# Multicriteria Optimization of Lower Limb Exoskeleton Mechanism
## 1 Introduction
The capabilities of standard non-reconfigurable quadruped Klann legs can be significantly extended by applying the method proposed in [24]. Reconfigurable legged robots based on the 1 DOF Klann mechanism are highly desired because they are effective on rough and irregular terrains, and they provide mobility in such terrain with simple control schemes. However, both [PERSON]'s solution and [PERSON]'s inspired leg designs are very cumbersome, especially since they cannot be used as lower limb exoskeleton since it does not fit the size limit and overall dimension restrictions. Other related works include [28; 29; 30; 31; 32; 33]. Numerous optimization techniques applied for dimensional synthesis were analyzed by [PERSON] and [PERSON] [12], considering two major groups: gradient-based methods and evolutionary algorithms, especially genetic algorithms. These algorithms can effectively explore the solution space for a global optimum; they can also tackle geometric constraints easily. The overview of dimensional optimization methods is presented by [PERSON] and [PERSON] as well [34]. Two critical aspects of the leg mechanisms performance were chosen to be optimized by [PERSON] [21]: minimizing the energy to improve the efficiency of the leg and lowering the requirement for larger motors and, second, maximization of the stride length. The optimization was performed using MATLAB's optimization toolbox. However, the goals of this work were not only the optimization but also to show that mechanism design should be considered for optimizations of a leg mechanism because they offer more control over the outcome of each solution and eliminate the analysis of impossible mechanisms that would otherwise be analyzed. The comparison between the trial-and-error and optimization results demonstrates an excellent improvement in the performance of the mechanism. The mechanism design theory was found to be an excellent tool for determining the link lengths when incorporated into the optimization because it offers greater control over the outcome of each solution. However, the final design of the leg in this work is very huge as well. A comprehensive study of optimization-based dimensional synthesis of leg mechanisms presented by [PERSON] [34]. The author showed that existing global optimization techniques rely on a random initial population and do not yield feasible designs. A new global optimization procedure, called homotopy-directed optimization, was proposed, which combines the distribution of initial solutions with gradient-based optimization: it selects initial linkage designs that solve the synthesis equations and uses gradient optimization with design refinement to obtain feasible designs. The minimization problem for each starting linkage was completed using Mathematica's built-in optimization algorithms. However, the accuracy of a generated straight-line segment of foot path is poor, and the relative horizontal velocity of the foot is not constant. The desired foot trajectory consists of two segments (Figure 1):  
1. straight-line segment \(A-B\) with stride \(L\), corresponding to the _support phase_ of step cycle (when the foot \(P\) is on the ground);
2. swing phase segment \(B-C-A\) with a step height \(h\) (the leg _transfer phase_). In [34] presented 6 configurations of an 8-bar leg mechanism, with three fixed pivots that make it strong and stable, validated on an experimental prototype. The paper emphasizes that this mechanism offers the largest stride-to-size ratio, allowing for the construction of a compact and lightweight walking mechanism with low inertia. Consequently, it is well-suited for speed walking. In this study, we synthesized a mechanism that is even more compact, comprising only six links. We introduced a novel synthesis method, and as the result of multicriteria optimization, we achieved a compact solution matching human anatomy with high accuracy of trajectory generation, optimized force transfer, minimized chassis height, and internal transfer of foot.