Study of inverse kinematic solutions in a hybrid robot with non-spherical wrist combining two industrial robot configurations

Finding effective solutions to the inverse kinematics problem (IKP) of serial robots remains a central issue in robotics. Numerous, often algebraic, methods exist, but a method is truly efficient only if it is accurate, fast, and exhaustive, i.e. provides all possible solutions, even without a closed-form expression. Beyond computing these solutions, understanding how the robot architecture influences their number is a key challenge, since very similar kinematics can yield very different solution sets because of a single geometric parameter. This paper investigates two very similar industrial cobots, the FANUC CRX-10iA and the Universal Robots UR3, both 6-DoF robots with a non-spherical wrist. Explicit IKP expressions exist for the UR3, whereas the CRX-10iA can admit up to 16 solutions for certain poses without a simple analytical form. To analyze this phenomenon, a hybrid parametric architecture, called RobHy, is introduced, interpolating between the CRX and UR3 kinematics and including all intermediate designs. By examining a set of representative 6D poses, the work characterizes how the number of IKP solutions varies with the RobHy parameter, highlights when RobHy exhibits more or fewer solutions than its parent robots, and elucidates the origin of the 16-solution cases.