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This may be more a problem than you expect, firstly there is a difference between the 'dexterous' and 'reachable' workspaces of a robot arm. The dexterous workspace is the volume the end effector can reach in any orientation and the reachable workspace is the volume that can be reached with the end effector in a limited set of orientations. We generally avoid moving beyond the dexterous workspace if possible, since by definition you'll be near a singularity.

I don't know the workings of Moveit in too much detail but mathematically if you request the end effector to simply be in a particular location then there are potentially a great many solutions.

One solution would be to try and estimate an end effector orientation beforehand that would give you a good chance of reaching that point. Since the robot arm will be at almost full reach one simple way of doing this would be to orient the end effector so it's facing in the same direction as the vector from the robot base to the desired end point. This should allow the arm to reach almost all of it's reachable volume.