russtedrake/underactuated

The course text for MIT 6.832 (and 6.832x on edX)

Underactuated Robotics

Algorithms for Walking, Running, Swimming, Flying, and Manipulation

This is the companion software for the textbook available at: https://underactuated.csail.mit.edu/

To cite this software (or the corresponding textbook), please use:

Russ Tedrake. Underactuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832). Downloaded on [date] from https://underactuated.csail.mit.edu/.

underactuated's Issues

Get rid of `from pydrake.all import *`

See RobotLocomotion/drake#7963

acrobot dircol example fails with --config snopt_fortran, but succeeds with the precompiled binaries

setting num_time_samples=25 resolves it, but at the cost of a much less optimal trajectory coming out.

cc @hongkai-dai, @jwnimmer-tri @jamiesnape . I guess we're not using the fortran snopt in the precompiled binaries yet?

planar rigid body visualization minor requests

the rimless wheel sim in #111 reveals two small quirks.

• cylinders viewed along their long axis are viewed by their bounding box instead of as a circle.
• xlim and ylim don't actual change the shape of the figure, so I get a LOT of ground.

planar visualizer "facecolor" constructor argument is unused (and the doc lies)

experimental mac and ubuntu builds have different timestamps

my current drake_version.json logic does not support that. so, as it stands, the links to the mac binaries in the text will be broken whenever drake_version is pointing to the (linux) experimental.

fyi @jamiesnape . (but unless there is a trivially different naming solution, i think this one is on me to fix).

minor typo: in 8.1 in MDP equation

In the final equation of 8.1, the p_n(x) on LHS should actually be p_{n+1}(x).

Time derivative of energy in a pendulum

The pendulum example in section 11.1 states:

Evaluating the time derivative of the energy reveals:
dE/dt = −b(θ')^2

My apologies if it's obvious, but where did this come from? If energy of the simple pendulum as a function of time was derived elsewhere in the book, maybe it would be good to add a reference to it from this example.

G(q) in the manipulator equations is a vector, so should really be g(q)

but then it would overlap with my cost functions...

Clarify the definition of cost-to-go as the integral of the running cost under the optimal controller

To resolve some of the confusion mentioned in https://piazza.com/class/ieatbtuzolu6wm?cid=123

Consider a notation change to support output feedback

Throughout the notes I use xdot = f(x,u) for the state-space dynamics, and g(x,u) for the running cost in optimal control. And then the few times I use output so far in the notes, I use y=h(x,u). This is not so uncommon (https://en.wikipedia.org/wiki/State-space_representation#Nonlinear_systems, https://en.wikipedia.org/wiki/Observability#Nonlinear_case).

But, it would be much more satisfying to have xdot = f(x,u), y = g(x,u). I could switch to e.g. c(x,u) for my running cost -- but would have to touch a lot of places in the text.

slow load times (for mathjax), even when viewing a single chapter

because it loads (and presumably renders) the entire book. should be able to render only the current chapter.

finish cubic polynomial lyapunov examples

code uses Vdot>0 => V>1, but the text is V<1 => Vdot<0. i should probably present both. + the line search idea.

clean up energy shaping / PFL notes using the Lyapunov version of the derivations

Cable-driven robots can be partially underactuated

The simplest example is a one-dimensional cable-driven robot actuated by a single motor that winds a cable the robot hangs from. If the actuator is falling at 1g the motor has at best unidirectional control over the motion. Of course this robot is fairly trivial, but people are building two-dimensional graffiti bots that hang from two cables and can move over a building wall; they suffer the same sort of constraint, and motion planning is nontrivial. More common is to overconstrain such robots; for example to use eight cables for a six-axis robot. I believe this is what is used for coarse positioning of the receiver room of the Chinese radio telescope FAST. These overconstrained systems always operate near but not in the going-slack region (which has a complicated shape), and many of them (okay not FAST) are interesting for rapid motion, since no motors need be moved.

controllability vs fully-actuated

As I can understand, the rank condition is almost the same and they seem to be the same concept.

Could you please correct or approve this?

All chapters after 1 are inaccessible

Looks like there's probably a missing html tag somewhere. I'm looking into it now.

Question about ../src/lyapunov/cubic_polynomial.py

Hello,

Can anyone help me explain the code of one line inside ../src/lyapunov/cubic_polynomial.py

"prog.AddSosConstraint((V-rho) * x.dot(x) - lambda_ToExpression() * Vdot) "

Why the SOS constraint is like above?

I feel like it should be like " -Vdot - lambda_ToExpression() * ( rho - V ) ". But it will cause some bugs when I tried this expression.

Can you provide more info about how to use SOS optimization to get the ROA?

Thanks!

add macos coverage on CI

circleci now supports mac, but it's not in drake-external-examples yet
drake-external-examples uses travis for macos

either is aok.

Minor: missing transpose in 3rd line of necessary conditions in 12.4.3

set_1: A little confusing to have code in `Part B: Written Component`.

It was a little confusing to have Part B: Written Component be the part which contains the code.
Would it be possible to reword this to mention that it has the code as well?

Minor: dangling right parentheses in appendix examples

e.g.

A.1 Simple Double Pendulum)

Possible mistake or lack of clarity in formula in chapter 2.

In the final few paragraphs of chapter 2: a feedback linearization solution to stabilize pendulum in vertical position is presented. u = 2gcos(theta)/l. It is not clear how this input policy will stabilize the pendulum at theta = pi. Maybe the intended formula was u' = 2gcos(theta/2)/l?

drake's meshcat bump seems to have broken this repo

https://circleci.com/gh/RussTedrake/underactuated/981

@gizatt -- any ideas?

Minor Typo in chapter 2

I know it's a minor typo, but shouldn't the range of x in this line be
$x(0) \in (-\pi,\pi)$ rather than $x(0) \in (\pi,\pi)$ ..?

Minor Typo in 2.2.3: `know` should be `now`

Snippet:

Before we continue, let me know give you [...]

define modules for any files that need to be included

for instance, the quadrotor2d folder just imports a few methods from it's neighboring file. but this complicates the colab workflow.

then I can simplify the "path" logic in the underactuated_scratchpad

Minor typo in 1.3: 'cos' should be 'sin'

Shouldn't the cos in chapter 1 section 3 "Feedback-Cancellation Double Pendulum" example be sin ..?

Line 874
\begin{align*} \ddot \theta_1 &= -\frac{g}{l}\sin\theta_1 -b\dot\theta_1 \\

Line 879
{\bf M}\begin{bmatrix} -\frac{g}{l}s_1 - b\dot{q}_1 \\ 0 \end{bmatrix}

In the "as_single_pendulum.py" example it's

# Cancel double pend dynamics and inject single pend dynamics.

torque[:] = Cv - tauG + \
           M.dot([-self.g / length * sin(q[0]) - b * v[0],
           -kp * q[1] + kd * v[1]])

set_1: Rather than `.get_mutable_state().get_mutable_continuous_state().get_mutable_vector()`, can use `get_mutable_continuous_state_vector()`

This would make the code a little more brief with the sugar method.

NOTE: This was incorporated into the suggestion for #79.

Issues during native Mac install via binaries

Would have just made PR for first issue but not sure if this was particular to something on my system

Following instructions here

Issue 1

Needed this:

export PYTHONPATH=/opt/drake/lib/python2.7/site-packages:${PYTHONPATH}

instead of

export PYTHONPATH=/opt/drake/install/lib/python2.7/site-packages:${PYTHONPATH}

(don't have a /opt/drake/install)

Issue 2

Petes-MacBook-Pro:russdrake pflomacpro$ python -c 'import pydrake; print(pydrake.__file__)'
Traceback (most recent call last):
  File "<string>", line 1, in <module>
  File "/opt/drake/lib/python2.7/site-packages/pydrake/__init__.py", line 8, in <module>
    from . import common
  File "/opt/drake/lib/python2.7/site-packages/pydrake/common.py", line 3, in <module>
    from ._common_py import *
ImportError: dlopen(/opt/drake/lib/python2.7/site-packages/pydrake/_common_py.so, 2): Library not loaded: /usr/local/opt/[email protected]/lib/libvtkFiltersSources-8.0.1.dylib
  Referenced from: /opt/drake/lib/python2.7/site-packages/pydrake/_common_py.so
  Reason: image not found

Looks like vtk issues (maybe is finding a different vtk I have?)

add python linter (e.g. from drake) to ctest

@jamiesnape -- would appreciate if you have any pointers on this?

matplotlib visualizer complaints

Not sure where visualizer development is at but getting these:

/usr/lib/python2.7/dist-packages/matplotlib/figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "

Running the block of code twice makes the warning go away, and displays a static image

Quick look around suggests there are fixes for this warning: rasterio/rasterio#686

duplicate figure numbers when viewing with chapter=_

Link to PDF Files in Bibliography

Hi,
Link to PDF Files in Bibliography returns 404.
http://groups.csail.mit.edu/robotics-center/papers/Asada86.pdf
Could someone update the website to add the directory?
Thanks

Problem when using SOS to do lyapunov analysis

Hello, I wanna use SOS to do the lyapunov analysis of the simple pendulum. There's no bug for my code but I got V = 0 and lambda = 0 which indicates obviously that something goes wrong. Can you help me have a look at my code?

I just followed the following formulation to find the V.

import math
import numpy as np

from pydrake.all import (Jacobian, MathematicalProgram, SolutionResult,
                         Variables)


def dynamics(x):
    return [x[1]*x[2], -x[0]*x[2], -(x[2] + 9.81*x[0])]


prog = MathematicalProgram()
x = prog.NewIndeterminates(3, "x")

# Define the Lyapunov function.
(V, constraint1) = prog.NewSosPolynomial(Variables(x), 2)
Vdot = Jacobian([V.ToExpression()], x).dot(dynamics(x))[0]

# Define the Lagrange multipliers.
(lambda_, constraint2) = prog.NewSosPolynomial(Variables(x), 4)

prog.AddSosConstraint(-Vdot - lambda_.ToExpression()*(pow(x[0],2) + pow(x[1],2) - 1))

result = prog.Solve()

assert(result == SolutionResult.kSolutionFound)

print(prog.SubstituteSolution(V.ToExpression()))
print(prog.SubstituteSolution(lambda_.ToExpression()))

Originally posted by @Jingwen-Zhang-Aaron in #145 (comment)

push more examples to colab?

Could add their icon to my jupyter notebook script, to allow people to open it either locally or online:
https://colab.research.google.com/github/googlecolab/colabtools/blob/master/notebooks/colab-github-demo.ipynb

support animations in planar_multibody_visualizer

We either need to have a SignalLogger that understand abstract values, or (probably the shorter path), teach PlanarMultibodyVisualizer to record the artists on each frame
https://matplotlib.org/gallery/animation/dynamic_image.html

enable support for cross-chapter references in chapter-only display

used to work by rendering everything with mathjax (but that was slow). now that I render only the displayed chapter, the cross-references break. ideally i'd be able to process, but not render the hidden chapters. presumably i could insert commands to link to different chapter displays, too.

i also want to facilitate cross-chapter references in the non-math text, too.

autapse plot with w=3 is misleading because the axes do not have equal units

From:
https://www.youtube.com/attribution_link?a=poYknHOAIyEcWJOc&u=/watch%3Fv%3DB5hrKtlBkGw%26lc%3Dz230u10bjxa3xznn2acdp43512baqonvsxwvvebvnl1w03c010c.1529845462647786%26feature%3Dem-comments

The slope of the line should, of course, never be greater than 1 even as w → ∞.

purge all uses of RigidBody*

add "RegionOfAttraction" method to drake

and finish cubic_polynomial, time-reversed van der pol, and the starburst pattern from smark.

Minor Typo in 8.3.2: `restrict` should be `restricting`

Snippet:

We can make another dramatic simplification by restrict ourselves to [...]

make some elements expandable

e.g., the table of contents. a few of the longer derivations.

simple_continuous_time_system fails to build on mac

@jamiesnape

I've verified that this is also true on shambhala/drake_cmake_installed (I get the same errors):

[ 50%] Building CXX object src/CMakeFiles/simple_continuous_time_system.dir/simple_continuous_time_system.cc.o
In file included from /Users/russt/underactuated/src/simple_continuous_time_system.cc:9:
In file included from /Users/russt/drake-build/install/include/drake/systems/analysis/simulator.h:3:
In file included from /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/algorithm:640:
In file included from /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/memory:635:
In file included from /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/iterator:417:
In file included from /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/iosfwd:90:
In file included from /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/wchar.h:119:
In file included from /usr/include/wchar.h:91:
In file included from /Users/russt/drake-build/install/include/fmt/time.h:13:
In file included from /Users/russt/drake-build/install/include/fmt/format.h:38:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:83:32: error: unknown type name 'string'
    explicit logic_error(const string&);
                               ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:100:34: error: unknown type name 'string'
    explicit runtime_error(const string&);
                                 ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:115:59: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit domain_error(const string& __s) : logic_error(__s) {}
                                                          ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:125:63: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit invalid_argument(const string& __s) : logic_error(__s) {}
                                                              ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:135:59: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit length_error(const string& __s) : logic_error(__s) {}
                                                          ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:145:59: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit out_of_range(const string& __s) : logic_error(__s) {}
                                                          ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:155:58: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit range_error(const string& __s) : runtime_error(__s) {}
                                                         ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:165:61: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit overflow_error(const string& __s) : runtime_error(__s) {}
                                                            ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/stdexcept:175:62: error: unknown type name 'string'
    _LIBCPP_INLINE_VISIBILITY explicit underflow_error(const string& __s) : runtime_error(__s) {}
                                                             ^

add links to sections and examples

in the table of contents, and the drake example listing in the drake appendix

set_1: RunPendulumSimulation does not log initial condition

In the problem assignment, when plotting, x(t = 0) is shown as [0, 0], rather than [1, 0] (from logger.get_data()).
This can be solved by setting the initial state on the simulator's context before running initialization. One way would be to change the code to:

# Set the initial conditions for the simulation.
context = diagram.CreateDefaultContext()
state = context.get_mutable_continuous_state_vector()
state.SetFromVector(x0)

# Create the simulator.
simulator = Simulator(diagram, context)

\cc @peteflorence @gizatt

planar_rigid_body_visualizer edgecolor is not visible

For the purely grey double pendulum, it makes for a pretty visually unappealing render. Everything looks much sharper with the black edge.

I see you've set edgecolor='k', but it's not working (at least not on my machine... though the pendulum works fine). i spent a minute looking at it, but @gizatt would appreciate if you could take this one.

interactive slider pendulum/torque_slider_demo.py

It works for me by adding this at the top:
from pylab import *

and replacing simulator.StepTo(args.duration) with

plt.pause(0.1)
for i in range(1000000):
	plt.pause(0.000000001)
	simulator.StepTo(i)

It's not a good solution, but from my understanding is that simulator is a C++ code and I don't understand how it would interactively updated from mathplotlib?

customize elib script interaction

capture repeated elib entries (and give the same number)
write refs to the end of each chapter?

Example 1.1: Typo in \qddot equation, Coriolis terms missing \qdot product

The rigid body equations in terms of \qddot are presently written as:
q¨=M^{−1}(q)[τg(q)+Bu−C(q,q˙)]

but it seems that it should be:
q¨=M^{−1}(q)[τg(q)+Bu−C(q,q˙)q˙]

print symbolic dynamics.