Design of patterns in tubular robots using DNN-metaheuristics optimization

Highlights

• A DNN-metaheuristic design optimization framework is presented.

• The tube pattern of continuum tubular robots is optimized to reduce instability.

• No manual parametric study or sensitivity analysis is required.

• Optimized designs exhibit lower EI/GJ values compared to existing designs.

Abstract

Concentric-tube robots for minimally invasive surgery pose a potential risk of tissue rupture because of the structural instabilities caused by high value of bending-to-torsional-stiffness ratio (EI/GJ). In this study, a novel optimization method based on metaheuristic optimization accelerated by a deep neural network (DNN)-based surrogate model to obtain optimized pattern parameters is presented. The method minimizes EI/GJ while conforming to the minimum compliance constraints and geometric restrictions. The proposed optimization process utilizes a DNN trained using 855 datasets generated by finite element analysis that cover the pattern design parameter space. The pattern design parameters were derived from topology optimization. The results demonstrate that the proposed optimization method yielded pattern designs that outperformed previous designs within a reasonable time frame (less than 900 s) without requiring manual parametric study or sensitivity analysis.

Introduction

Concentric-tube robots represent a type of continuum tubular robot comprising concentrically assembled precurved elastic tubes [1,2]. They are particularly well-suited for minimally invasive surgery because they can assume curves of complex shapes in three-dimensional space and possess sufficient stiffness to steer tissue and manipulate tools inside body cavities [3,4]. The most distinctive characteristic of this type of robot is that its distal end is steered and advanced through the rotation and translation of the precurved tubes relative to each other. Actuators are attached only to the proximal ends of the tubes, affording mechanical simplicity and small-scale design.

However, under certain conditions, torsion of the precurved tubes causes structural instability. Torsional deformation caused by the relative rotation of the precurved tubes is unavoidable and causes a lag in the transmission of the rotation angle. In particular, the tubes may abruptly move from one minimum-energy point to another during operations, which is often called the “snapping problem” [4,5]. In prior research [4,5], the condition for stability has been derived. It can be summarized as

$$L\kappa \sqrt{\frac{EI}{GJ}}<\frac{\pi }{2},$$

where L is the overlapping length, and κ is the curvature of the tube. In Eq. (1), EI and GJ represent bending and torsional stiffness, respectively. This condition shows that the key factor for eliminating instability is the low ratio of bending stiffness to torsional stiffness (EI/GJ).

In this study, we aim to optimize the anisotropic pattern design of continuum tubular robots to solve the instability problem. An optimization process was devised to achieve this goal using a deep neural network (DNN)-metaheuristic optimization framework. The main contribution of this study is the development of an optimization methodology for reducing the EI/GJ of tube robots while satisfying the minimum compliance constraint for securing the desired tube performance. A DNN model was trained as a finiteelement (FE) surrogate from the data generated by the FE analysis (FEA) of a topology-optimized tube pattern. Metaheuristic-based optimization of the tube design variables with this DNN-based surrogate model is used to generate an optimized design.

Many studies have been conducted to solve the snapping problem [5], [6], [7], [8], [9]. An intuitive and trivial solution limits the curvature but restricts the workspace. Recently, intensive research has been conducted on the patterning methods. Researchers have refined the material properties to solve instability problems [10], [11], [12]. Laser machining of through-hole patterns on precurved tubes is an efficient technique to change the structural bending and torsional stiffness of the tube. Several patterning methods for continuum tubular robots have been studied to provide an anisotropic mechanical property [10,[13], [14], [15], [16]].

Fig. 1 summarizes previous designs for through-hole patterning on tubes used to assign anisotropic mechanical properties. Different pattern shapes and distributions were employed for the applications in each study. Dog bone shapes [12], multilayer helical tubes [11], and long horizontal slit patterns [10,17] have been proposed to mitigate the snapping issue. A horizontal split pattern [15] was used to maximize the variable stiffness functionality. However, in these studies, the general pattern shape was determined based on engineering intuition.

Determining the general pattern shape is the starting point of the parametric design optimization process. The basic shape significantly affects the final performance of the patterned tube; therefore, selecting the general shape through an optimization process, rather than an intuitive selection, may be beneficial. Topology optimization has been proposed in various fields (aerospace, mechanical, biomechanical, and civil engineering) [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]. Luo et al. [14] first attempted to employ topology optimization to identify a pattern shape that reduces EI/GJ. Although the performed topology optimization reached non-converged results due to the mesh dependence or local minimum problem [18], a diamond shape was determined, and a low EI/GJ value (0.14) was obtained. Park et al. [16] also determined rectangular columns as the general shape of the pattern, by utilizing topology optimization to maximize the variable stiffness functionality, where three different setups for the optimization were considered to confirm the convergence of the results.

Once the general shape of the pattern has been obtained and the design variables have been determined accordingly, a follow-up parametric study is necessary to determine the optimal values of the variables. However, because of the large number of possible combinations, this parametric study has often been performed through limited sensitivity analysis with the assumption of independence of variables [[10], [11], [12],14,15,17,31,32].

Recently, research has been conducted on the full search of the design space to optimize the pattern shape with an automated FE analysis [13,16]. Researchers have attempted to search a design space fully for auxetic [13] and rectangular [16] patterns. In [16], the design for the given stiffness constraints was optimized manually using the results of a fully searched design space.

However, as the shape of the pattern becomes more complex, the numbers of design variables and possible combinations increase exponentially. The design space to be searched is excessively wide in the case of the optimization problem for multivariable functions. Therefore, optimizing the design using the existing fullsearch method is time consuming. In addition, manual optimization based on the results of the fully searched space still requires appropriate engineering decisions.

Design optimization algorithms have been frequently used in various fields of science and engineering to solve optimization problems [33], [34], [35], [36], [37], [38], [39], [40], [41] converted from real-world application problems [42], [43], [44], [45]. Gradient-based optimization methods, such as solid isotropic material with penalization method or ground structure approach [20], are highly efficient in searching for optimal solutions based on gradient information. However, finding a global optimal solution through gradient-based optimization when solving constrained nonlinear problems is challenging. The optimization results are highly sensitive to the initial values and are prone to becoming trapped in the local optima. In contrast, metaheuristic-based optimization methods, such as genetic algorithms (GAs) [46], particle swarm optimization (PSO) [47], ant colony optimization (ACO) [48], wild horse optimizer [49], growth optimizer [50], and teaching–learning-based optimization (TLBO) [51], may effectively find the global optimum in the entire design space. However, these methods require thousands or even millions of objective evaluations. To reduce the computational cost of numerous evaluations during optimization iterations, a surrogate model is required instead of an FE method (FEM)-based evaluation. Objective evaluations performed using surrogate models, such as polynomial response surfaces, support vector machines, and artificial neural networks (NNs), can provide a global optimal solution within a reasonable amount of time [52], [53], [54], [55], [56], [57], [58].