Thank you for the question and admirable curiosity about integrating the diverse fields of robotics, neuroscience and artificial intelligence in your independent study.
I cannot recommend what you can pursue in your independent study but these are some steps I will take to get a better understanding of the project:
1) Define the goals of the project/study well. If you wish to have aspects of robotics, neuroscience and artificial intelligence, one area you can look to is how robots can improve living conditions. For instance, in many elderly homes in Japan, robots are deployed to keep the elderly engaged and safe. You can also use the Internet to look at what researchers or companies are using robots for. This will help you generate ideas to further investigate robot-human interactions.
2) Try to learn about the current work in this field. Japan is definitely the top nation for the use of robots. Other countries such as Singapore and China are also catching up. For instance, Singapore has launched the Smart Nation Initiative, and plans to make use of robots to improve the health and service industries. You might also want to visit museums which have robots and speak to curators to understand why they use robots to interact with their visitors.
I have tried looking at museums in USA but there aren’t many that uses robots. There is an exhibition featuring ‘Robot Revolution’ in the Museum of Science + Industry in Chicago which you might consider visiting. You can try emailing folks at museums in Japan and Europe who have already started using robots in their operations as well.
3) Lastly, I would highly recommend understanding the resources you can access (from your school, family, community and the Internet) before you plan your study. This is to prevent future problems such as lack of time and information for your project.
One other valuable resource is local university near you. Check out if there is any university faculty working on robotics/neuroscience near you, especially in the departments of computer/electrical/biomedical engineering and neuroscience, or other inter-departmental programs. If your project interests them, you might even be able to visit the labs and plan a project with them.