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Continuous Symmetries and Observability Properties in Autonomous Navigation

Agostino Martinelli 1
1 E-MOTION - Geometry and Probability for Motion and Action
LIG - Laboratoire d'Informatique de Grenoble, Inria Grenoble - Rhône-Alpes
Abstract : This paper considers the problem of estimation in autonomous navigation from a theoretical perspective. In particular, the investigation regards problems where the information provided by the sensor data is not sufficient to carry out the state estimation (i.e. the state is not observable). For these systems, it is introduced the concept of continuous symmetry. Detecting the continuous symmetries of a given system has a very practical importance. It allows us to detect an observable state whose components are non linear functions of the original non observable state. In order to illustrate the power of this concept, its application to a fundamental calibration problem is here presented. This paper provides two distinct contributions. The first one is the introduction in the frame work of autonomous navigation of this concept of continuous symmetry. The second one is the introduction of a simple and efficient strategy to extrinsically calibrate a bearing sensor (e.g. a vision sensor) mounted on a vehicle and simultaneously estimate the parameters describing the systematic error of its odometry system. The strategy uses a single point feature. Many accurate simulations and real experiments with the robot e-Puck equipped with encoder sensors and a camera show the robustness the efficiency and the accuracy of the proposed strategy.
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Contributor : Agostino Martinelli Connect in order to contact the contributor
Submitted on : Thursday, October 1, 2009 - 1:43:07 PM
Last modification on : Tuesday, October 19, 2021 - 11:16:56 PM
Long-term archiving on: : Wednesday, June 16, 2010 - 12:16:31 AM


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  • HAL Id : inria-00421233, version 1



Agostino Martinelli. Continuous Symmetries and Observability Properties in Autonomous Navigation. [Research Report] RR-7049, 2009. ⟨inria-00421233v1⟩



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