SHP: Smooth Hypocycloidal Paths with Collision-free and Decoupled Multi-robot Path Planning

Generating smooth and continuous paths for robots with collision avoidance, which avoid sharp turns, is an important problem in the context of autonomous robot navigation. This paper presents novel smooth hypocycloidal paths (SHP) for robot motion. It is integrated with collision-free and decoupled multi-robot path planning. An SHP diffuses (i.e., moves points along segments) the points of sharp turns in the global path of the map into nodes, which are used to generate smooth hypocycloidal curves that maintain a safe clearance in relation to the obstacles. These nodes are also used as safe points of retreat to avoid collision with other robots. The novel contributions of this work are as follows: (1) The proposed work is the first use of hypocycloid geometry to produce smooth and continuous paths for robot motion. A mathematical analysis of SHP generation in various scenarios is discussed. (2) The proposed work is also the first to consider the case of smooth and collision-free path generation for a load carrying robot. (3) Traditionally, path smoothing and collision avoidance have been addressed as separate problems. This work proposes integrated and decoupled collision-free multi-robot path planning. 'Node caching` is proposed to improve efficiency. A decoupled approach with local communication enables the paths of robots to be dynamically changed. (4) A novel 'multi-robot map update' in case of dynamic obstacles in the map is proposed, such that robots update other robots about the positions of dynamic obstacles in the map. A timestamp feature ensures that all the robots have the most updated map. Comparison between SHP and other path smoothing techniques and experimental results in real environments confirm that SHP can generate smooth paths for robots and avoid collision with other robots through local communication.