基于分布式模型预测控制的多机器人协同编队

doi:10.12382/bgxb.2023.0851

摘要/Abstract

摘要：

多机器人协同系统具备强鲁棒性和容错性,可显著提高整体效率并完成复杂任务。当前多机器人编队常采用集中式架构,此方式依赖中央决策模块,尤其在处理众多机器人的协同任务时存在可扩展性不足、可解性低的问题。提出了一种基于领导者-跟随者方法的分布式模型预测控制器(DMPC),处理多机器人协同编队任务。基于运动学和图网络,对机器人和系统通信进行建模。将编队问题中的轨迹跟踪和队形保持任务分解,分别对领导者和跟随者设计了模型预测控制器。设计了编队队形矩阵,并将其与通信图网络结合,以实现一致性控制或编队控制。各机器人独立决策、并行计算,在面对较多数量机器人的协同编队时表现出更好的准确性和可扩展性。同时,该控制器的设计中还考虑了控制输入变化,有助于减小能耗。设计了数值仿真及方案对比,并通过物理仿真实验,验证了所设计的控制策略的有效性。

关键词: 多机器人系统, 模型预测控制, 编队控制, 轨迹跟踪

Abstract:

Multi-robot cooperative system has strong robustness and fault tolerance, which can greatly improve the overall efficiency and complete the complex tasks. At present, the multi-robot formation often adopts a centralized architecture, which relies on the central decision-making module. In particular, there are problems of insufficient scalability and low solvability when dealing with the collaborative tasks of a large number of robots. A distributed model predictive controller (DMPC) based on leader-follower method is proposed to deal with multi-robot cooperative formation tasks. The robot motion and system communication are modeled based on kinematics and graph network. The trajectory tracking and formation keeping tasks in the formation problem are decomposed, and the model predictive controllers are designed for the leader and followers, respectively. A formation matrix is designed and combined with the communication graph network to achieve consensus or formation control. Independent decision-making and parallel computing of each robot show better accuracy and scalability for the collaborative formation of a large number of robots. At the same time, the design of the controller also takes into account the change of control input, which helps to reduce energy consumption. Numerical simulation and scheme comparison are designed, and the effectiveness of the designed control strategy is verified by physical simulation experiment.

Key words: multi-robot system, model predictive control, formation control, trajectory tracking

中图分类号:

TP242.6

李曹妍, 郭振川, 郑冬冬, 魏延岭. 基于分布式模型预测控制的多机器人协同编队[J]. 兵工学报, 2023, 44(S2): 178-190.

LI Caoyan, GUO Zhenchuan, ZHENG Dongdong, WEI Yanling. Multi-robot Cooperative Formation Based on Distributed Model Predictive Control[J]. Acta Armamentarii, 2023, 44(S2): 178-190.

图/表 18

图1 机器人底盘运动学模型

Fig.1 Kinematics model of robot chassis

图2 无向图和有向图

Fig.2 Undirected graph and directed graph

图3 四移动机器人的有向通信网络

Fig.3 Directed communication network of four mobile robots

图4 多机器人一致性轨迹跟踪效果(直线轨迹)

Fig.4 Consensus trajectory tracking result of multi-robot (linear trajectory)

图5 领导者轨迹跟踪误差(直线轨迹)

Fig.5 Trajectory tracking error of leader (linear trajectory)

图6 跟随者一致性跟踪误差(直线轨迹)

Fig.6 Consensus tracking errors of the followers (linear trajectory)

图7 多机器人编队控制轨迹跟踪效果 (MPC圆形轨迹)

Fig.7 Trajectory tracking result of multi-robot formation control (MPC circular trajectory)

图8 领导者轨迹跟踪误差(MPC圆形轨迹)

Fig.8 Trajectory tracking error of leader (MPC circular trajectory)

图9 跟随者编队误差(MPC圆形轨迹)

Fig.9 Formation errors of the followers (MPC circular trajectory)

图10 MPC编队控制输入

Fig.10 MPC formation control input

图11 MPC综合编队误差

Fig.11 MPC integrated formation error

图12 多机器人编队控制轨迹跟踪效果 (状态反馈圆形轨迹)

Fig.12 Trajectory tracking result of multi-robot formation control (state feedback circular trajectory)

图13 领导者轨迹跟踪误差(状态反馈圆形轨迹)

Fig.13 Trajectory tracking error of leader (state feedback circular trajectory)

图14 跟随者编队误差(状态反馈圆形轨迹)

Fig.14 Formation errors of the followers (state feedback circular trajectory)

图15 状态反馈编队控制输入

Fig.15 Formation control input of state feedback

图16 状态反馈综合编队误差

Fig.16 State feedback integrated formation error

图17 曲线轨迹跟踪编队控制物理仿真实验场景

Fig.17 Physical simulation of curve trajectory tracking formation control

图18 编队控制系统控制实际轨迹与参考轨迹图

Fig.18 Actual trajectories and reference trajectory of the formation control systems

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