Handling Transitions across Singularities for UR-Like Serial Robots
Ivan Boschi, Alessandro De Toni, Roberto Di Leva, Edoardo Ida', Marco Carricato
AI summary
Problem
For non-cuspidal serial robots like UR cobots, transitioning between inverse kinematics solution branches requires crossing singular configurations, but existing methods lack straightforward techniques to maintain joint variable continuity and differentiability during these transitions, often causing tracking errors or motion interruptions.
Approach
The authors develop a computationally efficient algorithm that monitors Jacobian determinant factors to detect singularities and automatically selects the inverse kinematics solution branch minimizing joint displacement, ensuring smooth transitions while handling wrist singularities via 4-bar mechanism interpolation.
Key results
- Ensures continuous and differentiable joint trajectories across shoulder, elbow, and wrist singularities
- Eliminates tracking errors and motion interruptions common with standard UR controllers
- Provides a real-time, closed-form algorithm suitable for industrial digital controllers
- Validated through simulation and physical experiments on a UR5e robot
Why it matters
It provides robot programmers and control engineers with a reliable method to safely navigate cobots through singularities without sacrificing path accuracy or motion smoothness.
Abstract
The inverse kinematics (IK) of serial robots admits multiple solutions, making the selection of the desired one poten- tially 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 Do- mains (UDs), which are separated by surfaces defined by singular configurations. Within each UD, a single IK-solution branch cor- responds 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 im- portance 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, en- suring continuity and differentiability of the joint variables. The proposed method is evaluated against competing ones, both in simulation and experimentally, showing significant advantages.