# Optimizing Exoskeleton Design with Evolutionary Computation: An Intensive Survey

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## Abstract

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## 1. Introduction

#### Search Strategy and Eligibility Criteria

## 2. Background

#### 2.1. Background on Exoskeletons

**Assistance:**Assistive exoskeletons augment users’ physical abilities to help them perform real-time activities that might be challenging to be completed alone. These devices can be used by (i) people with disabilities in their daily lives or (ii) healthy workers while performing physically demanding tasks in a workspace (see Figure 2a). Regardless of the target users, these devices must be capable of adapting their operation to perform different tasks or to interact with different objects. They must be portable, lightweight, and easy to wear while applying high interaction forces. They must achieve the range of motion of the anatomical joints without harming users when functionality limits are reached. Finally, these devices should feel highly transparent to follow the physical guidance of users. Observing/tracking movement performance is neither mandatory nor favorable.**Physical Rehabilitation:**Rehabilitative exoskeletons are used in clinical settings to treat patients suffering from physical or neurological disabilities (see Figure 2b). Due to users’ limited functional capabilities, rehabilitative exoskeletons must be easy to wear without a predefined initial orientation (i.e., the device adapts to the patient’s position rather than the opposite) and provide high output forces with respect to the actuator size adopted for the exoskeleton. The range of motion of anatomical joints must be achieved without harming patients when functionality limits are reached. Patients should be able to perform different actions with no prior control or mechanical design change thanks to the devices’ instant adaptability. Rehabilitation exoskeletons allow patients to actively participate in therapy exercises and monitor their progress in muscular activity. Unlike assistive devices, they are often grounded and do not need to be portable.**Haptic Rendering:**Haptic exoskeletons render an artificial sense of touch in response to virtual interactions or remotely operated real interactions (see Figure 2c). They must be wearable to track users’ joint movements to control the interactions performed by virtual avatars or remote robots. Similarly to assistive devices, portability and instant adaptability are crucial. Haptic exoskeletons must feel highly transparent to follow users’ physical guidance, especially when there is no interaction at the virtual/remote site. Since the target user profile is assumed to be healthy, the wearability or the amount of output forces is not as crucial as for other applications but is preferred.

**Workspace:**The workspace is the range of motion the user is allowed while wearing an exoskeleton. Exoskeletons must respect the natural movements of users’ limbs to ensure safety, and their mechanical limits must not exert force on human joints once they reach their natural limits. An exoskeleton must be comfortable, as users wear the device during operation. The kinematic and ergonomic design must be ensured not to cause any pain or fatigue.- –
- While designing an exoskeleton, the mechanical joints must be aligned with the anatomical joints with minimal mechanical changes and cover the overall range of motion for the anatomical joints they are aligned with. This allows the exoskeleton to be inherently safe, ergonomic, and comfortable. To achieve this outcome, an optimization algorithm must retrieve the best link lengths and the actuated motion to either (i) maximize the operational workspace for each assisted joint or (ii) maximize a different design requirement and simultaneously ensure that the natural workspace is covered via constraints.

**Force Transmission:**The human body has highly complex kinematics. For example, the human wrist can be modeled with three DoFs [31] (flexion, pronation, and radial deviation), the human finger with four DoFs [32] (one for the distal interphalangeal joint, one for the proximal interphalangeal joint, and two for the metacarpophalangeal joint), etc. The anatomic joints’ complexity (and their proximity to each other) has led designers to decouple the actuators from the joints and transmit the actuator forces through linkage-based mechanical devices—whether they are made of rigid or soft materials. In addition, linkage-based transmission allows designers to augment the transmitted forces through effective kinematic chains and lower the actuator size. The efficacy of its force transmission should be evaluated based on (i) the size of the wearable actuator components, (ii) the amount of force/torque rendered on the user’s joints safely and comfortably, and (iii) the ratio between the actuated and output forces for each independent joint.- –
- While designing an exoskeleton, an optimization algorithm should retrieve the best link lengths to maximize the force transmission for each assisted joint or for the overall targeted task (e.g., grasping a one-liter water bottle or lifting a five-kilogram storage box). Using such optimization techniques could also yield the same output forces with smaller actuators, improving the portability/wearability of the system as well.

**Adjustability/Calibration:**Unlike prosthesis devices, exoskeletons are not custom-made for each potential user with different limb sizes. This lack of customization might cause misalignment, harm users, or work with a limited operational workspace or performance. In addition, especially for rehabilitative applications, wearing an exoskeleton should be equal and pain-free for every user.- –
- While designing an exoskeleton, an optimization algorithm should ensure the same performance for users of all sizes. There are three ways of achieving this outcome: (i) maximize the allowed range of limb sizes with no focus on other metrics, (ii) maximize the allowed range of limb sizes while optimizing another design requirement simultaneously, or (iii) maximize one of the previously detailed design requirements while ensuring an acceptable range of adjustability to different limb sizes via constraints.

**Size:**While some full-arm exoskeletons need to be carried by a base due to their high weight [13], there is a great deal of research on reducing their weight and making them portable [33]. Exoskeletons can have improved portability by minimizing the mechanical components’ size or weight.- –
- While designing an exoskeleton, an optimization algorithm should ensure the same performance with the smallest set of link lengths as much as possible by (i) minimizing the link lengths while other performance measures are fixed at a reasonable and predefined level via constraints or (ii) maximizing a different design requirement and simultaneously ensuring the acceptable set of link lengths to be covered via constraints.

#### 2.2. Background on Optimization and Evolutionary Computation

#### 2.2.1. Optimization Problems

#### 2.2.2. Optimization Methods

- Objective functions are usually complex (i.e., nonlinear, non-convex, discontinuous, discrete, mixed, and multimodal), and the effectiveness of the exact methods is not guaranteed [37];
- Robust solutions are preferred over global ones (i.e., when the optimal solution lies on a peak of the function, a small change in its value causes instability to the system, whereas a sub–optimal solution lying in a plateau area is less susceptible to change) [38];
- Reliable solutions are preferred over global ones, as uncertainty in the search space might lead to infeasible optimal solutions (i.e., in violation of the constraints) [39].

#### 2.2.3. Evolutionary Computation

## 3. Mechanical Design Optimization

#### 3.1. Exoskeleton Design with Evolutionary Computation Techniques

#### 3.1.1. Genetic Algorithms (GAs)

`ga`.

**single objective function**:

**multiple objective functions**. There are several GAs specifically developed to approach MOOPs, which we will detail separately.

#### Weight-Based Genetic Algorithm (WBGA)

- Yoon et al. [60] retrieved the optimal joint locations that minimize (i) the misalignment of the exoskeleton and (ii) the frame protrusion of their shoulder exoskeleton for assistive use;
- Asker et al. [61] retrieved the optimal link lengths that (i) maximize the force transmission and (ii) minimize the misalignment between a human and their knee exoskeleton for assistive use;
- McDaid [65] retrieved the optimal link lengths that (i) maximize the workspace, (ii) maximize the distance from robot singularities, and (iii) minimize the size of their leg exoskeleton for rehabilitation; and
- Yu et al. [69] retrieved the initial conditions that minimize (i) displacement and (ii) dynamics of the hydraulic cylinder composing the joint of their knee exoskeleton for assistive use.

#### Elitist Non-Dominated Sorting Genetic Algorithm (NSGA–II)

`gamultiobj`.

- Li et al. [51] retrieved the optimal link lengths that (i) maximize the force transmission and (ii) minimize the difference between contact forces and reduce the ejection phenomenon (i.e., fingers push the targeted object away instead of grasping it) while satisfying an accepted range of motion on their hand exoskeleton for assistive use;
- Lee et al. [54] retrieved the optimal rotational angles and joint distribution that maximize (i) the accuracy and dexterity through an index estimating the kinematic performance of specific posture (the global condition index) and (ii) the minimum distance between the links and the centerline (the interference safety margin) of their wrist exoskeleton for rehabilitation and haptic use;
- Hunt et al. [55] retrieved the optimal actuator location, maximizing its stiffness volume both for (i) translation and (ii) rotation of their shoulder exoskeleton for assistive use;
- Deboer et al. [62] retrieved the optimal link lengths, spring stiffness values, angles, and displacements that minimize (i) the peak power and (ii) the total length of the two actuators of their leg exoskeleton for assistive use;
- Paez et al. [63] retrieved the optimal link lengths and joint locations that minimize (i) the moment load at the joint, (ii) the difference between the natural human posture and that observed while wearing the exoskeleton to promote a natural torso motion, and (iii) the torque deviation to match a linear profile while independently maximizing the torque output of their knee exoskeleton for assistive use; and
- Rituraj et al. [68] retrieved the optimal link lengths and angles that minimize (i) the maximum distance between the actuators and (ii) the load on the device of their assistive/rehabilitative knee exoskeleton for rehabilitation and assistive use.

#### 3.1.2. Swarm Intelligence (SI)

- Du Z. et al. [57] independently retrieved (i) the optimal link lengths that minimize the misalignment between human and robot and (ii) the optimal rope position of the cable-driven mechanism that maximizes the torque actuating their arm-support exoskeleton for assistive use;
- Tian et al. [64] retrieved the optimal link lengths that minimize the force transmission of their leg exoskeleton for wheelchair assistive use to support the user from sitting to standing; and

#### 3.1.3. Differential Evolution (DE)

- Zakaryan et al. [58] used a weight-sum-based DE [59] to retrieve the optimal link and joint weights that minimize (i) the total mass of the device, (ii) the maximal magnitudes of cable tensions, and (iii) the maximal difference between magnitudes of agonist–antagonist cable tensions (i.e., to resemble the structure of the natural muscular system of human limbs) of their arm exoskeleton for rehabilitation.

#### 3.2. Designs with Other Optimization Techniques (Non-Evolutionary)

#### 3.2.1. Interior Point Algorithm (IPA)

`fmincon`.

- Xu et al. [85] retrieved the optimal link lengths that minimize the difference between the workspace covered by the human and their hand exoskeleton for rehabilitation;
- Secciani et al. [87] retrieved the optimal geometrical parameters that allow the kinematics to minimize the error to the desired trajectories of their hand exoskeleton for assistive use;
- Kulkarni et al. [88] retrieved the optimal link lengths that minimize the difference between the workspace covered by the human and their wrist exoskeleton for assistive use over two joints (one joint is optimized, while the other joint is modeled as an inequality constraint);
- Balser et al. [90] retrieved the optimal parameters of the cable-driven actuator (i.e., radius, cable, and pulley) and link lengths that minimize the difference between the torques generated by the human and their shoulder exoskeleton for assistive use;
- Anderson et al. [93] retrieved the optimal “mechanical parameters” (The authors left the description of these mechanical parameters intentionally abstract, and they reported that “the system-specific mechanical design will determine which variables affect the model outputs”) that minimize the reflected inertia of their leg exoskeleton for rehabilitation and assistive use;
- Kim et al. [96] retrieved the optimal position and pressure of pneumatic actuators that minimize the average energy consumption rate of the human joint while running using their leg exoskeleton for assistive use;
- Xiao et al. [95] retrieved the optimal link lengths and structural angle that minimize the torque exerted by their knee exoskeleton for assistive use; and
- Bougrinat et al. [97] retrieved the optimal link length and angles that maximize the artificial lever arm (i.e., the perpendicular distance between the joint and the line of action) of their ankle exoskeleton for assistive use.

#### 3.2.2. Levenberg–Marquardt Algorithm (LMA)

- Amirpour et al. [82] retrieved the optimal link lengths that (i) minimize the difference between worst-case workspace dexterity and isotropy and (ii) minimize the distance between the angle of the forces exerted on finger phalanges and the perpendicular direction on their hand exoskeleton for haptic use; and
- Bianchi et al. [83] retrieved the optimal link lengths that minimize the maximum value of the torque of their hand exoskeleton for rehabilitative use.

#### 3.2.3. Geometric Differentiation (GD)

- Liang et al. [84] retrieved the optimal joint shape (i.e., link lengths and their poses) that minimizes the joint workspace and trajectory of humans and the hand exoskeleton for rehabilitation and assistive use. They particularly focused on designing a flexible joint based on the anatomy of grasshoppers (a model that can also be observed in crustaceans such as crabs and lobsters). They proposed a GD-based optimization algorithm (Congjugate Surface Optimization Algorithm) that evaluates the fingertip’s path during flexion and extension motion.

#### 3.2.4. Goal Attainment Method (GAM)

`fgoalattain`.

- Qin et al. [86] retrieved the optimal link lengths that minimize the misalignments between the finger joints (one objective for each joint, for a total of two joints) and their hand exoskeleton for rehabilitation.

#### 3.2.5. Pareto Local Search (PLS)

- Vatsal et al. [89] retrieved the optimal design parameters (joint angles, spring parameters, moments, and forces) that minimize muscle effort rates during realistic dynamic tasks (each muscle is defined as a separate objective function, resulting in an MOOP) while using their shoulder exoskeleton for assistive use.

#### 3.2.6. Nelder–Mead Simplex Method (NMSM)

`fminsearch`.

- Malizia et al. [94] retrieved the optimal properties (spring location, spring resting length, and angle between spring and leg) that minimize the error between the desired torque and the actual torque exerted by their leg exoskeleton for assistive use.

#### 3.2.7. Simulated Annealing (SA)

- Malizia et al. [94] enhanced the results of the primary optimization method (as discussed in Section 3.2.6, the authors primarily used NMSM) by outdistancing the starting parameters of each optimization attempt from the optimal values found in the previous attempt on their leg exoskeleton for assistive use.

## 4. Discussion

#### 4.1. Discussion on Optimization Methods

#### 4.1.1. Wrong use of the term “MOGA”

#### 4.1.2. Popularity of NSGA–II and Interior Point Algorithm

`gamultiobj`, so designers do not need to have complete knowledge of the algorithm specifics and can use it as a black box, likely making it the fastest MOEA in the literature. Even so, we found that most of the studies reviewed in this survey specifically mentioned the name NSGA–II, showing that the authors have sufficient knowledge about EA rather than simply relying on a black-box method. There are a few exceptions to this observation: Hunt et al. [55] only reported that the MATLAB Optimization Toolbox was used, without mentioning NSGA–II, whereas Rituraj et al. [68] stated that they used NSGA–II in the MATLAB environment, although it is not clear if they used the toolbox or recreated the algorithm from scratch. Lastly, Paez et al. [63] reported that NSGA–II allowed them to mutate over the possible populations of solutions through a definition of the objectives, which clearly refers to the ability to select the appropriate design parameters out of a pool of trade-off solutions rather than specifying fixed preferences among objectives and obtaining only one solution (e.g., WBGA).

`fmincon`command of the MATLAB Optimization Toolbox and can be used for constrained, non-linear, multivariable functions.

#### 4.1.3. Simplified Implementation of WBGA

#### 4.1.4. When to Use Different EC Methods

#### Multi Modality

#### Multi Objective

#### Choosing the Right MOEA

#### Hybrid Techniques: Combining Different Optimization Methods

#### 4.2. Recommendations for Future Engineer Designers

#### 4.2.1. Advantages of EC over Other Methods for Mechanical Design of Exoskeletons

#### Non-Differentiable and Complex Design Spaces

#### Global Optimization in Wide or Multi–Objective Search Spaces

#### Solution Exploration and Diversity

#### Robustness to Noisy or Incomplete Data

#### Encouraging Innovative Designs

#### 4.2.2. Importance of Using Mathematical Optimization in Engineering

#### 4.2.3. Considerations for Optimal Control

#### 4.2.4. Considerations for Structural Optimization

#### 4.2.5. Importance of Detailing the Optimization Method

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Examples of solutions retrieved with weighted-sum methods for a generic bi–objective minimization problem. Each set of weights represents a different Pareto-optimal solution defined by the slope of the line intersecting the front. In (

**a**), by assigning the same value to each weight, only the trade–off solution (A) is retrieved; better values for each objective were ignored (e.g., ${A}_{1}^{*}$ is the minimum of ${f}_{1}$, whereas ${A}_{2}^{*}$ is the minimum of ${f}_{2}$, and A is exactly in between). In (

**b**), no solution can be found between B and C (the front inscribed in the red hull) because other solutions in the convex section can be found with the same slope, which would better optimize the objective with a larger weight (i.e., with higher priority).

Requirement | Metrics |
---|---|

User safety | Workspace, calibration |

High output forces | Force transmission |

Portability | Force transmission, size |

Wearability | Calibration, size |

Joint tracking | Calibration |

Adaptability to different tasks | Workspace, force transmission |

Abbreviation | Algorithm |
---|---|

GA | Single-Objective Genetic Algorithm [40,46] |

NSGA–II | Elitist Non-Dominated Sorting Genetic Algorithm [47] |

WBGA | Weight-Based Genetic Algorithm [48] |

PSO | Particle Swarm Optimization [49] |

DE | Differential Evolution [50] |

**Table 3.**Exoskeletons optimized with evolutionary techniques in terms of application (assistance (A), rehabilitation (R), or haptic (H)), optimization metric (force transmission (FT), workspace (W), or size (S)), and optimization method.

Authors | Limb | Application | Metrics | Optimization Method |
---|---|---|---|---|

Li et al. [51] | Hand | A | FT, W | NSGA–II [52] |

Du J. et al. [53] | Hand | R | FT | GA [40,46] |

Lee et al. [54] | Wrist | R, H | FT, W | NSGA–II [47] |

Hunt et al. [55] | Arm | A | FT | NSGA–II [47] |

Tschiersky et al. [56] | Arm | A | FT | GA [40,46] |

Du Z. et al. [57] | Arm | A | FT, W | PSO [49] |

Zakaryan et al. [58] | Arm | R | FT, S | DE [50,59] |

Yoon et al. [60] | Arm | A | W | WBGA [47] |

Asker et al. [61] | Leg | A | FT, W | WBGA [48] |

Deboer et al. [62] | Leg | A | FT, S | NSGA–II [47] |

Paez et al. [63] | Leg | A | FT, W | NSGA–II [47] |

Tian et al. [64] | Leg | A | S | PSO [49] |

McDaid [65] | Leg | R | W | WBGA [48] |

Xu et al. [66] | Leg | R | FT | PSO [49,67] |

Rituraj et al. [68] | Leg | A, R | S, FT | NSGA–II [47] |

Yu et al. [69] | Leg | A | FT | WBGA [48] |

Abbreviation | Algorithm |
---|---|

LMA | Levenberg–Marquardt Algorithm [73,74] |

GD | Geometric differentiation [75] |

IPA | Interior point algorithm [76,77] |

GAM | Goal attainment method [78] |

PLS | Pareto local search [79] |

SA | Simulated annealing [80] |

NMSM | Nelder–Mead simplex method [81] |

**Table 5.**Exoskeletons optimized with non-evolutionary techniques in terms of application (assistance (A), rehabilitation (R), or haptic (H)), optimization metric (force transmission (FT), workspace (W), size (S), or adjustability/calibration (AC)), and optimization method.

Authors | Limb | Application | Metrics | Optimization Method |
---|---|---|---|---|

Amirpour et al. [82] | Hand | H | W, AC | LMA [73,74] |

Bianchi et al. [83] | Hand | R | FT, S | LMA [73,74] |

Liang et al. [84] | Hand | A, R | W | GD [75] |

Xu et al. [85] | Hand | R | W | IPA [76,77] |

Qin et al. [86] | Hand | R | AC | GAM [78] |

Secciani et al. [87] | Hand | A | AC | IPA [76,77] |

Kulkarni et al. [88] | Wrist | A | W | IPA [76,77] |

Vatsal et al. [89] | Arm | A | FT | PLS [79] |

Balser et al. [90] | Arm | A | FT | IPA [76,77] |

Vazzoler et al. [91,92] | Arm | A | FT | IPA [76,77] |

Anderson et al. [93] | Leg | A, R | FT | IPA [76,77] |

Malizia et al. [94] | Leg | A | W | SA [80], NMSM [81] |

Xiao et al. [95] | Leg | A | FT | IPA [76,77] |

Kim et al. [96] | Leg | A | AC | IPA [76,77] |

Bougrinat et al. [97] | Ankle | A | S | IPA [76,77] |

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Stroppa, F.; Soylemez, A.; Yuksel, H.T.; Akbas, B.; Sarac, M.
Optimizing Exoskeleton Design with Evolutionary Computation: An Intensive Survey. *Robotics* **2023**, *12*, 106.
https://doi.org/10.3390/robotics12040106

**AMA Style**

Stroppa F, Soylemez A, Yuksel HT, Akbas B, Sarac M.
Optimizing Exoskeleton Design with Evolutionary Computation: An Intensive Survey. *Robotics*. 2023; 12(4):106.
https://doi.org/10.3390/robotics12040106

**Chicago/Turabian Style**

Stroppa, Fabio, Aleyna Soylemez, Huseyin Taner Yuksel, Baris Akbas, and Mine Sarac.
2023. "Optimizing Exoskeleton Design with Evolutionary Computation: An Intensive Survey" *Robotics* 12, no. 4: 106.
https://doi.org/10.3390/robotics12040106