Multi-robot Rigid Formation Navigation via Synchronous Motion and Discrete-time Communication-Control Optimization (2510.02624v2)

Abstract: Rigid-formation navigation of multiple robots is essential for applications such as cooperative transportation. This process involves a team of collaborative robots maintaining a predefined geometric configuration, such as a square, while in motion. For untethered collaborative motion, inter-robot communication must be conducted through a wireless network. Notably, few existing works offer a comprehensive solution for multi-robot formation navigation executable on microprocessor platforms via wireless networks, particularly for formations that must traverse complex curvilinear paths. To address this gap, we introduce a novel "hold-and-hit" communication-control framework designed to work seamlessly with the widely-used Robotic Operating System (ROS) platform. The hold-and-hit framework synchronizes robot movements in a manner robust against wireless network delays and packet loss. It operates over discrete-time communication-control cycles, making it suitable for implementation on contemporary microprocessors. Complementary to hold-and-hit, we propose an intra-cycle optimization approach that enables rigid formations to closely follow desired curvilinear paths, even under the nonholonomic movement constraints inherent to most vehicular robots. The combination of hold-and-hit and intra-cycle optimization ensures precise and reliable navigation even in challenging scenarios. Simulations in a virtual environment demonstrate the superiority of our method in maintaining a four-robot square formation along an S-shaped path, outperforming two existing approaches. Furthermore, real-world experiments validate the effectiveness of our framework: the robots maintained an inter-distance error within $\pm 0.069m$ and an inter-angular orientation error within $\pm19.15^{\circ}$ while navigating along an S-shaped path at a fixed linear velocity of $0.1 m/s$.

• The paper introduces a hold-and-hit communication-control framework that optimizes discrete-time cycles to minimize tracking errors in rigid multi-robot formations.
• It employs a Discrete-time Error Minimization control law to ensure precise curvilinear navigation while addressing nonholonomic movement constraints and network delays.
• Simulations and real-world experiments with TurtleBots show that the approach robustly maintains formation integrity under varying conditions.

Multi-Robot Rigid Formation Navigation via Synchronous Motion and Discrete-time Communication-Control Optimization

Introduction to Multi-Robot Systems

Multi-Robot Systems (MRS) are pivotal for applications requiring cooperative tasks such as surveillance and transportation. Rigid formation control, where robots maintain a specific geometric configuration, is essential, particularly when collaborative motion is required over complex paths. Conventional leader-follower paradigms, where follower robots track a leader's movements, rely heavily on observation. This can lead to lagged responses, potentially disrupting formations, as followers often lack direct communication from the leader.

Figure 1: Cooperative transportation with the leader-follower scheme.

Proposed Communication-Control Framework

The paper introduces a "hold-and-hit" communication-control framework compatible with the Robotic Operating System (ROS). This framework synchronizes robot movements effectively against network delays and packet loss through discrete-time communication-control cycles. It combines robust synchronization with an intra-cycle optimization approach allowing rigid formations to adhere to predefined curvilinear paths despite nonholonomic movement constraints.

Figure 2: Sequence diagram of the hold-and-hit mechanism.

Nonholonomic Constraints and Navigation

The paper tackles nonholonomic constraints, which limit vehicular robots' path-following capabilities, complicating navigation along curvilinear routes. Traditional methods often approximate continuous-time kinematics for robot control, which can cause divergence due to error accumulation. The authors propose a Discrete-time Error Minimization (DEM) control law facilitating precise path navigation in rigid formations compatible with discrete-time systems.

Simulation and Comparative Analysis

The paper carried out simulations using TurtleBot robots navigating an S-shaped path. The simulation results demonstrated the superiority of the proposed approach in maintaining formation integrity compared to both discrete-time and continuous-time leader-follower methods.

Figure 3: Cooperative transportation with four nonholonomic wheeled robots. The blue square represents an object on top of the group. The dashed line is the predefined path towards the target.

Simulation results under varied conditions showed that the hold-and-hit framework paired with the DEM control law minimizes errors effectively, outperforming other methods in maintaining rigid formations even when increasing the target velocity or control cycle duration.

Real-World Application

Experiments confirmed the effectiveness of this framework in real-world scenarios despite unknown noise coefficients and network communication uncertainties. The approach successfully maintained formation during cooperative transportation tasks using WiFi-network-enabled TurtleBots.

Figure 4: A real-world MRS was developed to demonstrate the cooperative transportation scenario. (a) Four physical TurtleBots were arranged in a square formation. (b) The team of robots collectively lifted a wooden board.

Conclusion

The introduced framework and methodology provide significant advancements in synchronizing multi-robot navigation through nonholonomic pathways using wireless communication. The robustness of the approach against network-induced delays and packet-loss positions it as a practical solution for industrial and cooperative transportation applications. Further work might focus on adapting the hold-and-hit framework for large-scale implementations involving various nonholonomic robots.

Overall, the research bridges gaps in synchronization and error minimization for MRS, promoting autonomous robotic collaboration in real-time scenarios.