I understand that you are keen to know about the impact of the gripper's roll angle on the reachable poses for the UR5e robot. Your observation about the variation in the number of reachable poses with different roll angles is interesting.
For a UR5e robot, this variation can occur due to its kinematic configuration and the nature of the inverse kinematics solver. The UR5e robot, like many other robotic arms, has multiple solutions for a given end-effector pose due to its redundant degrees of freedom. This can result in different reachable poses depending on the roll angle.
Key Points to Consider:
- Degrees of Freedom: The UR5e robot has 6 degrees of freedom, which can lead to multiple solutions for the same end-effector pose. Different roll angles can lead to different configurations, resulting in variations.
- Inverse Kinematics Solver: The Generalized Inverse Kinematics (GIK) solver might have different tolerances or convergence criteria for different orientations, leading to variations in the number of solutions found.
- Numerical Stability: The numerical stability of the solver can also play a role. Small changes in roll angles might lead to different numerical behaviors in the solver.
- Workspace Boundaries: The workspace of the UR5e robot is not perfectly spherical, that means it has boundaries that can affect the reachability of certain poses depending on the roll angle.
I hope this helps.
