In the case of the traditional differential approach of solving the inverse kinematic task, depending on the desired trajectory that may approach, reach, and cross the boundaries of non-singular domains or domains of different degree of singularity, certain joint velocities may take huge values. Within the singularity it may happen that the desired task cannot exactly be solved, and that this imprecise solution has one or more degree of freedom in its ambiguity. The motion planner provided with end-point position and orientation data with respect to the workshop’s Cartesian frame does not have satisfactory information for locally resolving ambiguity. The rather modern approaches follow global way of thinking and apply Genetic Algorithms or similar evolutionary methods requiring huge computational power. The here presented approach is a compromise between these essentially different cases. For non-singular points it applies a fast algorithm to the differential solution, while near and in the singularities the Complex Algorithm combining the primary (that is tracking the prescribed data as precisely as possible) and secondary (complementary aspects applied in ambiguity resolution) requirements in an efficient way. The method is illustrated by calculations for particular trajectories in the case of a 6 DOF robot arm.
Analysis and boundary value problems on singular domains: An approach via bounded geometry
