IEEE held the 2015 International Conference on Robotics and Automation (ICRA) in Seattle, WA this past May where I presented work on Closed Loop Task Space Control of an Interleaved Continuum-Rigid Manipulator.
This work builds upon that presented at IROS 2014 by closing the manipulator control loop. The paper describes this general task-space topology:
The forward path uses the manipulator inverse kinematics to find the joint commands that accomplish the desired task space command. This command is executed by the manipulator, whose resulting tip pose is sensed by a 6 degree-of-freedom electromagnetic tracker. Computing the measured task position from this pose and comparing with the desired task forms the task space error. Multiplying this error by the inverse of the manipulator Jacobian gives joint space velocity increments; these increments and their magnitudes indicate 'directions' the manipulator should move to reduce the task space error. These integral controllers on each of the joints accumulate these errors until the error is eliminated.
Two experiments were conducted with this controller, one configuration lay near the neutral axis with the other highly articulated.
For this pointing task, a fifth, virtual joint -- the tip-to-target distance -- was added to the four physical joints.
The twenty targets are executed step-wise, with 5 s each for refinement, proceeding counterclockwise from the lowermost point (such that 20s == 3 o'clock and 50s == 12). Several things can be observed in these results:
- the convergence changes with the configuration,
- the rigid manipulator (red) tends to excite faster dynamics than the flexible,
- the rigid joints become more useful at higher catheter articulations, and
- the accuracy of the refinement is a function of the configuration which leads to more dithering when highly articulated.
Better results were realized after the camera-ready deadline but shown at ICRA. The primary improvement came from shifting the integral controllers from joint to task space, and replacing the simple inverse with a multi-iteration numerical inverse kinematics. The presented controller moves the commanded task (by way of the integral controllers) while the IK algorithm ensures that the task is realizable. Much more will be said on this in future work, so for now see the highlight talk above and the interactive poster below.