Localisation et navigation de robots UPJV, Département EEA M2 EEAII, parcours ViRob Année Universitaire 2017/2018 Fabio MORBIDI Laboratoire MIS Équipe Perception ique E-mail: fabio.morbidi@u-picardie.fr Mercredi 10h00-12h30 et jeudi 9h30-12h00 Salles 304 et TP204
2 Multi-robot localization (research overview)
3 General 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 Beacon or landmark q i =[x i,y i,θ i ] T 2 1
4 What a robot sees... The circled robot is equipped with a laser rangefinder perception of the surrounding environement: shaded gray Beacon Teammate
5 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 A A A B B B Cooperative positioning with multiple robots, R. Kurazume, S. Nagata, S. Hirose, in Proc. IEEE Int. Conf. ics and Automation, vol. 2, pp. 1250-1257, 1994
6 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 Measurement q i =[x i,y i,θ i ] T q j =[x j,y j,θ j ] Fixed frame T
7 Cooperative localization: measurement equation Let us assume that at step k, robot observes robot using its exteroceptive sensor. The measurement equation is then: r ij z ij (k) =h(q i (k), q j (k)) + r ij (k), 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 two Jacobians (row vectors): H i = h(q i, q j ) q i, H j = h(q i, q j ) q j
8 Cooperative localization: measurement equation In 2D, 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
9 Cooperative localization: measurement equation Let and. Relative bearing : Relative distance : Relative orientation (linear equation) :
10 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 of the robots q i q j ( q i q j ), i, j, will converge 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 Localization, A. Martinelli, R. Siegwart, in Proc. IEEE/RSJ Int. Conf. Intelligent s and Systems, pp. 1471-1476, 2005 Distributed Multirobot Localization, S.I. Roumeliotis, G.A. Bekey, IEEE Trans. ics and Automation, vol. 18, n. 5, pp. 781-795, 2002
11 Cooperative localization: observability No robot with absolute localization capabilities: Estimated poses Actual poses with absolute localization capability: GPS The estimated and actual poses are close to each other
12 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: -to-robot relative pose estimation from range measurements", X.S. Zhou, S.I. Roumeliotis, IEEE Trans. ics, vol. 24, n. 6, pp. 1379-1393, 2008
13 Relative Mutual Localization Measurement Measurement
14 Absolute Mutual Localization 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 Known by robot Measurement Known by robot AML is solved if RML is solved and the agents are localized in their fixed frames
15 Multi-robot localization: problem summary Cooperative Positioning: two groups of robots are alternatively 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
16 Multi-robot SLAM (research overview)
17 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
18 SLAM problem Critical issue in SLAM Loop-closure Gap Map built End Start Gap For more details on SLAM, see the survey paper: Simultaneous localization and mapping: part I, H.H. Durrant-Whyte, T. Bailey, in IEEE. Autom. Mag., vol. 13, n. 2, pp. 99-110, 2006 See video SLAM2
19 Cooperative SLAM (C-SLAM) In a simple 2-D C-SLAM problem, a team mobile robots move continuously and randomly in a planar environment, while recording measurements of the relative positions (distance and bearing) of other robots in the team and of point beacons detected in the environment Beacon 1 Beacon 2 Beacon 3 1 Measurement 2 Measurement Estimating uncertain spatial relationships in robotics, R.C. Smith, M. Self, P. Cheeseman, in Autonomous Vehicles (Eds. I. Cox, G. Wilfong), Springer, pp. 167-193, 1990
20 C-SLAM (cont d) The robots use proprioceptive measurements to propagate their position estimates, and are equipped with exteroceptive sensors (e.g. laser rangefinders) that enable them to measure the relative position of other robots and beacons An extended Kalman filter is often used to fuse the measurements together, and produce estimates of the position of the robots and beacons Beacon 1 Beacon 2 Beacon 3 1 2 See video C-SLAM
21 C-SLAM: some variations on the theme C-SLAM using a set-membership approach: 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. ics and 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. ics 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. ics Research, vol. 25, n. 12, pp. 1273-1286, 2006