5 ms·
Everyday life may be a stretch, however some higher-end quadrotors are able to navigate safely in complex indoor environments by generating trajectories that mi
by antegamisou 4y ago
Everyday life may be a stretch, however some higher-end quadrotors are able to navigate safely in complex indoor environments by generating trajectories that minimize the snap, the second derivative of acceleration.
- lake_vincent 4y agoWait, meaning the third derivative of the what is already the second derivative of position - so snap = 5th derivative of position? Is there an intuitive explanation for this? Just checking my understanding.
- flobosg 4y agoSnap, or jounce, is the fourth derivative of position.
- jdougan 4y agoI thought that was called "jerk".
- marcianx 4y ago0th derivative = position 1st derivative = velocity 2nd derivative = acceleration 3rd derivative = jerk 4th derivative = snap 5th derivative = crackle 6th derivative = pop I just learned the last 3 due to this discussion and Wikipedia[1][2]. [1]: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv... [2]: https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop
- deleted 4y ago[deleted]
- Sharlin 4y agoJerk is the third derivative of position and is very familiar to anyone who has ever ridden a bus or other vehicle with not-so-smooth acceleration curves.
- moralestapia 4y agoAre there intuitive examples of snap, crackle and pop? What are they used on? (Very nice to think about)
- dougmwne 4y agoIntuitively I think you would be able to tell the difference between a jerk and a snap. In a car experiencing jerk, you would find yourself no longer able to balance against acceleration and you would sway. In a snap, you would not just sway, but really bounce around. Think the difference between hitting the gas pedal in ludicrous mode vs hitting the gas pedal while driving over potholes. Crackle and pop, I have no idea if you could tell the difference.
- N19PEDL2 4y agoAn interesting fact: it has been shown ([0], [1]) that human body movements are performed in such a way as to minimize the jerk, so the jerk is used in robotics to make humanoid robot movements look more natural. [0] https://doi.org/10.1109/TAC.1984.1103644 https://doi.org/10.1109/TAC.1984.1103644 [1] https://doi.org/10.1523/JNEUROSCI.22-18-08201.2002 https://doi.org/10.1523/JNEUROSCI.22-18-08201.2002
- nl 4y agoLinked elsewhere, the Wikipedia page is pretty good: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv... The Wikipedia page on Jerk also has a good explanation for the how people feel that: https://en.wikipedia.org/wiki/Jerk_(physics) https://en.wikipedia.org/wiki/Jerk_(physics) I'm unsure if we can really feel Snap and beyond.
- lqr 4y agoTo elaborate: Since a quadrotor can only generate thrust in one direction, any smooth trajectory through space specifies a unique pitch/roll attitude at each moment in time. The attitude at time t is determined by the trajectory's acceleration at time t, along with gravity. Therefore, angular velocity is determined by jerk - the rate at which this thrust vector is changing. The angular velocity cannot be changed instantaneously, because the quadrotor can only exert a finite torque about its rotational axes. So we need to design trajectories that do not attempt to change the angular velocity -- and hence, the jerk -- too quickly. Therefore, we should try to minimize something like the maximum norm of the snap along the trajectory. In practice we often minimize the integral of the squared norm of the snap, because it can be posed as a convex quadratic optimization problem with respect to the control points of a spline.
- teeray 4y agoIt’s also incredible that strapping on FPV goggles and practicing can build an intuitive sense for this. Brains are amazing.