A high-performance control algorithm based on a curvature-dependent decoupled planning approach and flatness concepts for non-holonomic mobile robots

This paper proposes a high-performance control strategy for an efficient manipulation of non-holonomic mobile robots in environments cluttered with static obstacles. Firstly, and based on the decoupled planning approach, a new algorithm for fast and safe motions planning is introduced. This algorithm defines the robot path as a sequence of smoothly interpolated functions using (η3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta ^3$$\end{document}) splines and then assigns a suitable curvature-dependent smooth motion profile to describe the robot velocity along such path. In order to achieve fast motions which fulfill all system constraints, the velocity profile is defined as a chain of local profiles smoothly linked together. Each of the local profiles is defined as a smooth limited-jerk function, which is obtained by applying a moving average FIR filter to a classic limited-acceleration profile. The appropriate bounds on velocities and accelerations of trapezoidal acceleration profiles are fixed according to the physical limits of the robot and the maximum bounds on the curvature in the corresponding path segment. The boundary conditions of the local profiles are assigned to ensure that the robot moves from its starting position without stopping until it reaches the goal configuration. Once the motion reference trajectories are obtained, a robust flatness-based feedback controller was defined to ensure the robust and the accurate execution of the planned tasks. Practical tests, using the P3DX model, have been reported to evaluate the performances of the proposed control strategy.