Deformable Voronoi diagrams for robot path planning in dynamic environments

Abstract

Path planning for mobile robots is a complex problem. However, it becomes more challenging when it comes to planning paths in dynamic environments. This is because the robot needs to reach an agreement between the need of having efficient and optimal paths and the need to deal with unexpected obstacles. The proposed algorithm for this work is based on two concepts, the Voronoi Diagram used for the environment representation and the Deformation Retracts which are integrated into the system to enable the path planner to deal with the effect of the moving obstacle by deforming the Voronoi Diagram. The fusion of the aforementioned two concepts, Voronoi Diagrams and Deformation Retracts, which are from two related mathematical disciplines (Computational geometry and Algebraic topology), has not yet been considered in robotics applications. The proposed system first extracts the collision-free space by computing a Generalised Voronoi Diagram (GVD) and generates a pre-planned robot path, then the deformation retract is applied on the free space of the Voronoi Diagram created after an interference due to a moving obstacle. The map is deformed, and the initial path is updated to an alternative path if it exists. One important feature of this algorithm is that it is complete because it generates a solution (path) and the dimension of the map has been reduced to one which represents the retracted free space in the environment. This makes the new system applicable to robot navigation in complex environments, and in other research areas such as computer games, virtual reality, and computational geometry to mention but a few. Simulation results of some environments demonstrate the effectiveness of the new algorithm. The findings of this work have shown that Voronoi Diagram and Deformation Retracts Path planning for mobile robots is a complex problem. However, it becomes more challenging when it comes to planning paths in dynamic environments. This is because the robot needs to reach an agreement between the need of having efficient and optimal paths and the need to deal with unexpected obstacles. The proposed algorithm for this work is based on two concepts, the Voronoi Diagram used for the environment representation and the Deformation Retracts which are integrated into the system to enable the path planner to deal with the effect of the moving obstacle by deforming the Voronoi Diagram. The fusion of the aforementioned two concepts, Voronoi Diagrams and Deformation Retracts, which are from two related mathematical disciplines (Computational geometry and Algebraic topology), has not yet been considered in robotics applications. The proposed system first extracts the collision-free space by computing a Generalised Voronoi Diagram (GVD) and generates a pre-planned robot path, then the deformation retract is applied on the free space of the Voronoi Diagram created after an interference due to a moving obstacle. The map is deformed, and the initial path is updated to an alternative path if it exists. One important feature of this algorithm is that it is complete because it generates a solution (path) and the dimension of the map has been reduced to one which represents the retracted free space in the environment. This makes the new system applicable to robot navigation in complex environments, and in other research areas such as computer games, virtual reality, and computational geometry to mention but a few. Simulation results of some environments demonstrate the effectiveness of the new algorithm. The findings of this work have shown that Voronoi Diagram and Deformation Retracts techniques are a good combination for solving path planning problem using Deformable Voronoi Diagram for mobile robot in a dynamic environment.