Probabilistic approaches to the AXB=YCZ calibration problem in multi-robot systems
Interest in multi-robot systems has grown rapidly in recent years. This is due in part to the reduced cost of such systems and in part to the increased difficulty of the tasks that they can address. A multi-robot system is usually composed of several individual robots such as mobile robots or unmann...
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| Published in | Autonomous robots Vol. 42; no. 7; pp. 1497 - 1520 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.10.2018
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | Interest in multi-robot systems has grown rapidly in recent years. This is due in part to the reduced cost of such systems and in part to the increased difficulty of the tasks that they can address. A multi-robot system is usually composed of several individual robots such as mobile robots or unmanned aerial vehicles. Many problems have been investigated for multi-robot system such as motion planning, collision checking and scheduling. However, not much has been published previously about the calibration problem for multi-robot systems despite the fact that it is the prerequisite for the whole system to operate in a consistent and accurate manner. Compared to the traditional hand–eye & robot–world calibration, a relatively new problem called the
A
X
B
=
Y
C
Z
calibration problem arises in the multi-robot scenario, where
A
,
B
,
C
are time-varying rigid body transformations measured from sensors and
X
,
Y
,
Z
are unknown static transformations to be calibrated. Several solvers have been proposed previously in different application areas that can solve for
X
,
Y
and
Z
simultaneously. However, all of the solvers assume a priori knowledge of the exact temporal correspondence among the data streams
{
A
i
}
,
{
B
i
}
and
{
C
i
}
. While that assumption may be justified in some scenarios, in the application domain of multi-robot systems, which may use ad hoc and asynchronous communication protocols, knowledge of this correspondence generally cannot be assumed. Moreover, the existing methods in the literature require good initial estimates that are not always easy or possible to obtain. To address this, we propose two probabilistic approaches that can solve the
A
X
B
=
Y
C
Z
problem without a priori knowledge of the temporal correspondence of the data. In addition, no initial estimates are required for recovering
X
,
Y
and
Z
. These methods are probabilistic in the sense of viewing the sets
{
A
i
}
,
{
B
i
}
, and
{
C
i
}
as samples drawn from underlying probability density functions. This is what allows these methods to work in the absence of temporal correspondence. However, measurement errors are not explicitly modeled, and so the results are sensitive to the sort of noise that is ubiquitous in real world data. We therefore introduce ways to add robustness to noise, including a hybrid method which combines traditional
A
X
B
=
Y
C
Z
solvers with the probabilistic methodology and an iterative method for refinement to add robustness in the case of noisy experimental data. It is shown that the new algorithm is robust to both noise and the loss of correspondence information in the data. These methods are particularly well suited for multi-robot systems, and also apply to other areas of robotics in which
A
X
B
=
Y
C
Z
arises. |
|---|---|
| ISSN: | 0929-5593 1573-7527 |
| DOI: | 10.1007/s10514-018-9744-3 |