Experimental initial conditions.

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.

本文针对由n台差分驱动移动机器人（differential drive mobile robots）构成的编队系统，提出了一种基于移动框架（mobile frames）的链式编队策略。考虑编队内两台相邻机器人Ri与Ri+1，期望跟随机器人Ri+1追踪主领航机器人Ri延迟τ个时间单位的轨迹。如此一来，跟随机器人Ri+1将成为编队中Ri+2的领航机器人，依此类推。采用该编队策略后，相邻两台机器人间的尾随距离将随领航机器人Ri的运动速度自适应调整。移动框架固连于机器人机体，使得机器人Ri的位姿可通过Ri+1机体上的移动框架进行解算。该策略的核心前提为：主领航机器人R1可遵循由有界线速度v₁(t)与角速度ω₁(t)生成的任意轨迹。对于编队中的其余机器人，跟随机器人Ri+1的期望轨迹通过对领航机器人Ri的延迟轨迹进行估计得到，该估计期望轨迹的获取基于Ri机器人的当前与过往输入速度信息。为正式证明该编队策略的收敛性，本文推导了编队内任意相邻两台机器人间相对位姿的时变方程，并提出了一种基于本地测量的反馈控制律，以实现机器人Ri+1收敛至机器人Ri此前生成轨迹延迟τ个时间单位的目标轨迹。为此，本文采用了李雅普诺夫（Lyapunov）稳定性分析方法。最后，通过数值仿真与实时实验对该链式编队方案的有效性进行了验证，实验结果表明其具备良好的收敛性能。