The choice of position control or force control need not be a binary decision.
Should you emphasize that we couldn't control both motion and force in the same direction?
29 Matching Annotations
- Dec 2023
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manipulation.csail.mit.edu manipulation.csail.mit.edu
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manipulation.csail.mit.edu manipulation.csail.mit.edu
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and note† that
This is not clear to me how \(b'(s) = 2 \ddot{s}\)
I think \(b'(s) = 2 \dot{s} \ddot{s}\)
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solutions the come from
type: that come
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do specify and end-effector pose
typo: we do not only specify the end-effecor pose
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manipulation.csail.mit.edu manipulation.csail.mit.edu
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the largest eigenvalue corresponds to the direction of least curvature (the squared dot product with this vector is the largest)
According to this, "the first eigenvector (the one whose corresponding eigenvalue has the largest absolute value) is the direction of greatest curvature (second derivative)." This also contradicts with Exercise 5.4
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manipulation.csail.mit.edu manipulation.csail.mit.edu
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Point cloud registration with known correspondences
This would be better with identical x-y axis ranges for both images
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manipulation.csail.mit.edu manipulation.csail.mit.edu
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station.py file directly
I think it is better to make it clear that
MakeHardwareStationis part of the specificmanipulationpackage, not the genericpydrakepackage. -
I've put together a simple example to let you explore some of the various robot arms that are popular today. Let me know if your favorite arm isn't on the list yet!
Images in Deepnote are unavailable,
NameError: name 'RenderDiagram' is not defined.
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- Jan 2023
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underactuated.mit.edu underactuated.mit.edu
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The examples for each chapter that has them will be in a .ipynb file right alongside the chapter's html file, and the notebook exercises are all located in the exercises subdirectory.
Cannot install this properly. Using pip, I assume the underactuated root directory is: "python3.9/site-packages/underactuated"
It does not have html or examples or exercises, only tests.
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underactuated.mit.edu underactuated.mit.edu
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In this example, in the case of no noise, you see clearly that 2 states describe most of the behavior, and we have diminishing returns after 4 or 5:
What does this implies? Do we really need our 4-D dynamics for control design? If yes, does it mean that this approach fails?
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were
typo: where
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underactuated.mit.edu underactuated.mit.edu
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setting an infinite
My interpretation is that you want to penalize final value error really hard so you set Qf to inf, right?
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underactuated.mit.edu underactuated.mit.edu
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his choice of cost function
I know it makes sense with later analysis but I am still confused about the interpretation of this cost on the effect of w. Intuitively, w = 0 will maximize this sum and it is definitely not the worst case.
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or average-cost formulations,
typo: missing 1/N
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underactuated.mit.edu underactuated.mit.edu
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p, initialized with
in the previous notion of prob. density function, one needs the integral of p(x) to be 1. This does not hold here.
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underactuated.mit.edu underactuated.mit.edu
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to
typo => "do"
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underactuated.mit.edu underactuated.mit.edu
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ith u(t)=1 (from any initial condition)
Why u(t) = 1? We find u(t) via LQR right?
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If your aim is to stabilize a non-periodic path through state-space, but do not actually care about the timing, then formulating your stabiliza
I am thinking about the case when the controller tries to make the system stop on the orbit. So the stability is still valid?
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underactuated.mit.edu underactuated.mit.edu
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The conventional wisdom is that taking these extra plant derivatives is probably not worth the extra cost of computing them; in most cases iLQR converges just as quickly (though the details will be problem dependent).
My take-away is DDP generally offers more accurate solutions but requires more calculations.
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drotor is differentially flat in the outputs
They perform all sorts of acrobatics but I feel like they require trajectory for {x,y,z} and roll/pitch rather than yaw.
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bed for the shooting algorithm above:
I assume \(\partial{x}[n] == \partial{x} \) at the denominator
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spline coefficients were the decision variables.
This is confusing. I though decision vars are at break points. Look at the above formulation, min over x[.] u[.]
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They give us precisely what we need to add the dynamics constraint to our optimization at the collocation times:
How does collocation point (midpoint) constraint guarantee x(k+1) = x(k) + int()
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But numerical integrators are designed to solve forward in time, and this represents a design constraint that we don't actually have in our direct transcription formulation.
What is the meaning of this? We already had constraint btw x[n+1] = f(x[n]).
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underactuated.mit.edu underactuated.mit.edu
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Again, we would need ∃ as the quantifier on u instead of
I am confused. Does there exist u making that min() < 0?
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This is because we can write
min over u should be equality.
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ctions, as well, so:
I guess you should explain the condition on \(\dot{V} < \dot{\rho}\)
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underactuated.mit.edu underactuated.mit.edu
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We can use this approach to design an approximation to the optimal controller for the (torque-limited) swing-up of the pendulum!
This code does not work!
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- Dec 2022
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underactuated.mit.edu underactuated.mit.edu
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This means that the length of our velocity vector is no longer the same as the length of our position vector.
They are never the same?
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