Tim Bailey
Constrained Initialisation for Bearing-Only SLAM
IEEE International Conference on Robotics and Automation, 2003
DescriptionThis paper investigates the feature initialisation problem for bearing-only SLAM. Bearing-only SLAM is an attractive capability due to its relationship with cheap vision sensing, but initialising landmarks is difficult. First, the landmark location is unconstrained by a single measurement, and second, the location estimate due to several measurements may be ill-conditioned. This paper presents a solution to the the feature initialisation problem via the method of "constrained initialisation", where measurements are stored and initialisation is deferred until sufficient constraints exist for a well-conditioned solution. A primary contribution of this paper is a measure of "well-conditioned" for initialisation within the traditional extended Kalman Filter (EKF) framework.
AbstractSimultaneous Localisation And Mapping (SLAM) is a stochastic map building method which permits consistent robot navigation without requiring an a priori map. The map is built incrementally as the robot observes the environment with its on-board sensors and, at the same time, is used to localise the robot. Typically, SLAM has been performed using range-bearing sensors, but the development of a SLAM implementation using only bearing measurements is desirable as it permits the use of sensors such as CCD cameras, which are small, reliable and cheap. However, bearing-only SLAM is hindered by the feature initialisation problem, where the estimated location of a new map landmark cannot be determined from a single measurement, and combined information from multiple measurements may be ill-conditioned. This paper presents a solution to the feature initialisation problem called constrained initialisation, which defers the use of sensor information until initialisation becomes wellconditioned. Measurements may be used out-of-sequence and all the available information can be incorporated without inconsistency. Furthermore, this method operates within the conventional extended Kalman Filter (EKF) framework of the SLAM algorithm.
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AddendumSeveral developments regarding this paper. First, the order of constraints in Section IV may be obviated by simply iterating over the constraint sequence using an iterated smoother to refine model linearisation (in fact, an IEKF will do as there is no prediction involved). Second, an efficient approximation of the relative entropy (KL-divergence) now exists for Gaussian mixtures, which might be applicable to the bearing-only problem. And third, computing a threshold on the relative entropy may or may not be a good general indicator of "well-conditioned"; a proper measure needs to be found and justified.
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