- freely available
Sensors 2013, 13(1), 1247-1267; doi:10.3390/s130101247
2. Related Work
3. Problem Formulation and Solving
- Obstacle avoidance: provide collision-free navigation for the UGV during the execution of its mission through visual feedback from a low cost mini UAV.
- Obstacle mapping: obtaining the global position of the obstacles and built a geo-referenced map from it.
3.1. Coordinate Frames and Definitions
3.2. Sensor Geometric Model
3.2.1. Intrinsic Parameters
3.2.2. Extrinsic Parameters
- Obtaining the obstacle position in the world coordinate frame and apply all geometric transformations (i.e., forward camera model) from the pixel plane to the world reference frame.
- Obtain the distance from the UGV to the obstacle in meters in the image plane, and compute the obstacle position in the world reference frame from the UGV position and orientation in the world reference frame (given by a GPS). Herein, there is no need to translate the coordinates to the world frame.
3.2.3. Lens Distortions
3.3. Features Extraction
|Algorithm 1 UGV pose extraction.|
|1:||Countors ← FindCountours(Image<gray>)|
|2:||if 3 < length(Countors) then|
|3:||P ← GetPolygn(Contours)|
|4:||Point<px,Py> ← Centroid(P)|
|6:||M ← getMomentums(P)|
|7:||α ← Angle(M)|
|Algorithm 2 Obstacle position extraction.|
|1:||C ← HoughCircles(Image<gray>)|
|3:||r ← Radius(C)|
4. Position Estimation
4.1. Ground Robot Pose Estimation
- Vehicle ModelThe vehicle model represents its three-dimensional pose (position and orientation). This pose can be parametrized as s = [t, ψ]T = [x, y, z, φ, θ, ψ]T, where t = [x, y, z]T are the Universal Transverse Mercator (UTM) coordinates and the relative height of the vehicle, and Ψ = [φ, θ, ψ]T are the Euler angles on the X-Y-Z axis also known as Roll, Pitch, Yaw.In order to use an EKF to estimate the pose of the robot, it is necessary to express it as Multivariate Gaussian Distribution s ∼ N (μ, Σ). This distribution is defined by a six-element column vector μ, representing the mean values. Moreover, a six-by-six symmetric matrix Σ represents the covariance.Now it is necessary to define a non-linear conditional probability density function f (s (k), u (k + 1)) which represents the probability of the predicted position given the current vector state s(k) and the control vector u(k + 1).It is also very useful to define a global UGV transformation TUGV consisting of a rotation matrix R(Ψ) obtained from the Euler angles, and a translation t in the global reference frame.
- Measurement ModelsThe vehicle pose is updated according to the readings from three different sensors: The internal odometry of the UGV, a IMU sensor and a GPS. Thus, it is necessary to create a model that links the measurements of each sensor with the global position of the mobile robot. As was done with the pose of the vehicle, the observations of the sensors need to be expressed as Gaussian Distribution; this means that they should provide a vector of mean values and a symmetrical matrix of covariances.As it was done for the estimated UGV pose, a transformation Ti is defined for each measurement. These transformations are:
With the transformations defined, it is possible to define a probability density function for each one of them. In all cases, the H matrix (necessary to compute the estimation of the EKF) will be an identity matrix of dimension six. For the GPS and the IMU, the covariance associated with the rotation or translation, which are not provided, will be replaced by very high values.
- OdometryThe odometry provides a relative position and orientation constraint. To be able to use these measurements in a global reference frame, the transformation between two successive readings of the odometry (Todom−read(k) → Todom−read(k+1)) is calculated, and the resulting transformation is applied to the previous estimated position of the UGV.
- GPS.The readings from the GPS are converted to UTM using the equations form USGS Bulletin 1532 , and they are used to provide a global position constraint. However, the GPS does not provide information for the orientation of the robot, so only the position should be taken into account.
- IMU.The IMU readings are pre-processed to fuse the gyroscopes, accelerometers and magnetometers. In order to provide a global constraint of the orientation of the UGV, no position or translation constraints are obtained from this sensor.
4.2. Transformations and Obstacle Pose Estimation
6.2. Real Environment
7. Concluding Remarks
- Choset, H.; Lynch, K.; Hutchinson, S.; Kantor, G.; Burgard, W.; Kavraki, L.; Thrun, S. Principles of Robot Motion: Theory, Algorithms, and Implementations; MIT Press: Boston, MA, USA, 2005. [Google Scholar]
- Krotkov, E. Position Estimation and Autonomous Travel by Mobile Robots in Natural Terrain. Kent Forum Book. 1997. Available online: http://www.ri.cmu.edu/pub_files/pub3/krofkov_eric_1997_2/krotkov_eric_1997_2.pdf (accessed on 3 January 2013).
- Moseley, M.B.; Grocholsky, B.P.; Cheung, C.; Singh, S. Integrated long-range UAV/UGV collaborative target tracking. Proc. SPIE 2009, 7332. [Google Scholar] [CrossRef]
- Li, W.; Zhang, T.; Klihnlenz, K. A vision-guided autonomous quadrotor in an air-ground multi-robot system. Proceedings of 2011 IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, 9–13 May 2011; pp. 2980–2985.
- Chaimowicz, L.; Kumar, V. Aerial shepherds: Coordination among uavs and swarms of robots. In Distributed Autonomous Robotic Systems 6; Springer: Tokyo, Japan, 2007; pp. 243–252. [Google Scholar]
- Ishikawa, S.; Kuwamoto, H.; Ozawa, S. Visual navigation of an autonomous vehicle using white line recognition. IEEE Trans. Patt. Anal. Mach. Intell. 1988, 10, 743–749. [Google Scholar]
- Matsumoto, Y.; Inaba, M.; Inoue, H. Visual navigation using view-sequenced route representation. Proceedings of 1996 IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 22–28 April 1996; pp. 83–88.
- Dao, N.X.; You, B.J.; Oh, S.R. Visual navigation for indoor mobile robots using a single camera. Proceedings of 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), Edmonton, AB, Canada, 2–6 August 2005; pp. 1992–1997.
- Cherubini, A.; Chaumette, F. Visual navigation with obstacle avoidance. Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA, USA, 25–30 September 2011; pp. 1593–1598.
- Grocholsky, B.; Dille, M.; Nuske, S. Efficient target geolocation by highly uncertain small air vehicles. Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA, USA, 25–30 September 2011; pp. 4947–4952.
- Dille, M.; Grocholsky, B.; Nuske, S. Persistent Visual Tracking and Accurate Geo-Location of Moving Ground Targets by Small Air Vehicles. Proceedings of AIAA Infotech@Aerospace Conference, St. Louis, MO, USA, 29–31 March 2011.
- Rao, R.; Kumar, V.; Taylor, C. Visual servoing of a UGV from a UAV using differential flatness. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), Las Vegas, NV, USA, 27 October–1 November 2003; pp. 743–748.
- Elfes, A.; Bergerman, M.; Carvalho, J.R.H.; de Paiva, E.C.; Ramos, J.J.G.; Bueno, S.S. Air-ground robotic ensembles for cooperative applications: Concepts and preliminary results. Proceedings of 2nd International Conference on Field and Service Robotics, Pittsburgh, PA, USA, 29–31 August 1999; pp. 75–80.
- Vidal, R.; Rashid, S.; Sharp, C.; Shakernia, O.; Kim, J.; Sastry, S. Pursuit-evasion games with unmanned ground and aerial vehicles. Proceedings of IEEE International Conference on Robotics and Automation, Seoul, Korea, 21–26 May 2001; pp. 2948–2955.
- Phan, C.; Liu, H. A cooperative UAV/UGV platform for wildfire detection and fighting. Proceedings of Asia Simulation Conference: 7th International Conference on System Simulation and Scientific Computing, Beijing, China, 10–12 October 2008; pp. 494–498.
- Chaimowicz, L.; Grocholsky, B.; Keller, J.F.; Kumar, V.; Taylor, C.J. Experiments in Multirobot Air-Ground Coordination. Proceedings of the 2004 International Conference on Robotics and Automation, Barcelona, Spain, 18–22 April 2004; pp. 4053–4058.
- MacArthur, E.Z.; MacArthur, D.; Crane, C. Use of cooperative unmanned air and ground vehicles for detection and disposal of mines. Proc. SPIE 2005, 5999, 94–101. [Google Scholar]
- Valente, J.; Barrientos, A.; Martinez, A.; Fiederling, C. Field tests with an aerial–ground convoy system for collaborative tasks. Proceedings of 8th Workshop de RoboCity2030-II: Robots Exteriores, Madrid, Spain, 2 December 2010; pp. 233–248.
- Snyder, J.P. Map Projections: A Working Manual; Supersedes USGS Bulletin 1532; U.S. Geological Survey, U.S. Government Printing Office: Washington, DC, USA, 1987. [Google Scholar]
- Gadeyne, K.; BFL: Bayesian Filtering Library. 2001. Available online: http://www.orocos.org/bfl (accessed on 3 January 2012).
- Garzón, M.; Valente, J.; Zapata, D.; Chil, R.; Barrientos, A. Towards a ground navigation system based in visual feedback provided by a mini UAV. Proceedings of the IEEE Intelligent Vehicles Symposium Workshops, Alcal de Henares, Spain, 3–7 June 2012.
- Reynolds, C.W. Steering Behaviors For Autonomous Characters. Proceedings of Game Developers Conference, San Jose, CA, USA, 15–19 March 1999; pp. 763–782.
|Mean Square Error (m)||Standard Deviation|
|Mean Pos X (m)||Std. Dev. X||Mean Pos Y (m)||Std. Dev. Y|
|Average Frequency (Hz)||Max. Period (s)||Min. Period (s)|
|UGV Navigation System||10||0.103||0.096|
|Image and Data Processing||37||0.102||0.010|
|Trajectory Time:||39 s|
|UGV Max Speed||0.3 m/s|
|UGV Mean Speed||0.2048 m/s|
|UAV Max altitude||4.812 m|
|UAV Mean altitude||4.51 m|
|Total Trajectory Distance:||10.1999 m|
|Mean Pos X (m)||Std. Dev. X||Mean Pos Y (m)||Std. Dev. Y|
© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).