Unsupervised learning of metric representations from slow features
A method of unsupervised learning of a metric representation and a corresponding system for a mobile device determines a metric position information for a mobile device from an environmental representation. The mobile device comprises at least one sensor for acquiring sensor data and an odometer system configured to acquire displacement data of the mobile device. An environmental representation is generated based on the acquired sensor data by applying an unsupervised learning algorithm. The mobile device moves along a trajectory and the displacement data and the sensor data are acquired while the mobile device is moving along the trajectory. A set of mapping parameters is calculated based on the environmental representation and the displacement data. A metric position estimation is determined based on a further environmental representation and the calculated set of mapping parameters.
1. A method for determining a metric position information for a mobile device based on an environmental representation, the method comprising:
generating sensor data by at least one sensor mounted on the mobile device;
acquiring displacement data of the mobile device by an odometer system; and
generating an environmental representation R based on the sensor data by applying an unsupervised learning algorithm,
wherein the mobile device moves along a trajectory T, wherein the displacement data and the sensor data are acquired while the mobile device is moving along the trajectory T, and the trajectory T comprises plural curve segments S i , the method further comprising
calculating a set of mapping parameters W based on the environmental representation R and the displacement data, wherein the plural curve segments S i are parameterized by curve parameters in the step of calculating the set of mapping parameters W,
determining a metric position estimation based on a further environmental representation and the calculated set of mapping parameters W, and
segmenting the trajectory T into the curve segments S i with a set of curve parameters for each curve segment S i ,
wherein in the step of calculating the set of mapping parameters, the set of mapping parameters W and the set of curve parameters are calculated by minimizing on all curve segments S i a difference measure between positions obtained by means of the displacement data on the one hand and corresponding positions obtained by means of a feature vector determined by unsupervised learning on the other hand.
2. The method for determining a metric position information according to claim 1 , wherein
the plural curve segments S i include at least one curve type of a straight line, a nearly straight line, a circle, a circle segment, a sigmoidal curve, a sine curve, a spline or a polynomial curve of a low order.
3. The method for determining a metric position information according to claim 1 , wherein
the odometer system acquires the displacement data from at least one of a wheel odometer, a visual odometer and an inertial measurement unit.
4. The method for determining a metric position information according to claim 1 , wherein
the unsupervised learning algorithm uses a slowness learning algorithm, in particular a slow feature analysis.
5. The method for determining a metric position information according to claim 1 , wherein
the step of calculating the set of mapping parameters is performed during a training phase M 1 or during an initial operating phase or at scheduled intervals or continuously and incrementally.
6. The method for determining a metric position information according to claim 1 , wherein
the step of calculating the set of mapping parameters W is repeated when an inconsistency between the metric position information and the displacement data is detected.
7. The method for determining a metric position information according to claim 1 , wherein
the step of calculating the set of mapping parameters W is repeated when a residual exceeds a threshold in the step of calculating the set of mapping parameters.
8. The method for determining a metric position information according to claim 1 , wherein
the set of mapping parameters W is calculated as affine regressions for the location of the mobile device, in particular as two affine regressions for a two-dimensional location of the mobile device on a planar surface.
9. The method for determining a metric position information according to claim 1 , wherein
the set of mapping parameters W is calculated as nonlinear regressions, for example quadratic regressions, or by fitting with a neural network.
10. The method for determining a metric position information according to claim 1 , wherein
the set of mapping parameters W are calculated by solving an optimization problem using a set of linear equations E, or by using a simplex algorithm, or by a gradient descent on the set of linear equations E.
11. The method for determining a metric position information according to claim 10 , wherein
the set of mapping parameters W are calculated by gradient descent on the set of linear equations E, wherein derivatives of the set of linear equations E are computed before.
12. The method for determining a metric position information according to claim 1 , wherein
parameters for calculating the set of mapping parameters W are initialized based on at least a part of the displacement data.
13. The method for determining a metric position information according to claim 1 , further comprising
transforming, by at least one of rotating, minoring and shifting the calculated metric position estimation to a desired coordinate system.
14. The method for determining a metric position information according to claim 13 , wherein
the set of mapping parameters W is calculated for the desired coordinate system which is centered in a base station of the mobile device.
15. The method for determining a metric position information according to claim 13 , wherein
the set of mapping parameters W for the desired coordinate system centered in a base station of the mobile device are calculated by
constraining an optimization to a reference map position as an initial trajectory point in the base station, or
correcting the set of mapping parameters W in a post-processing step including at least one of rotating, shifting and mirroring the mapping to match an initial portion of the displacement data corresponding to an initial portion of the trajectory T.
16. The method for determining a metric position information according to claim 1 , wherein
the step of the mobile device moving along a trajectory T is part of a learning phase M 1 for learning the environmental representation R from the sensor data, wherein a memory of the mobile device is configured to store the sensor data acquired during the learning phase M 1 , or
the step of the mobile device moving along a trajectory T is performed after the learning phase M 1 has been performed.
17. The method for determining a metric position information according to claim 16 , wherein
the step of calculating the set of mapping parameters W is performed during the learning phase M 1 for learning the environmental representation R from the sensor data, wherein an online learning algorithm for learning the environmental representation R is used.
18. The method for determining a metric position information according to claim 1 , wherein
the step of calculating the set of mapping parameters W is performed alternately with a learning step of learning the environmental representation R from the sensor data.
19. A computer program embodied on a non-transitory computer-readable medium, said medium being encoded with program-code which, when the program is executed on a computer or digital signal processor, controls the computer or digital signal processor to execute the method according to claim 1 .
20. A system for determining a metric position information of a mobile device from an environmental representation, the mobile device comprising:
at least one sensor configured to acquire sensor data, and
an odometer system configured to obtain displacement data of the mobile device,
the system comprising an electronic control unit configured to generate an environmental representation R generated from the sensor data by applying an unsupervised learning algorithm,
wherein the electronic control unit is configured to calculate a set of mapping parameters W based on the environmental representation and the displacement data,
wherein the displacement data and the sensor data are acquired while the mobile device is traveling along a trajectory T, and the trajectory T comprises plural curve segments S i and the plural curve segments S i are parameterized by curve parameters when calculating the set of mapping parameters W,
wherein the system is further configured to calculate the metric position estimation based on the environmental representation R and the calculated set of mapping parameters W,
wherein the electronic control unit is configured to segment the trajectory T into the curve segments S i with a set of curve parameters for each curve segment S i , and
wherein the electronic control unit is configured to calculate the set of mapping parameters W and the set of curve parameters by minimizing on all curve segments S i a difference measure between positions obtained by means of the displacement data on the one hand and corresponding positions obtained by means of a feature vector determined by unsupervised learning on the other hand.
21. The system for determining a metric position information according to claim 20 , wherein
the mobile device comprises a mobile robot, a robotic lawn mower, a robotic cleaner, a moveable portion of a robot, or a smartphone.
22. A method for determining a metric position information for a mobile device based on an environmental representation, the method comprising:
generating sensor data by at least one sensor mounted on the mobile device,
acquiring displacement data of the mobile device by an odometer system, and
generating an environmental representation R based on the sensor data by applying a slowness learning algorithm,
wherein the mobile device moves along a trajectory T, wherein the displacement data and the sensor data are acquired while the mobile device is moving along the trajectory T, and the trajectory T comprises plural curve segments S i , the method further comprising
calculating a set of mapping parameters W based on the environmental representation R and the displacement data, wherein the plural curve segments S i are parameterized by curve parameters in the step of calculating the set of mapping parameters W,
determining a metric position estimation based on a further environmental representation and the calculated set of mapping parameters W, and
segmenting the trajectory T into the curve segments S i with a set of curve parameters for each curve segment S i ,
wherein in the step of calculating the set of mapping parameters, the set of mapping parameters W and the set of curve parameters are calculated by minimizing on all curve segments S i a difference measure between positions obtained by means of the displacement data on the one hand and corresponding positions obtained by means of a slow feature vector on the other hand.
23. A system for determining a metric position information of a mobile device from an environmental representation, the mobile device comprising:
at least one sensor configured to acquire sensor data, and
an odometer system configured to obtain displacement data of the mobile device,
the system comprising an electronic control unit configured to generate an environmental representation R generated from the sensor data by applying a slowness learning algorithm,
wherein the electronic control unit is configured to calculate a set of mapping parameters W based on the environmental representation R and the displacement data,
wherein the displacement data and the sensor data are acquired while the mobile device is traveling along a trajectory T, and the trajectory T comprises plural curve segments S i , and the plural curve segments S i are parameterized by curve parameters when calculating the set of mapping parameters W,
wherein the system is further configured to calculate the metric position estimation based on the environmental representation R and the calculated set of mapping parameters W,
wherein the electronic control unit is configured to segment the trajectory T into the curve segments S i with a set of curve parameters for each curve segment S i , and
wherein the electronic control unit is configured to calculate the set of mapping parameters W and the set of curve parameters by minimizing on all curve segments S i a difference measure between positions obtained by means of the displacement data on the one hand and corresponding positions obtained by means of a slow feature vector on the other hand.