Introduction This papers presents a two new approaches based on formal methods to identify the singularity configurations of a free floating manipulator. The approach is validated through numerical simulations. Contributions The paper is well written and clear. The problem is well stated and justified. The innovation is located in Section III and Section IV. In the first one the ability to exploit the interval arithmetic and the second one is based on Taylor models. In the second part, the ability to apply the configuration space constraints within a trajectory planning constrained approach is shown. The contribution is clear and relevant. However, there are several aspects that need to be clarified in the paper I have just few comments to improve the readability First, it would be nice to compare the proposed solution in the validation part comparing it with at the determinant of the generalized Jacobian. I believe it should possible in all cases presented in the simulation part. A table showing this comparison can be added to identify the accuracy and precision of the multiple approaches that can be employed to solve the problem. Second, it will be nice to show for a complex manipulator case, that the proposed solution is more efficient compared to the classic one involving the Jacobian computation. Third, the approach needs to be tested on an experimental platform to confirm its validity. Finally, I would like some clarifications on the heuristic pruning. Is the gradient descent only within the set of candidate locations within the given set close to ? The writing of that paragraph seems disconnected between the first part of that section and the second one. Some comparisons will respect to the start of the arts methods in terms of computation efficiency and runtime are needed. In Section IV c, I believe the condition 23 should not be verified because that represent the singularity case in the map. Section V b does not present the Taylor case, which nullifies the main purpose of the work. This cannot be neglected and postponed to future works since the Taylor approach is core algorithm in the paper. Conclusion The paper is well written, easy to follow, and the contribution is clear. However, there are several aspects that need clarifications and improvements to make the contribution stronger and clearly suitable for this type of conference.