Handling Transitions Across Singularities for UR-Like Serial Robots

The inverse kinematics (IK) of serial robots admits multiple solutions, making the selection of the desired one potentially challenging depending on the application at hand. For robots with a non-cuspidal architecture, a suitable strategy is to partition the joint space into independent regions, known as Uniqueness Domains (UDs), which are separated by surfaces defined by singular configurations. Within each UD, a single IK-solution branch corresponds to a specific robot posture. In this case, when an assigned task-space trajectory requires the robot to transition between UDs, a singular configuration must be crossed. Despite the practical importance of this issue, the existing literature lacks straightforward techniques for enabling such transitions. This paper proposes a method that facilitates switching between IK-solution branches when a task-space trajectory requires crossing a singularity, ensuring continuity and differentiability of the joint variables. The proposed method is evaluated against competing ones, both in simulation and experimentally, showing significant advantages.