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RobotLocomotion / drake

Model-based design and verification for robotics.
https://drake.mit.edu
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Documentation for DircolTrajectoryOptimization? #2906

Closed aespielberg closed 7 years ago

aespielberg commented 8 years ago

Hi all,

I'm trying to work on modifying DircolTrajectoryOptimization. However, I am finding the constraint_fun as written a bit hard to parse. I am wondering if there's any more detailed documentation of what the shared data pointers specifically point to? I'm also wondering specifically what the variables xcol, dxcol, xdotcol, and dxdotcol are w.r.t the cubic interpolation? Finally, is the Jacobian simply with respect to x0 and x1, or is it dependent on xdot0 and xdot1 in some way?

liangfok commented 8 years ago

I assume that since this relates to constraints, @ggould-tri would be in the best position to answer this question. Please feel free to reassign as necessary.

hongkai-dai commented 8 years ago

@liangfok @ggould-tri I wrote a lot of MATLAB code in DirectTrajectoryOptimization, I am happy to answer this one later tonight, if you do not mind.

liangfok commented 8 years ago

Nice! That'll be much appreciated!

hongkai-dai commented 8 years ago

@aespielberg , are you using the MATLAB interface? The shared_data in constraint_fun is introduced to cache the result and avoid redundant computation. For example, for a RigidBodyManipulator, computing its kinematics tree can be time consuming, so we cached the result in the kinsol object, as the return argument of doKinematics function. When we impose multiple kinematic constraints in trajectory optimization, these constraints can share the cached kinsol object, rather than computing the kinematics tree by their individual constraint_fun function. Also in DirectTrajectoryOptimization, we cache xdot and dxdot, since they are used for twice, when xdot,dxdot at i'th knot point is used in interpolating the [i,i+1] knot points, and [i-1,i] knot points.

The xcol, dxcol, etc are the value of the states at the collocation point. For more details on the math, you can refer to Hagraves paper "Direct trajectory optimization using nonlinear programming and collocation".

The Jacobian of the constraint is w.r.t x0,x1,u0,u1. We do not explicitly include the Jacobian w.r.t xdot0,xdot1 since they are not our decision variables. Implicitly, these Jacobian can be obtained by using xdot=f(x,u) and the Jacobian w.r.t x,u.

If you have further questions about DirectTrajectoryOptimization, please let us know. You can also talk with @mposa in our lab if we cannot reply you immediately.

ggould-tri commented 8 years ago

Unfortunately I have no knowledge of the matlab optimizer stack, so I'm not going to be much help here. But it sounds like Hongkai has the question well in hand :-)

hongkai-dai commented 8 years ago

@aespielberg , did the comments answer your question? Shall we close this issue, or you would like further discussion on this thread?

aespielberg commented 8 years ago

Thanks for the replies; I have been busy the last couple of days so I'm going to look into it tomorrow, I will let you know if I have further questions then.

Thanks!

On Thu, Jul 28, 2016 at 4:16 AM, Hongkai Dai notifications@github.com wrote:

@aespielberg https://github.com/aespielberg , did the comments answer your question? Shall we close this issue, or you would like further discussion on this thread?

— You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub https://github.com/RobotLocomotion/drake/issues/2906#issuecomment-235781998, or mute the thread https://github.com/notifications/unsubscribe-auth/ADbqdAChxGkJt7mQ564VDK8saZcU5RQHks5qaBDjgaJpZM4JTnpw .

hongkai-dai commented 7 years ago

@aespielberg is it OK if we close this issue?

aespielberg commented 7 years ago

Yes, sorry for forgetting to close it myself. I do recommend adding explicit documentation of the mathematics and representation (or references to them) to future Drake releases though.

-Andy S.

On Mon, Mar 13, 2017 at 2:47 PM, Hongkai Dai notifications@github.com wrote:

@aespielberg https://github.com/aespielberg is it OK if we close this issue?

— You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub https://github.com/RobotLocomotion/drake/issues/2906#issuecomment-286205619, or mute the thread https://github.com/notifications/unsubscribe-auth/ADbqdJV97e8fGuZBnHmFWgAfQOY1PxEnks5rlY9LgaJpZM4JTnpw .

hongkai-dai commented 7 years ago

I totally agree on the documentation. We are rewriting the code in C++, and the documentation is much cleaner there.