Design of a robotic device actuated by cables for human lower limb rehabilitation using self-adaptive differential evolution and robust optimization

Abstract

In engineering designed systems it is commonly considered that mathematical models, variables, and parameters are sufficiently reliable, i.e., there are no errors in modeling and estimation. However, the systems to be optimized can be sensitive to small changes in the designed variables causing significant changes in the objective function. Robust optimization is an approach for modeling optimization problems under uncertainty in which the modeler aims to find decisions that are optimal for the worst-case realization of the uncertainties within a given set of values. In this contribution, a self-adaptive heuristic optimization method, namely the Self-Adaptive Differential Evolution (SADE), is evaluated. Differently from the canonical Differential Evolution algorithm (DE), the SADE strategy is able to update the required parameters such as population size, crossover parameter, and perturbation rate, dynamically. This is done by considering a defined convergence rate on the evolution process of the algorithm in order to reduce the number of evaluations of the objective function. For illustration purposes, the SADE strategy is associated with the Mean Effective Concept (MEC) for insertion robustness, is applied to minimize forces applied in cables used for the rehabilitation of the human lower limbs by determining the positioning of motors. The results show that the methodology that was proposed (SADE+MEC) appears as an interesting strategy for the treatment of robust optimization problems.