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Controlling soft continuum robotic arms is challenging due to their hyper-redundancy and dexterity. In this paper we experimentally demonstrate, for the first time, closed-loop control of the configuration space variables of a soft robotic arm, composed of independently controllable segments, using a Cosserat rod model of the robot and the distributed sensing and actuation capabilities of the segments. Our controller solves the inverse dynamic problem by simulating the Cosserat rod model in MATLAB using a computationally efficient numerical solution scheme, and it applies the computed control output to the actual robot in real time. The position and orientation of the tip of each segment are measured in real time, while the remaining unknown variables that are needed to solve the inverse dynamics are estimated simultaneously in the simulation. We implement the controller on a multi-segment silicone robotic arm with pneumatic actuation, using a motion capture system to measure the segments' positions and orientations. The controller is used to reshape the arm into configurations that are achieved through combinations of bending and extension deformations in 3D space. Although the possible deformations are limited for this robot platform, our study demonstrates the potential for implementing the control approach on a wide range of continuum robots in practice. The resulting tracking performance indicates the effectiveness of the controller and the accuracy of the simulated Cosserat rod model.
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Solving Cosserat Rod Models via Collocation and the Magnus Expansion
Choosing a kinematic model for a continuum robot typically involves making a tradeoff between accuracy and computational complexity. One common modeling approach is to use the Cosserat rod equations, which have been shown to be accurate for many types of continuum robots. This approach, however, still presents significant computational cost, particularly when many Cosserat rods are coupled via kinematic constraints. In this work, we propose a numerical method that combines orthogonal collocation on the local rod curvature and forward integration of the Cosserat rod kinematic equations via the Magnus expansion, allowing the equilibrium shape to be written as a product of matrix exponentials. We provide a bound on the maximum step size to guarantee convergence of the Magnus expansion for the case of Cosserat rods, compare in simulation against other approaches, and demonstrate the tradeoffs between speed and accuracy for the fourth and sixth order Magnus expansions as well as for different numbers of collocation points. Our results show that the proposed method can find accurate solutions to the Cosserat rod equations and can potentially be competitive in computation speed.
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- Award ID(s):
- 1734461
- PAR ID:
- 10281088
- Date Published:
- Journal Name:
- 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- Page Range / eLocation ID:
- 8653 to 8660
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS45743.2020.9340827
