An Extrinsic Calibration Tool for Radar, Camera and Lidar

Abstract

joint extrinsic calibration of all three sensing modalities on multiple measurements.
Furtheremore, obtain simultaneous measurements for all these modalities.

Three different configurations of the optimization criterion are considered, namely

1. using error terms for a minimal amount of sensor pairs,
2. using terms for all sensor pairs with additional loop closure constraints,
3. by adding terms for struecture estimation in a probablistic model.

Results:

1. all configureations achieve good results for lidar to camera errors
2. fully connected pose estimation shows the best performance for lidar to radar errors when more than 5 board locations are used.

zero mean Gaussian noise

FCPE is the best

I. INTRODUCTION

3 related techniques:

1. Minimally connected pose estimation (MCPE)
2. Fully connected pose estimation (FCPE)
3. Pose and structure estimation (PSE)

II. RELATED WORK

extrinsic calibration is also known as pose estimation [14] and sensor registration.

Extrinsic calibration can in turn be divided into target-less and target-based procedures.

table I

A. Multi-modal calibration with lidar, camera and radar

B. Calibrating more than two sensors

minimally connected pose estimation

C. Contributions

1. First, three extrinsic
   calibration configurations to jointly calibrate lidar, camera
   and radar are investigated. We study the three configurations,
   required number of calibration board locations, and choice
   for the reference sensor using a real multi-modal sensor
   setup.
2. Second, we propose a calibration target design that
   is detectable by lidar, camera and radar.
3. Third, we provide
   an open-source extrinsic calibration tool for these sensors,
   with bindings to Robot Operating System (ROS) 1 .

III. PROPOSED APPROACH

It is implemented as an open-source tool with bindings to the ROS middleware, and which includes a tool that can update Unified Robot Description Format (URDF), to facilitate extensibility and application on real robotic platforms.

a) Calibration target design:

For lidar and camera, edges and corners are features which can be detected accurately and robustly.

However, rectangular(矩形的) shaped objects are difficult to localise in lidar as a nearly horizontal edge might not intersect with any of the lidar scan planes [9].
So use cirular shapes for lidar.

Our proposed calibration target design has four circular holes and additionally contains a single metal trihedral corner reflector in the center at the back of the board to provide strong radar reflections as well.

Furthermore, our calibration board is made from styrofoam(聚苯乙烯泡沫塑料) to not affect the detectability of the corner reflector [9].

标定板和孔洞的尺寸问题文章中有更详细描述。

b) Detection of calibration target:

Both camera and lidar detectors return the 3D
locations of the four circle centers.

The radar returns detections in a 2D plane and generates
for each reflection a measurement in polar coordinates and
a RCS value.

c) Calibration procedures:

first introduce extrinsic calibration for two sensors.

Since each sensor has a different Field of View (FOV),the calibration target may not always be detectable by all.

To parameterize
the 6 degrees of freedom of transformation T 1,2 , we use
parameter vector θ 1,2 = (t x , t y , t z , v x · α, v y · α, v z · α).

Additionally, we enforce the constraint that the projected
3D points lie within radar Field of View (FOV).

Pose estimation can now be formulated as an optimization
problem to find the optimal transformation which minimizes
the total error f (θ 1,2 ) between all K calibration targets,…

Our tool uses Sequential Least SQuares Programming
(SLSQP) from the SciPy library [25] for optimization.

d) Joint calibration with more than two sensors:

1. Minimally connected pose estimation (MCPE):

   minimally connected graph

2. Fully connected pose estimation (FCPE):

   consider optimizing transformations between all sensors at once, without a special reference sensor.

   In addition,the closed loop constraint is introduced to ensure that all loops l equal the identity matrix,

   optimization is potentially more robust against noisy observations from one reference sensor. The downside is that the number of error terms increases
   quadratically with the number of sensors. Furthermore, additional loop constraints must be added as well.

3. Pose and structure estimation (PSE):

   This configuration explicitly estimates the calibration board poses and the observation noise of each sensor.

   The objective is to estimate both the unknown structure M = (m 1 , · · · , m K ) of the true target poses in a fixed coordinate frame, and the transformation T M,i from the fixed frame to each sensor i, see figure 2c.

   The potential benefit is that this is a homogeneous error metric. Another benefit of such a probabilistic formulation is that prior knowledge on board and sensor poses could be included, we have not pursued this direction here. The disadvantages are that the optimization is more complex and that the loop closure constraint is not explicitly enforced.

IV. EXPERIMENTS

lidar => on roof
radar => behind bumper
stereo camera => behind windscreen

With these sensors, we have recorded a dataset with sensor measurements of 29 calibration board locations that are located in the FOV of all
sensors and in the working range of 5 m from the car.

The used measure is the Root Mean Squared Error(RSME).

a) Choice of MCPE reference sensor:

b) Comparison to baseline method:

c) Required number of calibration board locations:

The figure shows that when 10 boards are used, the errors for FCPE and PSE have converged to ≤ 2 cm for both l2c and l2r transforms. MCPE performs the worst for the RMSE of l2r, whereas FCPE performs the best with a RMSE of less than 1.5 cm when using all 29 board locations. We have observed that PSE is sometimes less robust.

d) Sensitivity to observation noise:

e) Qualitative results:

V. CONCLUSION

presented an open-source extrinsic calibration tool for
lidar, camera and radar, and proposed three configurations
to estimate the sensor poses from simultaneous detections
of multiple calibration board locations.

all configurations
can provide good calibration results.

Words

multi-modal 多模态
modalities 模式
dismount v. 下马
schematic [skiːˈmætɪk] adj. 略图的，纲要的
explicit 明确的
formalize 正式化，形式化
distinction n. 差别
focal 焦点的
skewness 偏斜
Field of View (FOV)
suboptimal 次优
abbreviations n. [əˌbriːviˈeɪʃn] 缩写
routine [ruːˈtiːn] 常规
heterogeneous [ˌhetərəˈdʒiːniəs] 各种各样的
normal vectors 法向量
centroids 质心
diagonal [daɪˈæɡənl] 斜线的
variances n.方差;变化幅度;差额
deviation n. 偏差
styrofoam n. 聚苯乙烯泡沫塑料
beam n. 光束
intersect v. 相交，交叉，合流
diameter [dīˈamədər] n. 直径

Complementation

对这篇文章的理解：

所谓多传感器的标定，就是要找到多个传感器在相同的作用域范围内，把他们的坐标系调整到同一位置上，使它们看到的角度和目标物体是在同一维度观察的。
要实现这个目标，就要构建一个loss function，表示的是各个坐标系之间的偏差，求一个最小化偏差的问题，从而实现标定的效果最好。

常见的求最小偏差的方法有：