Indirect adaptive control using the novel online hypervolume-based differential evolution for the four-bar mechanism

Four-bar mechanisms have increased their use in current applications from industrial to rehabilitation systems. These applications become more demanding over time, and the control systems are required to provide them higher accuracy, lower energy consumption, and an extended lifetime, among other conflicting features. In addition to the previously mentioned demands, four-bar mechanisms have highly nonlinear dynamics and are often subject to external loads that make them difficult to control. In this paper, an indirect adaptive control based on online multi-objective optimization is proposed to regulate the speed of the four-bar mechanism and increase its lifetime by smoothing the control action under the effects of uncertainties. This consists of a multi-objective optimization process for the online identification of the model parameters that fulfill the performance demands of the mechanism. In this process, a multi-objective optimization problem is stated and then solved by the novel Online Hypervolume-based Differential Evolution (O-HV-MODE) in such a way that several promising model parameter configurations are found in real-time, with different trade-offs among the performance demands. O-HV-MODE takes advantage of the past problem knowledge to accelerate the search for new solutions and uses the Hypervolume metric to increase their convergence and diversity. Then, a single model parameter configuration is selected based on the application necessities and is further used in the nonlinear compensator of the computed-torque controller, while a fixed-gain PD control loop is used for stabilization. The proposed control is validated through experimental tests and the reliability of the results with the 99% Confidence Interval test. Also, the proposal is compared with state-of-the-art linear and non-linear control approaches.