The velocity and acceleration constraints in the optimizer are not correct

[charlie-dog]

In the article, it say the "max linear velocity/acceleration". However, in the optimizer, the velocity/acceleration is only bound by three axes.

[yzhangec]

This is a convention used in many previous works, e.g. Fast-Planner, FUEL, ECHO, etc. In our enginnering implementation, we only accommodate velocity constraints for a single axis. For more details, please refer to Fast-Planner, which is the trajectory optimizer used in this work. You can adjust the optimizer to accommodate whole-body velocity constraints as needed.

[charlie-dog]

I did some modification to the code to constrain the linear velocity/acceleration, but I am not confident in my understanding of B-spline trajectory. Could you please tell me if my code is correct?

[charlie-dog]

Moreover, academically speaking, this convention is not rigorous.

[Chen-Albert-FENG]

Hi! Thank you for your suggestion. First, I think your code is logically correct. Secondly, I can provide one empirical reason why B-spline optimization adopts an axis-based constraint rather than a norm-based one. If you try using a norm-based penalty, you will sometimes find that some pieces of the optimized trajectory present a spiral shape, like the insufficient optimization case. To be easy but not rigorous, you can replace it with a conservative manner, just limiting the axis velocity under {YOUR_DESIRED_VELOCITY}/√3.

[charlie-dog]

Thanks for your help! @Chen-Albert-FENG