Robot Manipulator Control via Solving Four-Layered Time-Variant Equations Including Linear, Nonlinear Equalities and Inequalities

Robot manipulator control is a complicated multi-tasking problem in reality. It includes not only basic tracking task, but also additional tasks, such as conquering joint angle limits, posture control. However, most existing works only consider the goal of tracking and formulate it as single-layered time-variant problems, which leads to impracticality. In this work, robot manipulator control problem is formulated as four-layered time-variant equations including linear, nonlinear equalities and inequalities. Each layer formulates one subtask: The first layer of nonlinear equality describes basic tracking task based on forward kinematics; The second layer and third layer are inequalities, which describe joint angle upper and lower limits; The last layer is a linear equality with respect to joint angle velocity, which could be designed by user to describe other task, such as posture control. To solve this complicated four-layered time-variant problem, it is converted as single-layered equation based on the zeroing neural dynamics method. Then, continuous-time solution is proposed. Furthermore, discrete-time algorithm is proposed based on a third-order time-discretization formula and continuous-time solution. Numerical experiments illustrate the effectiveness and superiority compared to existing work.