feat(autoware_multi_object_tracker): new function to add odometry uncertainty

[technolojin]

Description

Add a new method that adds the odometry uncertainty to the object covariance.

1. Add an option to enable/disable the odometry uncertainty consideration
2. Implement the covariance converter from the odometry uncertainty to the object covariance
3. Refactor the covariance processing

The odometry message is a dummy, and will be replaced by system message.
Software architecture need to be determined to subscribe the odometry message.

Related links

This PR will be merged after PR autowarefoundation/autoware_launch#1196

• Link

How was this PR tested?

• disabled

• enabled - the object covariance is enlarged

• experiments
  Exaggerate parameters of odometry covariance to check the effect. The following results will not shown in the current PR parameters.

1. large x-x covariance - the covariance is extended to x direction (map coordinate)

5. large yaw-yaw covariance

6. large x-velocity covariance

Notes for reviewers

This function will not be implemented by default.

Interface changes

None.

Effects on system behavior

None.

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Codecov Report

Attention: Patch coverage is 0% with 69 lines in your changes missing coverage. Please review.

Project coverage is 28.43%. Comparing base (802f906) to head (03130da).
Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
..._tracker/lib/uncertainty/uncertainty_processor.cpp	0.00%	47 Missing ⚠️
...i_object_tracker/src/multi_object_tracker_node.cpp	0.00%	20 Missing ⚠️
...lti_object_tracker/src/processor/input_manager.cpp	0.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9139      +/-   ##
==========================================
- Coverage   29.81%   28.43%   -1.38%     
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  Files        1338     1306      -32     
  Lines      103301   101123    -2178     
  Branches    40233    39213    -1020     
==========================================
- Hits        30797    28757    -2040     
- Misses      69518    69622     +104     
+ Partials     2986     2744     -242     

Flag	Coverage Δ		*Carryforward flag
differential	0.00% <0.00%> (?)
total	28.46% <ø> (-1.35%)	⬇️	Carriedforward from 4c79e10

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[YoshiRi]

Do we have any explanation about these dummy parameters?

[technolojin]

At this PR, the imput will be a dummy fixed value.
After subscribing a new message is decided, it will be replaced by real one.

[YoshiRi]

memorize mathematical equations by chat ai.

Mathematical Formulations

Ego Motion Covariance

The motion covariance due to the ego vehicle's velocities over time dt:

$$ Q_{motion} = \begin{bmatrix} (x_{ego} \cdot dt)^2 & 0 \\ 0 & (y_{ego} \cdot dt)^2 \end{bmatrix} $$

Updated Ego Position Covariance

Including motion uncertainty:

$$ P_{ego pose} = P_{odom pose} + R_{ego} Q_{motion} R_{ego}^T $$

Updated Ego Yaw Covariance

Including angular motion uncertainty:

$$ COV_{yaw} = COV_{ego yaw} + (\theta_{ego} \cdot dt)^2 $$

Object Position Covariance Update

1. Add Ego Position Uncertainty:

$$ P_{object pose} = P_{object pose} + P_{ego_pose} $$

2. Add Effect of Ego Yaw Uncertainty:

$$ COV_{by yaw} = COV_{ego yaw} \times r^2 $$

$$ P' = R^T_b P_{object pose} R_b $$

$$
P'{yy} = P' + COV{by yaw}
$$

$$ P_{object pose} = R_b P' R^T_b $$

Object Velocity Covariance Update

1. Add Ego Velocity Uncertainty:

$$ \Delta \theta = \theta_{object} - \theta_{ego} $$

$$ P_{object twist} = P_{object twist} + R_{\Delta \theta} P_{ego twist} R^T_{\Delta \theta} $$

2. Add Effect of Ego Yaw Rate Uncertainty:

$$ COV_{by yaw rate} = COV_{yaw rate} \times r^2 $$

$$ P' = R^T_b P_{object twist} R_b $$

$$
P'{yy} = P' + COV{by yaw rate}
$$

$$ P_{object\_twist} = R_b P' R^T_b $$

[YoshiRi]

LGTM