This paper introduces an intelligent trajectory generator and a generalised proportional integral (GPI) control law for the movement of two carts on a circular motorised rail. The objective is to continuously monitor a person performing physical rehabilitation exercises and moving freely inside thecircle. Each cart is equipped with an red-green-blue depth (RGB-D) device so that the patient is monitored from two points of view. One RGB-D device is dedicated to track the body part being exercised, while the other focuses on the person’s face to detect his/her emotional state. The proposed feedback control scheme is based on an exact feed-forward action combined with a velocity vector structural estimation using a model-based integral state re-constructor. Furthermore, the proposed intelligent trajectory generator comprises the references required to move the carts based on the instantaneous position of the patient and the current position of both carts. It also establishes the role (master or slave) of each cart, the direction that each cart must follow, and it generates smooth trajectories that avoid collisions between the carts. Moreover, the paper introduces a description of the displacements of both carts and the positioning of the tilt and pan angles of each RGB-D sensor so as to track the patient’s face and the body from the best viewpoints. The performance of the intelligent trajectory generation and the control of the two carts were analysed with numerical simulations. A comparison was made between the developed GPI control and a standard proportional integral derivative (PID) control. The simulation results show the effectiveness of the trajectory planner, and demonstrate that the GPI control has a better dynamic response than the PID control as well as a better performance in terms of the integral squared tracking error, the integral absolute tracking error, and the integral time absolute tracking error.

中文翻译：

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智能轨迹计划器和广义比例积分控制，适用于两个在圆形轨道上装有红绿蓝深度传感器的小车

本文介绍了智能轨迹生成器和广义比例积分（GPI）控制律，用于控制两个小车在圆形电动轨道上的运动。目的是连续监视进行身体康复锻炼并在圆圈内自由移动的人。每个推车都配备了红绿蓝深度（RGB-D）设备，因此可以从两个角度监视患者。一种RGB-D设备专用于跟踪被锻炼的身体部位，而另一种则专注于人的脸部以检测其情绪状态。所提出的反馈控制方案基于精确的前馈作用，并结合了使用基于模型的积分状态重构器的速度矢量结构估计。此外，所提出的智能轨迹发生器包括基于患者的瞬时位置和两个推车的当前位置来移动推车的参考。它还确定了每个推车的角色（主机或从属），每个推车必须遵循的方向，并生成了避免推车之间发生冲突的平滑轨迹。此外，本文还介绍了两个推车的位移以及每个RGB-D传感器的倾斜和平移角度的位置的描述，以便从最佳角度跟踪患者的脸部和身体。通过数值模拟分析了智能轨迹生成的性能和两个小车的控制。在已开发的GPI控件和标准比例积分微分（PID）控件之间进行了比较。