Intelligent trajectory planner and generalised proportional integral control for two carts equipped with a red-green-blue depth sensor on a circular rail

Abstract

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 the circle. 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 reconstructor. 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.