Wearable Intertace for Teleoperation of Robot Arms - WITRA

A Big Difference Between Work Envelopes

This is nice challenge to WITRA because since the human arm and SCARA have different kinematics and work envelope geometries, it is not an easy task to accomplish. Generally speaking, the work envelope of the human arm is a section of a sphere. That is, we can reach, with our hand, a great variety of positions in space that are limited by a sphercial-like boundary. On the other hand, SCARA's work envelope, when seen from above is like shown on the next figures

Figure 1: SCARA's work envelope seen from above

Figure 2: SCARA's work envelope in a isometric view. The curves are sections of the work envelope. The full work envelope is continuous in z-direction

Thus, one can notice how different from our arm's work envelope this is. 

Mapping From One to the Other

To procede with the geometrical mapping, a decision was made: make it as simpler as possible. Therefore the "trick" is to find sections of each work envelope that have similar geometries. Regarding the human arm, when seen from above, in a horizontal plane, the user can reach a space that resembles a section of a circular ring, as shown in the figure below:

Figure 3: Human arm's reachable space in a horizontal plane seen from above. Picture source: http://www.theergonomicscenter.com/portal/workstation.shtml

 In this manner, we can consider a feasible work envelope for the human arm, when seen from above, a section of a circular ring with 140 degrees of amplitude. Similarly, there is a section of SCARA's work envelope that has the same geometry. This space is reached, basically, when theta1 is rotated from 20 degrees to 160 degrees. The next figure shows how each final work envelope looks like. 

Figure 4: User's and SCARA's work envelope used in WITRA

Now it is easy to map from one to the other by simply applying a linear relationship between (x,y) coordinates from the user arm's work envelope to SCARA's one. Finally, the z position is simpler to deal with and linearly mapped from the z-coordinate of the user's arm to d3 ou z-coordinate from SCARA. 

In conclusion, we now have a way to translate the positions that the user can reach to goal positions on the robot's end-effector. 

On the next update we'll show it working with the 3D animation in MATLAB. 

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