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As stated in the comments of the question, the orientation constraints bound the states allowed in the path, but does not affect the tolerances on the goal.

I used instead MoveGroupCommander.set_goal_orientation_tolerance (with a default value of 0.001) to relax the orientation tolerances on the goal, accepting paths ending in poses with different orientation.

I tested this in the same situation described in the question giving a tolerance of 20° (in radians) and it worked. It found the path shown in the following image:

Disadvantage is that I can't give different tolerances for different axis.

As stated in the comments of the question, the orientation constraints bound the states allowed in the path, but does not affect the tolerances on the goal.

I used instead MoveGroupCommander.set_goal_orientation_tolerance (with a default value of 0.001) to relax the orientation tolerances on the goal, accepting paths ending in poses with different orientation.

I tested this in the same situation described in the question giving a tolerance of 20° (in radians) and as shown in the next lines of code:

commander = moveit_commander.MoveGroupCommander(group_name)
...
commander.set_goal_orientation_tolerance(np.deg2rad(20))

And it worked. It found the path shown in the following image:

Disadvantage is that I can't give different tolerances for different axis.axis, but it worked as I intended.