Minimum-Time Trajectory Planning for a Differential Drive Mobile Robot Considering Non-slipping Constraints

We propose a real-time minimum-time trajectory planning strategy with obstacle avoidance for a differential-drive mobile robot in the context of robot soccer. The method considers constraints important to maximize the system’s performance, such as the actuator limits and non-slipping conditions. We also present a novel friction model that regards the imbalance of normal forces on the wheels due to the acceleration of the robot. Theoretical guarantees on how to obtain a minimum-time velocity profile on a predetermined parametrized curve considering the modeled constraints are also presented. Then, we introduce a nonlinear, non-convex, local optimization using a version of the Resilient Propagation algorithm that minimizes the time of the curve while avoiding obstacles and respecting system constraints. Finally, employing a new proposed benchmark, we verified that the presented strategy allows the robot to traverse a cluttered field (with dimensions of 1.5 m ×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} 1.3 m) in 2.8 s in 95% of the cases, while the optimization success rate was 85%. We also demonstrated the possibility of running the optimization in real-time, since it takes less than 13.8 ms in 95% of the cases.