# Multidimensional obstacle avoidance

Artificial potential barriers are known that allow robots to avoid obstacles. They are constructed as follows. https://authors.library.caltech.edu/106548/1/2010.09819.pdf

Can you please tell me how this approach is generalized to the case of limiting several coordinates of the controlled robot?

I am assuming that the desired application would be to control a quadrotor drone or similar platform.

The scalar representations of distance shown in the paper above can be represented in 2 ways (that I see). You could extend from the 2d plane to the 3d plane using the same vector norm function as before. This would mean that the mathematical operations would not change, just the low level data structure would be a 3 element vector instead of a 2 element vector.

You could also simply do all of those equations separately on the X, Y, and Z components of the pose vector at the same time. This could be implemented with 3 different threads running the same mathematical process. This is probably safer since you can then prioritize each axis exclusive of the others in case you have to navigate areas where one axis of motion is not going to require large position deltas.

Does that help?

• Yes, that clarifies. Thank you. By the way, this method can be used not only for quadcopters. There was another problem. When the variable reaches the zone of influence of the potential barrier, it gets stuck in it for some time. Could you help me with this too?
– ayr
Commented May 26, 2021 at 3:21
• Are you saying you want ideas on how to handle time spent in obstacles increasing without possibility of change in position? That is not discussed in the paper above and isn't relevant to the original question you have posted. I would not be surprised if there are papers that address this issue. If there is something not clarified, it needs to be asked about in the question. That said, given T initial and T current, I am sure you can come up with a formula to increase wall repulsion or goal attraction. Your original question and linked paper has nothing to do with time. Commented May 26, 2021 at 12:03
• Then if there are any difficulties, I will just ask a new question. Thank you.
– ayr
Commented May 26, 2021 at 13:07
• robotics.stackexchange.com/questions/22226/…
– ayr
Commented May 28, 2021 at 18:44