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Abstract：
A chain formation strategy based on mobile frames for a set of n differential drive mobile robots is presented. Considering two consecutive robots in the formation, robots Ri and Ri+1. It is intended that robot Ri+1 follows the delayed trajectory, τ units of time, of the leader robot Ri. In this way, the follower robot Ri+1 becomes the leader robot for robot Ri+ 2 in the formation and so on. With this formation policy, the trailing distance between two consecutive robots varies accordingly to the velocity of the Ri leader robot. Mobile frames are located on the body of the vehicles, in such a way that the position of robot Ri is determined with respect to the frame located on Ri+1 robot. The strategy relies on the fact that the general leader robot R1 describes any trajectory generated by bounded linear v1(t) and angular ω1(t) velocities. For the remaining vehicles in the string, the strategy considers a desired trajectory for the follower robot Ri+1 obtained by an estimation of the delayed trajectory of the leader robot Ri. This desired estimated trajectory is obtained under the knowledge of the actual and past input velocities of the Ri robot. To formally prove the convergence of the formation strategy, the equations describing the time variation of the relative posture between any pair of consecutive vehicles in the formation are obtained, and a feedback law based on local measurements is proposed to get the convergence of robot Ri+1 to the delayed trajectory, τ units of time, of the trajectory previously described by robot Ri. Lyapunov techniques are considered for this fact. The effectiveness of the chain formation solution is evaluated by means of numerical simulations and real time experiments showing an adequate convergence.
摘要：
针对一组n个差动驱动移动机器人，提出了一种基于移动框架的链条形成策略。考虑到编队中的两个连续机器人，机器人Ri和Ri+1。旨在使机器人Ri+1遵循延迟的轨迹，τ时间单位，领导者机器人Ri。这样,跟随机器人Ri+1在编队中成为机器人Ri+2的领导机器人，以此类推。有了这个编队政策，两个连续机器人之间的尾随距离根据Ri领导者机器人的速度而变化。移动框架位于车辆的车身上，以这样的方式确定机器人Ri相对于位于Ri+1机器人上的框架的位置。该策略依赖于以下事实：一般领导者机器人R1描述了由有界线性v1（t）和角ω1（t）速度生成的任何轨迹。对于字符串中的其余车辆，该策略考虑了通过估计领导者机器人Ri的延迟轨迹而获得的跟随机器人Ri+1的期望轨迹。在知道Ri机器人的实际和过去输入速度的情况下获得该期望的估计轨迹。为了正式证明编队策略的趋同，获得描述编队中任何一对连续车辆之间相对姿态的时间变化的方程，并提出了一种基于局部测量的反馈律，以获得机器人Ri+1对延迟轨迹的收敛性，τ时间单位，机器人Ri先前描述的轨迹。Lyapunov技术被认为是这个事实。通过数值模拟和实时实验来评估链形成解决方案的有效性，该实验显示出足够的收敛性。
