A Closed-Form Constraint Networks Solver for Maximum Likelihood Mapping

摘要

Maximum likelihood mapping is one of the approachesrnapplied to simultaneous localization and mapping problems.rnAccording to such formulation map estimation correspondsrnto the configuration that maximizes the likelihood associatedrnto a constraint network representing the map. Several efficientrniterative fixed-point techniques have been proposed to solve thisrnoptimization problem in practice, but with no regard to thernstructure of the solution.rnIn this paper, we present the closed-form solution for a genericrnconstraint network of planar poses. The fundamental assumptionrnconcerns the form of error function and the expression of therncorresponding gradient. Through algebraic manipulation, thernequations relating position variables to angular parameters arernderived. Furthermore, the solution is expressed by an orthogonalityrncondition between the vector of orientation parametersrnand an affine transformation of the same vector. The proposedrnalgorithm has been implemented and applied to solve the positionrnequations of a simple constraint network.