Tuning a PD+ controller by means of dynamic optimization in a mobile manipulator with coupled dynamics

This article presents the development of a dynamic optimization method for controller tuning. This is proposed because most traditional tuning methods for complex coupled dynamic models are based on experience, and thus lacking accuracy. The case study is a Mobile Manipulator that consists of an anthropomorphic manipulator and a differential mobile platform. The system model has a trajectory generator that includes the coupled kinematic model, the Jacobian model, the coupled dynamic model, and a Proportional-Derivative plus controller. The tuning of the model is obtained by solving an optimization problem, using the Differential Evolution algorithm. This optimization approach allows to minimize simultaneously the energy consumption and the error on the trajectory tracking by the end effector. A novel strategy is applied to formulate the objective function, including constant weights for balancing the minimization effect. The objective is to avoid an energy consumption equal to zero that represents an error condition of no motion. The results of the case study and its statistical analysis are presented. The best result was modeled in Solidworks and simulated in Matlab. This model was exported to Simscape Multibody™ of Matlab, and its simulation produced satisfactory results, suggesting that the proposed optimization method can be a useful tool to solve real engineering problems.