Analytical and experimental nonzero-sum differential game-based control of a 7-DOF robotic manipulator

Abstract

We formulate a Nash-based feedback control law for an Euler–Lagrange system to yield a solution to noncooperative differential game. The robot manipulators are broadly used in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler–Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

A Study of Knee Exoskeleton Configuration Based on Lower Limb Motion Characteristics Analysis

“…When the joints in the human-machine interface do not match, it is reflected in the inconsistent instantaneous center of the human-machine movement, and the binding will show a trend of movement and deformation. Thus, the assistance will be dispersed in the deformation of the binding, thereby affecting the fit between the exoskeleton and the human body and greatly reducing the assistance performance of the exoskeleton [23]. During exercise, the lower limbs have a considerable amplitude of motion.…”

Linear programming and its application in analysing game theory

“…In zero-sum situations, no cooperation and competition will appear in the relationship among the two sides which lead to the poor application, which is called a strictly competitive game [6]. In that case, non-zero-sum game can be both competitive and non-competitive which depends on the value of the sum [7]. For those kinds of complex situations, two criteria will be used to evaluate the feasibility of the model: Firstly, calculating accuracy, for example, a simple two-player zero-sum game called colonel-bolloto game, which can be commonly applied as a metaphor for electoral competition, to attract more voters to support the voters, two different political parties will put resources or money to reach the goal [8][9], a rapid enlarge will be caused as the increase of the regiments put in the battlefield and the mountains [10], Errors will be caused if the model's calculating accuracy is not qualified.…”