Efficient Path Planning Methods for Groups of Robots Based on Optimal Transport Theory
Abstract
Path planning for a group of robots (also known as distributed robotic systemin Engineering literature) aims at ?nding an e?cient route for each individual robotso that they swarm together to achieve a collective e -ect or a goal of cooperative orcompetitive nature. It is di -erent from path planning for a single robot in many ways.For example, often there is no speci?c destination given to each individual robot, yettheir ?nal positions must form an expected shape to cover a given surveillance area;robots can t collide with each other, in addition to avoiding obstacles; robots usedin group usually have lower functionalities, meaning they can only execute simpleoperations, and have limited communication capabilities. In this project, we establishmathematical models for several path planning problems for groups of robots withvarious tasks and constraints, and design fast and robust numerical algorithms tocompute solutions in a framework that leverage level set method, optimal transporttheory, and numerical stochastic di -erential equations (SDEs). More speci?cally, weconsider the following problems:1. Cooperative swarming: For a given number of robots, how to design a pathplanning strategy for each individual robot, so that they can swarm together toachieve a common goal, such as forming a desirable shape?2. Competitive swarming: What are the optimal paths for robots in a group thateach have their own goal, while they must avoid conicts along the paths.3. Swarming in unknown environments: How to design paths for robots swarmingin environments that some obstacles are not known a prior?Obviously, these problems are closely related, yet have signi?cant di -erences. Solv-ing one problem can have direct impact on the others. In addition to the aforemen-tioned problems that will be investigated in the near future, we also propose to tacklemore problems in our long term research e -orts. It is our primary target to developmodels, methods and most importantly, the fundamental theory for those problems.Our emphasis throughout the project is on the theoretical foundations.To carry out the research, we will work together with a group of researchersat Naval Surface Warfare Center (NSWC), Panama City, and researchers at ECEdepartment at Georgia Tech to leverage our combined expertise in applied and com-putational mathematics and engineering, especially in the areas of numerical SDEs,level set method, optimizations, control, and sensor technology. The results found bythis research will be disseminated by giving presentations in seminars and conferences,publishing in conference proceedings and journals. The problems in the projects areperfect topics that can be used to train graduate students and postdocs.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 19, 2018
- Source ID
- N000141812852
Entities
People
- Haomin Zhou
Organizations
- Georgia Tech Research Corporation
- Office of Naval Research
- United States Navy