Ordering-Flexible Multi-Robot Coordination for MovingTarget Convoying Using Long-TermTask Execution

TL;DR

This work addresses multi-robot target convoying with flexible spatial ordering by formulating target-approach and collision-avoidance as online constraint-based subtasks within a long-term task execution (LTTE) framework. By encoding these subtasks as control barrier function constraints and introducing slack variables, the method guarantees asymptotic convergence to an ordering-flexible convoying formation even in changing environments and with time-varying neighbor sets. Theoretical results show non-neighbor collision avoidance, convex-hull containment of the target, and stable ordering patterns, while 2D experiments and 3D simulations demonstrate robustness to disturbances, breakdowns, and static obstacles. The approach provides a scalable, constraint-driven alternative to fixed-ordering convoying, enabling resilient, energy-efficient coordination for complex urban and multi-robot missions.

Abstract

In this paper, we propose a cooperative long-term task execution (LTTE) algorithm for protecting a moving target into the interior of an ordering-flexible convex hull by a team of robots resiliently in the changing environments. Particularly, by designing target-approaching and sensing-neighbor collision-free subtasks, and incorporating these subtasks into the constraints rather than the traditional cost function in an online constraint-based optimization framework, the proposed LTTE can systematically guarantee long-term target convoying under changing environments in the n-dimensional Euclidean space. Then, the introduction of slack variables allow for the constraint violation of different subtasks; i.e., the attraction from target-approaching constraints and the repulsion from time-varying collision-avoidance constraints, which results in the desired formation with arbitrary spatial ordering sequences. Rigorous analysis is provided to guarantee asymptotical convergence with challenging nonlinear couplings induced by time-varying collision-free constraints. Finally, 2D experiments using three autonomous mobile robots (AMRs) are conducted to validate the effectiveness of the proposed algorithm, and 3D simulations tackling changing environmental elements, such as different initial positions, some robots suddenly breakdown and static obstacles are presented to demonstrate the multi-dimensional adaptability, robustness and the ability of obstacle avoidance of the proposed method.

Figures (15)

• Figure 2: Two spatial ordering sequences of a 6-robot hexagonal formation in 2D. (The circles represent the robots, and the red node the centroid.)
• Figure 3: Illustration of four kinds of ordering-flexible target convoying in 2D and 3D. (The circles in different colors represent the robots, and the red triangle is the target.)
• Figure 4: (a) The triangle-pattern convoying is achieved under the undesired equilibria: $\{\|x_{1,2}\|=\|x_{2,3}\|=\|x_{1,3}\|=r$, $\|x_{i,d}\|$$>0, i=1,2,3\}.$ (b) The square-pattern convoying is achieved under the undesired equilibria: $\{\|x_{1,4}\|=\|x_{1,3}\|=$$\|x_{2,4}\|=\|x_{2,3}\|=r, \|x_{i,d}\|>0,$$i=1,2,3,4\}$. (All the symbols have the same meaning as in Fig. \ref{['definition_convoying']}.)
• Figure 5: (a) The multi-AMR platform consists of three AMRs and a working space. (b) Sizes of two kinds of AMRs and detailed components. (c) The operation procedure of the target convoying consists of localization, LAN network and long-term task execution. (The solid arrows in subfigure (c) represent the physical connection, and the dashed arrows in subfigure (c) are the virtual connection.)
• Figure 6: Two experimental cases of ordering-flexible target convoying with different initial positions. Subfigures (a)-(b): Trajectories of three AMRs starting from different initial position form a convoying formation with distinct spatial orderings in Cases 1-2. Subfigures (c)-(d): Snapshots of initial positions of the three AMRs in Cases 1-2. Subfigures (e)-(f): Snapshots of final stable convoying formation formed by the three AMRs in Cases 1-2. (Here, the blue and red vehicles in subfigures (a)-(b) denote initial and the final positions of the three AMRs, respectively. The green circle denotes the moving target. Moreover, the lager AMR Hunter $1.0$ is labeled $1$, whereas the other two Scout Mini are specified with labels $2, 3$.)