The tail-flapping propulsion of a robotic fish forms a hydrodynamic pressure field that depends primarily on the flapping frequency and amplitude. In a two-robot aligned group, the tail of the front robot generates an oscillating pressure that is detectable by its follower. This paper proposes a position estimator for the follower to locate the position of the leading robotic fish. The position estimator uses the hydrodynamic pressure measured on a sensor array installed on the forefront of the following vehicle body. We derive a potential flow model to describe the pressure field of the leader in the presence of the follower. Using this pressure field model, we further derive an observability measure which is used to determine the relative positions of the leader and follower for which the position estimator will produce a reliable estimate. The position estimator employs the Levenberg–Marquardt algorithm, due to the nonlinearity of the pressure model. Results from the observability analysis show that a satisfactory estimation of the leader position is achieved when the leader is located directly ahead, on the starboard-bow, or the port-bow of the follower, similar to the formation pattern generally found in a school of fish. The observability analysis also shows that poor estimation is obtained when the leader is abeam of the follower. Tank experiments confirm the observability analysis and also demonstrate the use of the position estimator for feedback control by the follower.

机器鱼的拍尾推进形成了一个主要取决于拍打频率和幅度的流体动力压力场。在两个机器人对齐的组中，前部机器人的尾部会产生一个可被其跟随者检测到的振荡压力。本文提出了一种位置估计器，用于跟随者定位领先机器鱼的位置。位置估计器使用安装在后车车身前部的传感器阵列上测量的流体动力压力。我们推导出一个势流模型来描述在跟随者存在的情况下领导者的压力场。使用这个压力场模型，我们进一步推导出一个可观察性度量，用于确定领导者和跟随者的相对位置，位置估计器将对其产生可靠的估计。由于压力模型的非线性，位置估计器采用 Levenberg-Marquardt 算法。可观察性分析的结果表明，当领导者位于跟随者的正前方、右舷船头或左舷船头时，可以获得令人满意的领导者位置估计，类似于通常在学校中发现的队形模式。鱼。可观察性分析还表明，当领导者与追随者正对时，得到的估计很差。坦克实验证实了可观测性分析，并证明了位置估计器用于跟随器的反馈控制。可观察性分析的结果表明，当领导者位于跟随者的正前方、右舷船头或左舷船头时，可以获得令人满意的领导者位置估计，类似于通常在学校中发现的队形模式。鱼。可观察性分析还表明，当领导者与追随者正对时，得到的估计很差。坦克实验证实了可观测性分析，并证明了位置估计器用于跟随器的反馈控制。可观察性分析的结果表明，当领导者位于跟随者的正前方、右舷船头或左舷船头时，可以获得令人满意的领导者位置估计，类似于通常在学校中发现的队形模式。鱼。可观察性分析还表明，当领导者与追随者正对时，得到的估计很差。坦克实验证实了可观测性分析，并证明了位置估计器用于跟随器的反馈控制。