Following on our work in the 2013 International Conference on Robotics and Automation, we continued exploring interleaved continuum-rigid manipulation in the journal of Robotics and Autonomous Systems. We explored a number of new facets of this concept including evaluation of a new controller, the effects of rigid actuator saturation, the manipulation range overlap of the rigid and flexible joints, and increase in dexterity from the addition of the rigid joint.
The controller used in this paper is similar to that presented at ICRA 2013, but different from that described in the ICRA proceedings paper. This controller was inspired by a controller for hard drives where the position error is partitioned between fast and slow actuators. Applied to our interleaved continuum-rigid catheter experiment, this frequency partitioning takes the form:
The particular Df and Dr compensator design and tuning determines what error is directed to the flexible and rigid actuators, leaving a system that can be treated as if it has a single actuator. The Dl loop compensator then tunes this 'single system' to the desired performance, as follows:
Effects of Rigid Actuator Saturation
While the actuation ranges of the rigid and flexible actuators must overlap for the rigid actuator to be able to compensate for errors in the flexible actuator, the rigid and flexible actuators will have different actuation ranges. For example, in the experimental testbed the rigid actuator has ~10° of actuation range, while the flexible segment can articulate nearly 360°. If the rigid link reaches the end of its actuation range (that is it saturates), it will not be able to achieve the positions commanded it, leading to the following aberrant behavior:
We show that as the saturation increases the phase margin decreases quickly, leading to the oscillatory behavior seen above.
Since the rigid and flexible joints are different, we cannot always expect that the joint-space errors for each actuator will ideally overlap in task-space. Thus depending on the particular characteristics of the flexible and rigid joints and the manipulator configuration, there may be some flexible segment errors which the rigid link actuator cannot compensate:
The addition of the rigid link joint has the potential to beneficially increase the overall workspace of the manipulator:
In this notional example, the tip is required to always point horizontally. Despite both manipulators having three degrees of freedom, the different character of the rigid link joint substantially increases the workspace. So in addition to correcting for flexible segment errors, the rigid link joint can also greatly increase workspace, limited only by the particular rigid link joint design.
Conrad, Benjamin L.; Jung, Jinwoo; Penning, Ryan S.; Zinn, Michael R., "A Hybrid Continuum-Rigid Manipulation Approach for Robotic Minimally-Invasive Flexible Catheter Based Procedures," Robotics and Autonomous Systems, submitted July 2013.