Multi-robot localization

de robots

UPJV, Département EEA M2 EEAII, parcours ViRob

Fabio MORBIDI

Laboratoire MIS

Équipe Perception et Robotique E-mail: [email protected] Année Universitaire 2015/2016

Mercredi 10h00-12h30 et jeudi 9h00-12h30 salle TP202

Multi-robot localization

Multi-robot localization: problem formulation

  Multi-robot localization: estimation of the pose (the position and orientation , ), of a team of mobile robots with respect to a common reference frame using the proprioceptive and exteroceptive

measurements

Robot

Robot

Robot 1

Beacon or landmark

Robot 2 q_i = [x_i, y_i, θ_i]^T

What the robots see ...

The circled robot is equipped with a laser scanner, and this is its perception of the surrounding environement ...

Beacon Teammate robot

Cooperative positioning

  Idea: use the other robots in the team as moving beacons

  The robots are divided into two groups, A and B, and their positions are tracked by repeating move-and-stop actions:

1.  Group A remains stationary at a known position. Move group B and make it

position itself relative to group A using information from the proprioceptive sensors 2.  Stop group B after it has traveled an appropriate distance, and accurately measure

its position relative to the group-A robots

3.  Exchange roles of groups A and B and repeat the steps above 4.  Repeat this process until they reach the target positions

“Cooperative positioning with multiple robots”, R. Kurazume, S. Nagata, S. Hirose, in Proc. IEEE Int. Conf. Robotics Automation, vol. 2, pp. 1250-1257, 1994

A A A

B

B

B

Cooperative localization

  Cooperative localization: the problem of estimating the pose of a group of robots in a common fixed frame using

relative measurements among the robots

  In general, the ability of sensing each other improves the localization of the entire system obtained by simple odometry

  The fusion of proprioceptive and exteroceptive sensor information is usually performed using the EKF or a particle filter

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Robot

?

Robot

Measurement

Fixed frame

qi = [xi, yi, θi]^T

qj = [xj, yj, θj]^T

Cooperative localization: measurement equation

  Let us assume that at step k robot observes robot using its exteroceptive sensor. The measurement equation is then:

where is a zero-mean white Gaussian noise with covariance matrix   To implement the correction step of the EKF for solving the cooperative

localization problem, we need to compute the Jacobians and of with respect to and .

Robot

Robot

Fixed frame

zij(k) = h(qi(k), qj(k)) + rij(k),

rij

Cooperative localization: measurement equation

  In 2-D, there are three possibile types of relative measurements:

1.  Relative bearing 2. Relative distance 3. Relative orientation

  Other types of measurements can be taken into account as combinations of these three (e.g. relative position = relative bearing + relative distance)

Relative bearing Relative distance Relative orientation

Let and .   Relative bearing :

  Relative distance :

  Relative orientation :

Cooperative localization: measurement equation

Cooperative localization: observability

  If no robot has absolute localization capabilities, the multi-robot system is not observable, i.e. the error will increase indefinitely, and the estimate of the poses in will eventually diverge

  However, even if the team is lost in , the error on the relative poses between the robots , converges to zero

  If at least one robot has absolute localization capabilities (e.g., because it has a GPS or is able to detect a beacon of known position), the multi-robot system becomes observable, and the pose estimation error converges to zero   This happens since one robot is able to estimate its pose in and

the other robots are able to localize themselves with respect to it

For further details, see:

  “Observability Analysis for Mobile Robot Localization”, A. Martinelli, R. Siegwart, in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 1471-1476, 2005   “Distributed Multirobot Localization”, S.I. Roumeliotis, G.A. Bekey, IEEE Trans.

Robotics and Automation, vol. 18, n. 5, pp. 781-795, 2002

•  No robot with absolute localization capabilities:

Estimated poses

•  Robot with absolute localization capabilities:

Actual poses

The estimated and actual poses are “close”

to each other

Cooperative localization: observability

Relative Mutual Localization

  How can we avoid the observability problem of Cooperative Localization?

  We can provide each robot with a reference frame with respect to which it cannot get lost

  Let us define an attached moving frame for robot

  Relative Mutual Localization (RML): the problem of estimating the relative poses between the moving frames

  Each robot computes an estimate of the pose of the teammates in its reference frame. Each robot considers itself always in

  This approach is also called robo-centric or ego-centric

For more details, see :

“Robot-to-robot relative pose estimation from range measurements", X.S. Zhou, S.I. Roumeliotis, IEEE Trans. Robotics, vol. 24, n. 6, pp. 1379-1393, 2008

Relative Mutual Localization

Robot

Robot

Robot

?

?

Measurement

Measurement

Absolute Mutual Localization

  Robot has:

  A fixed frame

  An attached moving frame

  Absolute Mutual Localization (AML):

the problem of estimating the relative pose between the fixed frames using the relative measurements among the robots

  Applications:

  Map merging

  Cooperative exploration

  AML is solved if RML is solved and the agents are localized in their fixed frames

Robot Robot

?

Measurement

Known by robot

Known by robot

Multi-robot localization problems: summary

  Cooperative Positioning: groups of robots are used as moving beacons   Cooperative Localization: the robots estimate their pose in a common

fixed frame using relative measurements

  Relative Mutual Localization (RML): the robots estimate the change of coordinates among their attached frames using relative measurements

(localization of sensor networks: special case of RML in which the agents or robots are static)

  Absolute Mutual Localization (AML): the robots estimate the relative poses between their fixed frames using relative measurements

Multi-robot SLAM

SLAM problem

The SLAM problem asks if it is possible for a mobile robot to be placed at an unknown location in an unknown environment, and for the robot to incrementally build a consistent map of this environment while simultaneously determining its location within this map

See video SLAM1 Robot

•  Critical issue in SLAM

•  Loop-closure

See video SLAM2

For further details on SLAM, see the survey paper:

•  “Simultaneous localization and mapping: part I ”, H.H. Durrant-Whyte, T. Bailey, in IEEE Robotics & Automation Magazine, vol. 13, n. 2, pp. 99-110, 2006

Start End

Gap

Gap

SLAM problem

Map constructed

Cooperative SLAM (C-SLAM)

•  In a 2D C-SLAM,

a team

positions (range and bearing) of other robots in the team and of point beacons detected in the environment

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Beacon 1 Beacon 2

Beacon 3

Robot 1

Robot 2

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“Estimating uncertain spatial relationships in robotics”, R.C. Smith, M. Self, P. Cheeseman, in Autonomous Robot Vehicles (Eds. I. Cox, G. Wilfong),

Springer, pp. 167-193, 1990

Measurement

C-SLAM

•  The robots use proprioceptive measurements to propagate their position estimates, and are equipped with exteroceptive sensors (e.g. laser range finders) that enable them to measure the relative position of other robots and beacons

•  Typically, all measurements are fused together using an extended Kalman filter in order to produce estimates of the position of the robots and of the beacons

See video C-SLAM

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?

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Beacon 1 Beacon 2

Robot 1

Robot 2

?

?

Beacon 3

C-SLAM: some variations on the theme

  C-SLAM using set-membership estimation:

- “Simultaneous localization and map building for a team of cooperating robots:

a set membership approach”, M. Di Marco, A. Garulli, A. Giannitrapani, A. Vicino, IEEE Trans. Robotics Automation, vol. 19, n. 2, pp. 238-249, 2003

  C-SLAM using particle filters:

- “Multi-robot simultaneous localization and mapping using particle filters“, A. Howard, Int. J. Robotics Research, vol. 25, n. 12, pp. 1243-1256, 2006

  Derivation of analytical bounds for the positioning uncertainty in C-SLAM (in terms of number of beacons and robots, accuracy of robots’ sensors and

topology of the Relative Position Measurement Graph)

- “Predicting the performance of cooperative simultaneous localization and

mapping (C-SLAM)”, A.I. Mourikis, S.I. Roumeliotis, Int. J. Robotics Research, vol. 25, n. 12, pp. 1273-1286, 2006.