A convex optimization based approach for pose SLAM problems

This paper demonstrates that 2D pose SLAM has an underlining near convex structure when formulated as a least squares (LS) optimization problem. By introducing new variables and some approximations, the LS pose SLAM problem can be formulated as a quadratically constrained quadratic programming (QCQP) problem. The QCQP formulation can then be relaxed into a semi-definite programming (SDP) problem which is convex. Unique solution to the convex SDP problem can be obtained without initial state estimate and can be used to construct a candidate solution to the original LS pose SLAM problem. Simulation datasets and the Intel Research Lab dataset have been used to demonstrate that when the relative pose information contain noises with reasonable level, the candidate solution obtained through the relaxation is very close to the optimal solution to the LS SLAM problem. Thus in practice, the candidate solution can serve as either an approximate solution or a good initial guess for a local optimization algorithm to obtain the optimal solution to the LS pose SLAM problem.