| 摘 要: 多机器人系统通过多机协同与任务并行，能够突破单机器人在负载能力、空间覆盖及容错性等方面的物理局限，成为复杂场景高效作业的关键技术。针对多移动机器人的高精度协同需求，提出了一种SE(2)空间下的无路径刚体编队控制方法。通过定义虚拟控制中心，实现了编队任务与运动时序的完全解耦，而无需依赖预设的参数化路径。在控制律设计方面，先进行几何运动学分析以及误差动力学推导，进而引入非线性补偿角处理移动机器人的非完整约束，最后通过代数变换推导出了显式的解耦控制律来解决代数环问题。在Webots仿真环境下，以四台差速车为对象展开了编队控制实验，系统在直线、圆周及变曲率弧线等多种运动模式下均能保持稳定的几何构型，稳态跟踪误差可达毫米级别。同时对控制律中的关键参数进行了消融实验，分析了各参数对收敛速度与稳态精度的影响规律，探索在工程部署时参数值的选择倾向。实验结果表明，该方法具有良好的渐近收敛性与控制精度，为多移动机器人在仓储物流等复杂场景中的协同作业提供了一种简洁高效的工程化方案。 |
| 关键词: 多机器人系统 编队控制 SE(2)李群 虚拟结构法 李雅普诺夫稳定性 非完整约束 |
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| An SE(2)-Based Path-Free Rigid Formation Control Method for Mobile Robots |
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Luo Fengbing1,2,3, Wang Kuo1,2,3
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1.SIASUN Robot &2.amp;3.Automation Co., Ltd
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| Abstract: By leveraging multi-agent coordination and task parallelism, multi-robot systems (MRS) can transcend the physical limitations of single robots regarding payload capacity, spatial coverage, and fault tolerance, emerging as a pivotal technology for efficient operations in complex scenarios. To address the requirements for high-precision coordination among multiple mobile robots, this paper proposes a path-free rigid formation control method in SE(2) space. By defining a virtual control center (VCC), the framework achieves complete decoupling between formation tasks and motion timing, eliminating the dependency on pre-specified parameterized paths. In the synthesis of the control law, geometric kinematic analysis and error dynamics derivation are first conducted. Subsequently, a nonlinear compensation angle is introduced to handle the non-holonomic constraints of the mobile robots. Finally, an explicit decoupled control law is derived through algebraic transformation to resolve the algebraic loop problem. Formation control experiments were conducted using four differential-drive robots in the Webots simulation environment. The results demonstrate that the system maintains a stable geometric configuration across various motion modes—including linear, circular, and variable-curvature trajectories—with steady-state tracking errors reaching the millimeter level. Furthermore, ablation studies on key control parameters were performed to analyze their influence on convergence speed and steady-state accuracy, exploring parameter selection tendencies for practical engineering deployment. The experimental results show that the proposed method possesses excellent asymptotic convergence and control precision, providing a concise and efficient engineering solution for the collaborative operation of multi-mobile robots in complex scenarios such as warehouse logistics. |
| Keywords: Multi-robot System Formation Control SE(2) Lie Group Virtual Structure Lyapunov Stability Nonholonomic Constraints |
