Prescribed-time Consensus Control for Multi-agent Systems Under Complex Spatial Constraints
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摘要: 多智能体系统执行任务过程中需规避障碍、分布式交互信息, 以保证作业安全性、可靠性, 使得其作业空间受到防碰撞及障碍躲避的安全区域、通信连通性保持的智能体间有限相对位置约束. 为此, 本文研究在上述复杂空间约束下的多智能体预设时间一致性控制问题. 根据智能体与障碍物之间的安全距离, 区分多智能体系统作业过程为障碍规避模态及协同作业模态进行全作业过程描述. 在障碍规避模态, 除传统的智能体间及与障碍物碰撞安全距离约束外, 设计有通信距离约束的避障控制律, 保障在复杂空间障碍环境协同穿越情况下的作业安全性, 以及穿越障碍物后的分布式通信连通性, 防止协同避障后部分智能体断联、中断协同作业任务. 在协同作业模态, 针对传统有限时间稳定相关方法的收敛时间依赖系统初值的缺陷, 提出含时变增益的预设时间控制器设计方法, 实现在协同避障后初值不确定情况下的收敛时间预设, 提高了多智能体系统作业可靠性. 最后, 以二阶多智能体系统为例进行数值仿真, 验证了提出方法的有效性.Abstract: During the task execution, multi-agent systems (MAS) are required to avoid obstacles and exchange information in a distributed manner, so as to ensure operational safety and reliability. Consequently, the workspace of MAS is constrained by safety regions for collision and obstacle avoidance, as well as by limited relative position among agents that maintain communication connectivity. To address these challenges, this paper investigates the prescribed-time consensus control problem for MAS under the aforementioned complex spatial constraints. Based on the safe distance between agents and obstacles, the entire operational process is described by dividing it into two distinct modes, including the obstacle avoidance mode and the cooperative operation mode. In the obstacle avoidance mode, in addition to the traditional safety distance constraints for inter-agent and agent-obstacle collisions, an obstacle avoidance control law with communication distance constraints is designed. Such that the operational safety is ensured when cooperatively traversing complex spatial obstacle environments and preserves distributed communication connectivity after the obstacles are passed, thereby preventing agent disconnection and interruption of cooperative operational tasks after cooperative obstacle avoidance. As for the cooperative operation mode, to overcome the limitation of traditional finite-time stable methods whose convergence time depends on initial system conditions, a prescribed-time controller design method with time-varying gain is proposed, which achieves prescribed convergence time under uncertain initial conditions following cooperative obstacle avoidance, thus enhancing the operational reliability of MAS. Finally, numerical simulations are performed to verify the effectiveness of the proposed method, where a second-order MAS is taken as an example.
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图 2 智能体间距离和速度变化轨迹 ($ T_u=20\; \mathrm{s}$)
Fig. 2 Inter-agent distances and velocity variation trajectories ($ T_u=20\; \mathrm{s}$)
图 3 智能体间距离和速度变化轨迹 ($ T_u=12\; \mathrm{s}$)
Fig. 3 Inter-agent distances and velocity variation trajectories ($ T_u=12\; \mathrm{s}$)
图 4 智能体间距离和速度变化轨迹 (初始速度变化)
Fig. 4 Inter-agent distances and velocity variation trajectories (initial velocity change)
图 11 N字形轨迹的智能体间距离和速度变化轨迹
Fig. 11 Inter-agent distances and velocity variation trajectories of N-shaped trajectory
图 12 五边形轨迹的智能体间距离和速度变化轨迹
Fig. 12 Inter-agent distances and velocity variation trajectories of pentagonal trajectory
图 13 智能体间距离和速度变化轨迹 (参数误差下)
Fig. 13 Inter-agent distances and velocity variation trajectories (under parameter perturbations)
图 14 智能体间距离和速度变化轨迹 (外部干扰下)
Fig. 14 Inter-agent distances and velocity variation trajectories (under external disturbances)
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