Design Optimization of Pyramid-Shaped Transmission System for Multiarm Concentric-Tube Robots

Pyramid-shaped transmission system (TS) of multiarm concentric-tube robots (CTRs) offers advantages of convenient arrangement and collision avoidance of the actuation units. Generally, in such a TS, stainless steel tubes (SS tubes) are used to transmit torsion and translation to the distal nitinol (NiTi) manipulators, and they are angled into a bending unit and extended in parallel. Although the parametric determination of the TS is an indispensable part in the design of CTRs with pyramid-shaped TS, design optimization of such TS has not been systematically studied. This article presents an optimal design framework for the pyramid-shaped TS in multiarm CTRs. First, geometric constraints of the TS, including the relations of tube diameters, the shape and length of SS tubes, and the collision avoidance of actuation units, are introduced. Second, deformation constraints considering the bending and torsional twisting of SS tubes are derived. Then, the design problem is formulated as a constrained nonlinear multiobjective optimization problem that aims to minimize both the twist of SS tubes and the length of the innermost SS tube. To validate the efficacy of the proposed modeling and optimization methods, a multiarm CTR prototype with pyramid-shaped TS has been built based on the proposed framework. Experiments on the twisting angle of SS tubes and the positioning performance of the NiTi manipulators were carried out to evaluate the proposed optimization framework.