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In this paper, we study the back-end of simultaneous localization and mapping(SLAM) problem in deforming environment, where robot localizes itself andtracks multiple non-rigid soft surface using its onboard sensor measurements.An elaborate analysis is conducted on conventional deformation modellingmethod, Embedded Deformation (ED) graph. We demonstrate and prove that the EDgraph widely used in such scenarios is unobservable and leads to multiplesolutions unless suitable priors are provided. Example as well as theoreticalprove are provided to show the ambiguity of ED graph and camera pose. Inmodelling non-rigid scenario with ED graph, motion priors of the deformingenvironment is essential to separate robot pose and deforming environment. Theconclusion can be extrapolated to any free form deformation formulation. Insolving the observability, this research proposes a preliminary deformable SLAMapproach to estimate robot pose in complex environments that exhibits regularmotion. A strategy that approximates deformed shape using a linear combinationof several previous shapes is proposed to avoid the ambiguity in robot movementand rigid and non-rigid motions of the environment. Fisher information matrixrank analysis with a base case is discussed to prove the effectiveness.Moreover, the proposed algorithm is validated extensively on Monte Carlosimulations and real experiments. It is demonstrated that the new algorithmsignificantly outperforms conventional rigid SLAM and ED based SLAM especiallyin scenarios where there is large deformation.

An observable time series based SLAM algorithm for deforming environment