Singularity Maps of Space Robots and their Application to Gradient-based Trajectory Planning

We present a numerical method to compute singularity sets in the configuration space of free-floating robots, comparing two different criteria based on formal methods. By exploiting specific properties of free-floating systems and an alternative formulation of the generalized Jacobian, the search space and computational complexity of the algorithm is reduced. It is shown that the resulting singularity maps can be applied in the context of trajectory planning to guarantee feasibility with respect to singularity avoidance. The proposed approach is validated on a space robot composed of a six degrees-of-freedom (DOF) arm mounted on a body with six DOF.