Trajectory Optimization Puns

So I have a question about trajectory optimization. In the adrlab of Eth Zurich, they have these sensors right to see where the drone or any thing is there in the 3D space of the lab. In the lab when they do traj opt for drone they know the location for the end point, but in the real world how does traj opt works?. I can't seem to think of any explanation other than radar for traj opt in real world.

So I want to ask you guys, how do you do traj opt for algorithms that need traj opt like mpc etc in the real world.

Hi everyone! It occurred to me last night that one of the tools I use in my robotics research (I am a PhD student in Mechanical Engineering right now) can be used to analyze/test the Starship landing maneuver. The method falls under a field of control theory called “optimal control theory” which is all about – as the name suggests – using a systematic method to optimize your controller or control signal according to some objective measure.

I have been inspired to do this, in part because some internet arm-chair controls engineers in have suggested that issues with the landing maneuver are attributable to (and I am paraphrasing) SpaceX “haven’t tuned their PID parameters correctly yet,” or their trajectory is pitching over too far or something like that. I believe this is a bit of a Dunning-Kruger situation, and in my opinion, comes off a little offensive as it vastly underestimates the knowledge of SpaceX engineers. SpaceX have one of the most advanced aerospace controls and simulation research teams in the world. This analysis may help put into perspective one of the possible methods they use to plan a trajectory or do model-predictive-control (MPC).

#The Method Direct collocation is a trajectory optimization method that breaks down the time in which you want to control something into discrete time points and solves a problem that minimizes an objective which is computed across the trajectory (for instance, minimize the total propellant expended for a rocket by integrating the mass burn at each time point in the trajectory, or minimize the total time it takes to complete the task).

In specific, I am using a trapezoidal collocation method – as it is the easiest for me to code from scratch in a hurry. All of the code to solve this problem was written from scratch today. The problem I have specified is a bit more restricted and simplified than the actual landing problem.

Here are some of the modeling choices I have made:

##Endpoint Conditions I have started the problem at the approximate height (500 m) and vertical decent rate (90 m/s) of the Starship at the start of the SN10 landing burn according to some data from a video from FlightClub.io (tweet). I have started it at a pitch angle of 85 degrees. I have specified that it should land with zero velocity and zero pitch angle. I have allowed the total duration of the maneuver to be whatever it likes so the time interval is not fixed but a

https://arc.aiaa.org/doi/abs/10.2514/1.G005376

Trajectory optimization includes direct & indirect techniques such as shooting and collocation which solve the 2-pt boundary value problem whereas motion planning includes algs like RRT and A* which plan a path through a space.

My issue: given sufficient compute, both approaches will compute a path while adhering to constraints and minimizing some cost function... so what's the difference? When do you use one technique over the other?

We (finally) released camera-ready for our spotlight ICLR paper https://arxiv.org/abs/2002.09572. We argue that there is a "break-even point" on the optimization trajectory, which is encountered early in training.

Fun animation: http://kudkudak.github.io/assets/misc/G.gif

Abstract: The early phase of training of deep neural networks is critical for their final performance. In this work, we study how the hyperparameters of stochastic gradient descent (SGD) used in the early phase of training affect the rest of the optimization trajectory. We argue for the existence of the "break-even" point on this trajectory, beyond which the curvature of the loss surface and noise in the gradient are implicitly regularized by SGD. In particular, we demonstrate on multiple classification tasks that using a large learning rate in the initial phase of training reduces the variance of the gradient, and improves the conditioning of the covariance of gradients. These effects are beneficial from the optimization perspective and become visible after the break-even point. Complementing prior work, we also show that using a low learning rate results in bad conditioning of the loss surface even for a neural network with batch normalization layers. In short, our work shows that key properties of the loss surface are strongly influenced by SGD in the early phase of training. We argue that studying the impact of the identified effects on generalization is a promising future direction.

Thoughts? :)

In the context of control systems taking the cart pole problem as an example, as I understand, trajectory optimization is coming up with a sequence of control inputs u(k) that maximizes an objective function (ie. inverse of energy used to move the cart).

However, this description also sounds like optimal control?

What would be the difference between these terms?

Hello guys,

I've been trying to solve this problem where I optimize the trajectories of 2 drones that keep a fixed distance between them.

So the way I solve this problem was by applying the euclidean distance between them as an equality constraint:

sqrt((x_d2-x_d1).^2+(z_d2-z_d1).^2)-2

Besides that, I optimize the states and variables of both drones in the cost function as follows:

% center of mass

com_x = (x_d1+x_d2)/2;

com_z = (z_d1+z_d2)/2;

vector_drone1=[mode_diff_d1; mode_common_d1; theta_d1; x_velocity_d1 ;z_velocity_d1;angular_velocity_d1];

vector_drone2=[mode_diff_d2; mode_common_d2; theta_d2; x_velocity_d2 ;z_velocity_d2;angular_velocity_d2];

vector_drones=[com_x;vector_drone1;com_z;vector_drone2];

%reference to follow

ref_d1=[5*ones(H,1); zeros(H,1);10*ones(H,1);zeros(4*H,1)];

ref_d2=[5*ones(H,1); zeros(H,1);10*ones(H,1);zeros(4*H,1)];

ref=[ref_d1;ref_d2];

cost = sum(vecnorm(vector_drones-ref).^2);

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Drone 1 has the blue trajectory and drone 2 has the pink one.

So I tried 2 approaches:

- First, the trajectory of drone 1 starts at (0,0) and its position x initial condition has value =0. And the trajectory of drone 2 starts at (2,0) and its position x initial condition has value =2.

the beggining

the end

The problem is that it goes to an infeasible point and the trajectories don't finish in the position that it's supposed.

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So I tried another approached where both trajectories started at (0,0)

https://preview.redd.it/1zzmir1avzg51.png?width=545&format=png&auto=webp&s=694c02d418566ff37aed189da4fd027c74484e16

and It also converges to an infeasible point.

So my doubts are:

- Should I maintain the approach where both trajectories start at different positions so the constraint isn't violated a priori?

- I don't know why it converges to an infeasible point.

This is my code:

[https://github.com/preguica00/mpc2drones](https://github.co

First, I wanted to say that I'm aware this is more a matlab problem, but I wanted to talk with someone that really understands quadcopter/drone and what it is needed to control one.

So my problem is a optimization trajectory of a drone using model predictive control (mpc).

I'm struggling now more on the theoretical part of the problem.

See please the formulation of the problem I have on github link.

-----------------------------------------

So I run my MPC controller, that is, the optimization I do with fmincon function.

Then, my output is a optimal vector of both my 6 states and my 2 control variables.

I apply the first element of both control variables in the simulation of my model.

And then I calculate the current state that I will apply again back to the controller.

I think that part is ok.

-------------------------------------------------------

The problem is that in my MPC controller, I need to implement the dynamics of the model as an equality constraint. I thought that that was the difference between the states I optimize (that come out of fmincon) and the discretization of the system, but that doesn't work.

Someone suggest to me that the constraint should be the difference between the state I optimize in fmincon and the state that comes out of the simulation of the drone(simulate_step function). But I don't understand why. What's the point of discretizating the system if I don't use it though?

This is my code:

https://github.com/preguica00/MPC_drone

My problem is basically `discretization` function.

Thank you

A little project I did optimizing the path of a steering car using automatic differentiation in PyTorch.

http://blog.benwiener.com/programming/2019/05/14/steering-car.html

I'd love to know what you think!

• DOI/PMID/ISBN: https://doi.org/10.2514/6.2019-0260

• URL

• DOI/PMID/ISBN: N/A

• URL

The pre-packed PDF tutorials seem to assume quite a lot, so I was wondering if there were any video tutorials or something? I found one video of an Australian guy using TOT, but he seemed to be stumbling through it as though he was still learning how to use it.

I stumbled across an article about the "Evolutionary Mission Trajectory Generator" ( http://www.nasa.gov/content/goddard/nasa-technologist-makes-traveling-to-hard-to-reach-destinations-easier/#.V1GNRZOLRPU ) and remembered that I had read about the similar thing that Arrowstar made for KSP, KSP Trajectory Optimization Tool. Would it be possible to fire up the EMTG for the kerbin system too? Does it do things in a much different way than the KTOT? I just thought it was interesting and I'm sure some of you have thought about it.

I found this tutorial but it seems out of date and not specific to RSS. I am currently in 1988 in my playthrough and want to start doing complex flybys to save dv. Never could figure out how to use this thing during previous playthroughs.