A Lower Dimension Zeroing Neural Network for Time-Variant Quadratic Programming Applied to Robot Pose Control

Time-variant quadratic programming (TVQP) has widespread applications and often involves equality, inequality, and bound constraints. An effective solver for TVQP problems is zeroing neural network (ZNN), and nonlinear complementary problem function-based ZNN (NCP-ZNN) is a state-of-the-art ZNN solver that can handle equality and inequality constraints. However, when dealing with bound constraints, NCP-ZNN expands the dimension of the matrix and then introduces twice the number of Lagrange multipliers. To overcome this deficiency, this article develops a modified NCP-ZNN solver by introducing the first-order optimality conditions. Numerical validation is performed to substantiate the superior solving efficiency of the modified NCP-ZNN solver, which can achieve the same or lower order of residual errors compared with the original NCP-ZNN. Then, the modified NCP-ZNN solver is applied to the pose control of a redundant manipulator, demonstrating its superiority in solving practical problems.