[ImuFactor] Add an on manifold Imu Factor #279

bradley-solliday-skydio · 2022-12-20T00:48:42Z

Unit testing is left to a follow up commit.

The core use-facing api is found in

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h
symforce/slam/imu_preintegration/imu_factor.h

Unlike most other factors (/residual functions) in symforce, the
ImuFactor is a functor so as to store the pre-integrated values
with the function rather than in the Values. (There are a lot of
parameters that are constant and unique to each factor).

A python version of the ImuFactor class will come in a subsequent
commit.

Topic: on_manifold_imu_factor

bradley-solliday-skydio · 2022-12-20T00:48:45Z

Reviews in this chain:
└#279 [ImuFactor] Add an on manifold Imu Factor
　└#280 [ImuFactor] Unit test the on manifold ImuFactor
　　└#281 [ImuFactor] tangent space Imu Factor

bradley-solliday-skydio · 2022-12-20T00:48:45Z

#	head	base	diff	date	summary
0	b58932b1	1c44a943	diff	Dec 19 16:48 PM	17 files changed, 12543 insertions(+)
1	cb930c9d	1c44a943	diff	Dec 20 1:09 AM	7 files changed, 7430 insertions(+), 7384 deletions(-)
2	c75ca927	1c44a943	diff	Dec 20 19:54 PM	10 files changed, 7587 insertions(+), 7503 deletions(-)
3	ac03a31b	1c44a943	diff	Dec 21 0:49 AM	8 files changed, 5671 insertions(+), 8077 deletions(-)
4	6a10ac05	1c44a943	diff	Dec 21 2:12 AM	3 files changed, 11 insertions(+), 5 deletions(-)
5	d1c3e651	1c44a943	diff	Jan 3 13:30 PM	9 files changed, 7432 insertions(+), 7904 deletions(-)
6	49a9c23d	474f1bd5	diff	Jan 6 9:04 AM	12 files changed, 144 insertions(+), 5942 deletions(-)
7	cd66203d	474f1bd5	diff	Jan 6 9:51 AM	2 files changed, 6 insertions(+), 6 deletions(-)
8	164c5e3e	474f1bd5	diff	Jan 6 12:23 PM	4 files changed, 15 insertions(+), 17 deletions(-)
9	d7d5a05f	474f1bd5	diff	Jan 10 16:25 PM	8 files changed, 119 insertions(+), 19 deletions(-)
10	6e00ec4f	474f1bd5	diff	Jan 11 10:57 AM	2 files changed, 17 insertions(+), 6 deletions(-)
11	a74eae62	474f1bd5	diff	Jan 11 15:27 PM	5 files changed, 707 insertions(+), 692 deletions(-)
12	91255e99	474f1bd5	diff	Jan 11 15:33 PM	1 file changed, 2 deletions(-)
13	0fe0e7e5	474f1bd5	diff	Jan 11 18:31 PM	1 file changed, 4 insertions(+), 2 deletions(-)
14	e311bc4e	474f1bd5	diff	Jan 12 11:45 AM	13 files changed, 1060 insertions(+), 1019 deletions(-)
15	7970c6f0	474f1bd5	diff	Jan 12 12:42 PM	2 files changed, 4 insertions(+), 4 deletions(-)
16	63a4d237	474f1bd5	diff	Jan 12 16:23 PM	1 file changed, 1 insertion(+), 1 deletion(-)
17	9630e6b6	4c368815	diff	Jan 19 13:57 PM	10 files changed, 101 insertions(+), 40 deletions(-)
18	fa8474dd	4c368815	diff	Jan 19 18:41 PM	1 file changed, 2 insertions(+), 2 deletions(-)
19	9c6f3d96	4c368815	diff	Jan 20 10:32 AM	5 files changed, 633 insertions(+), 663 deletions(-)
20	b75e14bf	4c368815	diff	Jan 25 10:12 AM	3 files changed, 85 insertions(+), 85 deletions(-)
21	50a2f1da	4c368815	diff	Jan 25 21:09 PM	1 file changed, 1 insertion(+)
22	a83f3772	4c368815	diff	Jan 31 17:41 PM	4 files changed, 1022 insertions(+), 65 deletions(-)
23	111652d9	4c368815	diff	Jan 31 17:53 PM	2 files changed, 12 insertions(+), 7 deletions(-)
24	615a9a36	4c368815	diff	Jan 31 17:57 PM	1 file changed, 13 insertions(+), 11 deletions(-)
25	deda3fc9	4c368815	diff	Feb 1 14:33 PM	2 files changed, 7 insertions(+), 7 deletions(-)

symforce/slam/imu_preintegration/imu_factor.h

bradley-solliday-skydio

Had a lot of comments because there were quite a few areas I wanted feedback on.

As a note, if reviewing in the browser, the i shortcut hides (and reveals) all comments. Using it will likely make reviewing easier.

symforce/slam/imu_preintegration/generate.py

symforce/slam/imu_preintegration/imu_factor.h

symforce/slam/imu_preintegration/manifold_symbolic.py

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

symforce/slam/imu_preintegration/imu_factor.h

bradley-solliday-skydio · 2022-12-21T10:22:42Z

symforce/slam/imu_preintegration/imu_factor.h

+ * Based heavily on the on manifold ImuFactor found in GTSAM and on the paper:
+ *
+ * Christian Forster, Luca Carlone, Frank Dellaert, and Davide Scaramuzza,
+ * “IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation”,
+ * Robotics: Science and Systems (RSS), 2015.


Is this a sufficient citation? Should I put it in other places as well?

You could also cite the original paper by Lupton.

symforce/slam/imu_preintegration/manifold_symbolic.py

symforce/slam/imu_preintegration/imu_factor.cc

symforce/slam/imu_preintegration/manifold_symbolic.py

symforce/slam/imu_preintegration/imu_factor.h

symforce/slam/imu_preintegration/manifold_symbolic.py

aaron-skydio · 2022-12-28T00:23:01Z

Noting previous comments are here: bradley-solliday-skydio#48

aaron-skydio

Didn't get to symforce/slam/imu_preintegration/preintegrated_imu_measurements.h yet

CMakeLists.txt

gen/cpp/sym/factors/imu_manifold_preintegration_update.h

symforce/slam/imu_preintegration/generate.py

symforce/slam/imu_preintegration/manifold_symbolic.py

aaron-skydio · 2022-12-28T04:15:42Z

symforce/slam/imu_preintegration/manifold_symbolic.py

+        # Definitely correct, but not very amenable to CSE
+        def new_state_D(wrt_variables: T.List[T.Any]) -> sf.Matrix:
+            return sf.Matrix.block_matrix(
+                [
+                    tangent_jacobians(new_DR, wrt_variables),
+                    tangent_jacobians(new_Dv, wrt_variables),
+                    tangent_jacobians(new_Dp, wrt_variables),
+                ]
+            )
+
+        new_state_D_state = new_state_D([DR, Dv, Dp])
+        new_state_D_gyro_bias = new_state_D([gyro_bias])
+        new_state_D_accel_bias = new_state_D([accel_bias])


This seems like a fantastic thing to compare against the handwritten version in a unit test :)

Hmm. Yes. You're right. I'll come up with some way to make comparing them simple and clean.

Note. I haven't actually gotten around to this. Not sure about it's priority on whether it should be punted indefinitely, reserved for a follow up PR, or added to this one (or the unit test PR that will be merged at the same time as this one).

I guess I was hoping we'd do this in the unit test PR - it is a little unfortunate to just leave this here, pylint is right that constant tests are usually a bad sign. If we're not going to add this test in this PR or the unit test PR we should probably at least make this an argument to this function that defaults to the handwritten version

The only thing that had me hesitate was sorting out how to split out the two versions (auto-derivatives vs handwritten derivatives). The thing that made me hesitate about adding an argument to the function was that it would force us to use something like functools.partial to hide it from Codegen.

But, when I thought about it a bit more, I didn't see a better alternative. Anyway, since I made it possible to generate two separate versions, I went ahead and added the unit test to the unit test PR.

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

test/symforce_gen_codegen_test.py

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

aaron-skydio · 2022-12-28T06:38:25Z

symforce/slam/imu_preintegration/preintegrated_imu_measurements.cc

+  Rot3<Scalar> new_DR;
+  Vector3 new_Dv;
+  Vector3 new_Dp;
+  Matrix9 new_covariance;
+  Matrix3 new_DR_D_gyro_bias;
+  Matrix3 new_Dv_D_gyro_bias;
+  Matrix3 new_Dv_D_accel_bias;
+  Matrix3 new_Dp_D_gyro_bias;
+  Matrix3 new_Dp_D_accel_bias;


It almost seems like this set of things (maybe minus new_covariance) wants to be an LCM type generated from a python dataclass/Values, which would mean it could be one argument to this function (or the return value), and most of the copies below would just be assigning the LCM type, and some other things might be simpler as well. Just an idea, not necessarily sold on it

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

symforce/slam/imu_preintegration/imu_factor.cc

aaron-skydio

Looking good, mostly just minor documentation stuff

gen/cpp/sym/factors/imu_manifold_preintegration_update.h

gen/cpp/sym/factors/internal_imu_factor.h

aaron-skydio · 2023-01-12T02:55:21Z

gen/cpp/sym/factors/internal_imu_factor.h

+ *     DR_D_gyro_bias (sf.M33): Derivative of DR w.r.t. gyro_bias evaluated at gyro_bias_hat
+ *     Dp_D_accel_bias (sf.M33): Derivative of Dp w.r.t. accel_bias evaluated at accel_bias_hat
+ *     Dp_D_gyro_bias (sf.M33): Derivative of Dp w.r.t. gyro_bias evaluated at gyro_bias_hat
+ *     Dv_D_accel_bias (sf.M33): Derivative of Dv w.r.t. accel_bias evaluated at accel_bias_hat
+ *     Dv_D_gyro_bias (sf.M33): Derivative of Dv w.r.t. gyro_bias evaluated at gyro_bias_hat


Should use the same ordering as we do in the update probably (probably just match the ordering in the struct everywhere?)

Huh. I agree. Not exactly sure why I did it that way here. Done.

It still seems like we have gyro then accel in some places and accel then gyro in others? Not sure if something just hasn't been pushed yet

Oh. I thought you were getting at how here its the DR, Dp, Dv instead of DR, Dv, Dp. Here gyro appears first as there's no DR_D_accel_bias (as it's just zero, as naturally the orientation is independent of the acceleration).

As for the ordering of gyro and accel, I only spotted 3 locations where gyro came first: 1) The ordering of the members in PreintegratedImuMeasurements (which doesn't really affect anything, but I just changed it so accel is first there for consistency), 2) the internal symbolic function integrate_state (which I have also just changed to be accel first), and 3) in the temporary variable state_D_bias in imu_manifold_preintegration_update (which I am keeping as is because the variable names don't line up nicely if I switch the order).

Yep, (1) and (2) are what I was referring to. Fine to leave (3), although as a super-nitpick we could pick gyro first instead to match the ordering there

The interface of imu_manifold_preintegration_update is still backwards from the rest of the code, and I think we should fix it? And then the body of ImuPreintegrator::IntegrateMeasurement which calls ImuManifoldPreintegrationUpdate

Oops. Looks like I overlooked that function. Fixed.

symforce/slam/imu_preintegration/imu_factor.h

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

symforce/slam/imu_preintegration/imu_factor.h

symforce/slam/imu_preintegration/manifold_symbolic.py

gen/cpp/sym/factors/internal/internal_imu_factor.h

symforce/slam/imu_preintegration/imu_factor.h

symforce/slam/imu_preintegration/imu_preintegrator.h

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

aaron-skydio · 2023-01-18T00:14:45Z

symforce/slam/imu_preintegration/imu_factor.h

+ * A factor for using on-manifold IMU preintegration in a SymForce optimization problem.
+ *
+ * Assumes IMU bias is constant over the preintegration window. Does not recompute the


It would be good to include a description of we mean by "on-manifold" here

That's reasonable. Though, I've never actually seen a definition of tangent space pre-integration (I've neglected to read through the gtsam implementation details, and that's the only source I can think of as my googling prowess is not up to par). So this is what I've put and hopefully it is correct:

* A factor for using on-manifold IMU preintegration in a SymForce optimization problem. By * on-manifold, it is meant that the angular velocity measurements are composed as rotations * rather than tangent-space approximations.

I believe this is correct, I might say something like "By on-manifold, we mean that the integration is performed (and integrated states are represented) on the manifold, as opposed to in the tangent space of the initial state"

A short discussion of the benefits / differences of the on-manifold vs tangent representations would be great, if possible.

gen/cpp/sym/factors/imu_manifold_preintegration_update.h

symforce/slam/imu_preintegration/preintegrated_imu_measurements.h

aaron-skydio · 2023-01-18T00:23:28Z

gen/cpp/sym/factors/internal_imu_factor.h

+ *     DR_D_gyro_bias (sf.M33): Derivative of DR w.r.t. gyro_bias evaluated at gyro_bias_hat
+ *     Dp_D_accel_bias (sf.M33): Derivative of Dp w.r.t. accel_bias evaluated at accel_bias_hat
+ *     Dp_D_gyro_bias (sf.M33): Derivative of Dp w.r.t. gyro_bias evaluated at gyro_bias_hat
+ *     Dv_D_accel_bias (sf.M33): Derivative of Dv w.r.t. accel_bias evaluated at accel_bias_hat
+ *     Dv_D_gyro_bias (sf.M33): Derivative of Dv w.r.t. gyro_bias evaluated at gyro_bias_hat


It still seems like we have gyro then accel in some places and accel then gyro in others? Not sure if something just hasn't been pushed yet

aaron-skydio · 2023-01-18T02:15:48Z

symforce/slam/imu_preintegration/imu_preintegrator.h

+   *   accel_cov is the covariance of the accelerometer measurement
+   *   gyro_cov is the covariance of the gyroscope measurement


Also mentioned here, but we should say what units there are in - assuming the test is right it seems to me like maybe these aren't technically the covariances of the measurements, they're the imu noise densities?

Yeah, the tests are right. So the units should be (radians per time)^2 * time (or, perhaps more recognizably to some, (radians per time)^2 / frequency).

And I suppose it is also important to mention that the units are expected to be in terms of radians, not degrees.

I don't know of any simple words that clearly communicate the idea that it's the, idk, covariance density in frequency space or whatever, so I'll just append [(radians / time)^2 * time] to the ends of the lines.

Probably good to specify seconds here for the time also, since these numbers are sometimes quoted in hours - I think the square roots of these are sometimes called angle random walk / velocity random walk, but just the units should be sufficient

I do wonder if it's more expected / intuitive for these parameters to be the covariances, or the (squared) angle/velocity random walks - maybe @chao-qu-skydio @dominic-skydio have opinions? Any idea what other libraries (e.g. GTSAM) expect?

Are you talking about the names? I think xxx_cov is fine. My suggestion is to simply make it a 3x1 vector (gyro_var) instead of 3x3 matrix (gyro_cov). I've never seen a use case for a full covariance matrix on imu measurement.

Talking about the values - is it more expected for these to be the measurement covariances ((rad/s)^2) or the squared angle/velocity random walks ((rad / sqrt(Hz))^2)? I do wonder if they're the (squared) angle/velocity random walks if we should maybe name them differently, but I agree naming it xxx_cov is probably fine in either case

About making these diagonal, it does save a good number of ops: #279 (comment)

They should be the continuous-time noise density squared. The random walk is for the bias.
Most imu datasheets only report a single number for all 3 axes (or at most 3, 1 for each), so a full covariance is an overkill IMO.

Well, I've changed the covariances to just be the diagonal entries, as it gives an immediate 10% op-count reduction for the integration step, and it should always be easy to go back and add a full square covariance option if we really wanted it.

aaron-skydio

Just one remaining comment (linking here so it doesn't get lost): #279 (comment)

Left some other comments wrapping up threads, but that's the only one that has anything I think we should definitely address, otherwise I think this is good to go! I do think we should have the PR with tests mostly ready before we actually merge this one, although I don't think we need to wait for the tests PR to be approved

aaron-skydio

Calling out this so it doesn't get buried: https://github.com/symforce-org/symforce/pull/279/files#r1088224485

aaron-skydio · 2023-01-26T21:58:37Z

symforce/slam/imu_preintegration/generate.py

+            "new_DR_D_gyro_bias",
+            "new_Dp_D_gyro_bias",
+            "new_Dp_D_accel_bias",
+            "new_Dv_D_gyro_bias",
+            "new_Dv_D_accel_bias",


The output names here are backwards

Oh oops. Forgot about that. Thanks.

aaron-skydio · 2023-01-27T22:05:46Z

Still waiting on this one: https://github.com/symforce-org/symforce/pull/279/files#r1088224485

aaron-skydio

Awesome, let's go for it

aaron-skydio · 2023-02-01T02:08:22Z

symforce/slam/imu_preintegration/manifold_symbolic.py

+    # Singularity handling,
+    epsilon: T.Scalar,
+    # Configuration
+    use_handwritten_derivatives: bool = True,


Don't we want to default this to false?

Well, I was thinking that it made sense to use the handwritten version because the two versions should be the same (in terms of correctness), but the handwritten version is faster. So, as a signaling mechanism as to which version you should use, I thought it made sense to default to the faster one.

But, now that I think about it, there's really no need to give a default value. I don't think there's any harm though for me to independently want to change it.

I somehow read this option as the inverse, I thought this was defaulting to automatic derivatives. We should default to using the handwritten derivatives like this already is since that's what we think you should use

aaron-skydio · 2023-02-01T02:10:31Z

symforce/slam/imu_preintegration/generate.py

+        docstring="""
+    Alternative to ImuManifoldPreintegrationUpdate that uses auto-derivatives. Exists only to
+    help verify correctness of ImuManifoldPreintegrationUpdate. Should have the same output.
+    Since this function is more expensive, there is no reason to use it instead.
+        """


No need to change anything here, but textwrap.dedent is your friend

Unit testing is left to a follow up commit. The core use-facing api is found in - symforce/slam/imu_preintegration/preintegrated_imu_measurements.h - symforce/slam/imu_preintegration/imu_factor.h Unlike most other factors (/residual functions) in symforce, the ImuFactor is a functor so as to store the pre-integrated values with the function rather than in the `Values`. (There are a lot of parameters that are constant and unique to each factor). A python version of the `ImuFactor` class will come in a subsequent commit. Topic: on_manifold_imu_factor

This was referenced Dec 20, 2022

[ImuFactor] Unit test the on manifold ImuFactor #280

Closed

[ImuFactor] tangent space Imu Factor #281

Closed

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IMU Preintegration #160

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aaron-skydio deleted the bradley.solliday/revup/main/on_manifold_imu_factor branch March 11, 2023 01:20

		* accel_cov is the covariance of the accelerometer measurement
		* gyro_cov is the covariance of the gyroscope measurement

[ImuFactor] Add an on manifold Imu Factor #279

[ImuFactor] Add an on manifold Imu Factor #279

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bradley-solliday-skydio commented Dec 20, 2022 •

edited

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asa Jan 20, 2023 •

edited

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chao-qu-skydio Jan 19, 2023 •

edited

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