Motion Planning - Finding smooth optimal paths using Hybrid A*/Astar for autonomous vehicles

In this video, I have explained how hybrid A*/Astar algorithm works. This algorithm is particularly useful in finding smooth optimal paths going from start node to goal node. These paths can be tracked closely by self driving vehicles as this algorithm incorporates vehicle dynamics.

This is the fifth video in the series on "Motion Planning". In case you haven't watched the video on A*/Astar algorithm, here is the link:

If you have any questions/suggestions, let me know in the comments section.

Here are the time stubs for this video:
0:00 - Difference between Hybrid A*/Astar and A*/Astar
2:40 - How Hybrid Astar/A* works?
13:47 - More examples of paths given out by Hybrid A* & A*
15:18 - Hybrid A* being used in autonomous vehicles

[Ponemo]

Truly enlightening! Thank you very much for the great explanation!

[lucianomaia]

Jasvir, i cannot thank you enough, that was really well explained, thanks man, keep it up!

[wangshiyao]

This was great! You made a much better explanation than my prof. Thanks for taking the time to type out all the numbers and forumlas in the steps. They made a big difference!

[hanvitkim]

At 6:59, the Euclidean distance between start node and goal node is 5.831(sqrt(3^2+5^2)). and you said there is no additional cost (0).
then why is 6.03?? in total cost???

[Xavo]

Wow, you've helped me a lot. I have one question though. Do you calculate the cost to come and the cost to go using the continuous or the discrete coordinates? Could you also elaborate on the formulas to compute the next node in continuous coordinates? I am trying to do it, but I don't get the correct answer.

[wangshiyao]

This also means that our velocity values cannot be less than half the length of a grid right? Because otherwise we may forever be snapping back to the same grid.

If grid length = 1, our velocity is capped at 0.4, then if our first node is at 0.4, total cost = 2 and second node at 0.8, total cost = 3, we will drop the second node because it's total cost is higher than the previously calculated total cost for the discrete grid (= 2). And this happens even if we are moving in the right direction towards the goal right?

[bobroll]

I am confused about the calculation of continuous coord at 9.14, where <s, s1> gets continuous coord as [-0.86, -0.5, 30]. I don't know how can you get -0.5 as y coord. Even if it is the case, the calculation of total cost of g(n)=1.23 is not correct according to the distance from [0, 0, 0] to [-0.86, -0.5, 30] . Can anybody explain that？

[kamyarothman]

I wonder what is that additional cost?

[flankerli]

does anyone know how to get the angle(63) of <s, s6, s1> at 10:10?

[junweitoh]

How do you calculate theta? How did you get 63 at 10:08?