Analysis of Robotic Reach – Reachability Analysis

When designing a robotic workcell, the functions to be performed are known; however, the placement of the robotic manipulator and its workpieces are not known nor easily predicted. A reachability analysis tool has been developed to aid in determining the placement locations for the parts and the robot.

In one scenario (for painting the F-117 aircraft), the reachability analysis tool determined the zones on the plane which could be reached and the corresponding zones of space where the base of the robot could be placed to reach those locations. (See So, Where Do You Want Me To Put This Robot, Anyway?)

In another application, the robot's reach with a variety of end of arm tool designs was analyzed. The reachability analysis showed a "bubble" of reachable space with each tool configuration.

So, Where Do You Want Me To Put This Robot, Anyway?

If you want to get something done with a robot, you have to figure out where to put the thing so it can reach everything it needs to. If the robot is relatively large (with respect to the task at hand) and dextrous, it can be placed anywhere near the object and success will be forthcoming. "Relatively large quickly becomes too large in many applications. When coating airplanes (in our case, the F-117), it is completely too large. In these situations, a task is broken up into several pieces. But this means finding several good locations for robot placement. Finding one good location for a robot to do one task can (sometimes) be exceedingly difficult. Finding good locations for several overlapping and interacting tasks can elude even the most persistent of individuals.

We were having a hard time finding a place to put the robot to reach the top panel of the F-117. We were trying a random, place-by-eyeball method and had become convinced that it couldn't be done. We succeeded once again in proving that intuition and educated guesses are essentially useless when trying to assess what a robot can reach or how it will move. (If a robot has six joints, its motions are described in a six dimensional space. Our robot has seven joints and humans just can't intuit or visualize such things.)

Recognizing that it was unlikely we would be able to do this project on time and budget with the eyeball method, we turned to a concept partially developed a couple of years earlier. We dusted it off, filled it out and came up with a "reachability analysis tool." Given a task the robot must do (a path to follow), the reachability tool will calculate all the positions in space the robot can be placed and still reach everything. The result is displayed as a 3-D volume or iso-surface in a model of the workcell. This allows for immediate visual identification of the appropriate robot location.

While the top facet is the hardest to reach, all of the other facets (the F-117 does not have curved surfaces like most planes, it has flat, polygonal facets) had their own problems. By running this tool for each facet, we could see where the volumes overlapped. By carefully selecting the places where the most volumes overlapped, we could minimize the number of times the robot would have to be moved. This is highly desirable since moving the 10,000 lb., 20 ft tall robot is time consuming and hazardous. It was absolutely necessary to minimize robot moves in order to meet cost and schedule constraints for the production coating process.

Even when the process in question involves a single fixed robot and a small work object, this tool is proving valuable in optimizing performance. It can show all the places in the robot's workcell that the object can be placed and still be reached. This allows for much closer to optimal packing and placement of many objects in the robot workcell. Prior to this, designers had no visual feedback for selecting object placement. This software can also greatly aid robot tool design. In creating the tool to be placed on the end of the robot, the designer can see the effects that changes in tool length, angle and placement have on the robot's reachability. This tool is proving to be invaluable for extending robot capabilities and lowering system costs.