Concentric tube robots (CTRs) show particular promise for minimally invasive surgery due to their inherent compliance and ability to navigate in constrained environments. Due to variations in anatomy among patients and variations in task requirements among procedures, it is necessary to customize the design of these robots on a patient- or population-specific basis. However, the complex kinematics and large design space make the design problem challenging. In this article, we propose a computational framework that can efficiently optimize a robot design and a motion plan to enable safe navigation through the patient’s anatomy. The current framework is the first fully gradient-based method for CTR design optimization and motion planning, enabling an efficient and scalable solution for simultaneously optimizing continuous variables, even across multiple anatomies. The framework is demonstrated using two clinical examples, laryngoscopy and heart biopsy, where the optimization problems are solved for a single patient and across multiple patients, respectively.

One of the challenges in computational modeling is coupling models to solve multidisciplinary problems. Flow-based computational frameworks alleviate part of the challenge through a modular approach, where data flows from component to component. However, existing flow-based frameworks are inefficient when coupled derivatives are needed for optimization. To address this, we develop the modular analysis and unified derivatives (MAUD) architecture. MAUD formulates the multidisciplinary model as a nonlinear system of equations, which leads to a linear equation that unifies all methods for computing derivatives. This enables flow-based frameworks that use the MAUD architecture to provide a common interface for the chain rule, adjoint method, coupled adjoint method, and hybrid methods; MAUD automatically uses the appropriate method for the problem. A hierarchical, matrix-free approach enables modern solution techniques such as Newton--Krylov solvers to be used within this monolithic formulation without computational overhead. Two demonstration problems are solved using a Python implementation of MAUD: a nanosatellite optimization with more than 2 million unknowns and 25,000 design variables, and an aircraft optimization involving over 6,000 design variables and 23,000 constraints. MAUD is now implemented in the open source framework OpenMDAO, which has been used to solve aircraft, satellite, wind turbine, and turbofan engine design problems.