Trajectory Planning Algorithms in Two-Dimensional Environment with Obstacles

Abstract

This article proposes algorithms for planning and controlling the movement of a mobile robot in a two-dimensional stationary environment with obstacles. The task is to reduce the length of the planned path, take into account the dynamic constraints of the robot and obtain a smooth trajectory. To take into account the dynamic constraints of the mobile robot, virtual obstacles are added to the map to cover the unfeasible sectors of the movement. This way of accounting for dynamic constraints allows the use of map-oriented methods without increasing their complexity. An improved version of the rapidly exploring random tree algorithm (multi-parent nodes RRT – MPN-RRT) is proposed as a global planning algorithm. Several parent nodes decrease the length of the planned path in comprise with the original one-node version of RRT. The shortest path on the constructed graph is found using the ant colony optimization algorithm. It is shown that the use of two-parent nodes can reduce the average path length for an urban environment with a low building density. To solve the problem of slow convergence of algorithms based on random search and path smoothing, the RRT algorithm is supplemented with a local optimization algorithm. The RRT algorithm searches for a global path, which is smoothed and optimized by an iterative local algorithm. The lower-level control algorithms developed in this article automatically decrease the robot’s velocity when approaching obstacles or turning. The overall efficiency of the developed algorithms is demonstrated by numerical simulation methods using a large number of experiments.

Keywords

• mobile robots
• motion planning
• path planning
• motion control
• robot motion