Multi-objective particle swarm optimization for the structural design of concentric tube continuum robots for medical applications

Abstract

Concentric tube robots belong to the class of continuum robotic systems whose morphology is described by continuous tangent curvature vectors. They are composed of multiple, interacting tubes nested inside one another and are characterized by their inherent flexibility. Concentric tube continuum robots equipped with tools at their distal end have high potential in minimally invasive surgery. Their morphology enables them to reach sites within the body that are inaccessible with commercial tools or that require large incisions. Further, they can be deployed through a tight lumen or follow a nonlinear path. Fundamental research has been the focus during the last years bringing them closer to the operating room. However, there remain challenges that require attention. The structural synthesis of concentric tube continuum robots is one of these challenges, as these types of robots are characterized by their large parameter space. On the one hand, this is advantageous, as they can be deployed in different patients, anatomies, or medical applications. On the other hand, the composition of the tubes and their design is not a straightforward task but one that requires intensive knowledge of anatomy and structural behavior. Prior to the utilization of such robots, the composition of tubes (i.e. the selection of design parameters and application-specific constraints) must be solved to determine a robotic design that is specifically targeted towards an application or patient. Kinematic models that describe the change in morphology and complex motion increase the complexity of this synthesis, as their mathematical description is highly nonlinear. Thus, the state of the art is concerned with the structural design of these types of robots and proposes optimization algorithms to solve for a composition of tubes for a specific patient case or application. However, existing approaches do not consider the overall parameter space, cannot handle the nonlinearity of the model, or multiple objectives that describe most medical applications and tasks. This work aims to solve these fundamental challenges by solving the parameter optimization problem by utilizing a multi-objective optimization algorithm. The main concern of this thesis is the general methodology to solve for patient- and application-specific design of concentric tube continuum robots and presents key parameters, objectives, and constraints. The proposed optimization method is based on evolutionary concepts that can handle multiple objectives, where the set of parameters is represented by a decision vector that can be of variable dimension in multidimensional space. Global optimization algorithms specifically target the constrained search space of concentric tube continuum robots and nonlinear optimization enables to handle the highly nonlinear elasticity modeling. The proposed methodology is then evaluated based on three examples that include cooperative task deployment of two robotic arms, structural stiffness optimization under the consideration of workspace constraints and external forces, and laser-induced thermal therapy in the brain using a concentric tube continuum robot. In summary, the main contributions are 1) the development of an optimization methodology that describes the key parameters, objectives, and constraints of the parameter optimization problem of concentric tube continuum robots, 2) the selection of an appropriate optimization algorithm that can handle the multidimensional search space and diversity of the optimization problem with multiple objectives, and 3) the evaluation of the proposed optimization methodology and structural synthesis based on three real applications.