Redundant-Manipulator Minimal Motion via Different-Precision Discrete-Time Zhang Neural Dynamics Algorithms Especially Ten-Instant One

As a significant and basic robotic sub-topic, the problem of optimal MPC (motion planning & control) of ordinarily redundant manipulator widely exists in many fields, such as industry and daily-life applications. Following previous work, the aim of this paper is at solving the problem of velocity-level minimal joint motion planning & control (VLMJMPC) in a way of discrete time. Firstly, the VLMJMPC problem is introduced and analyzed using Zhang neural dynamics (ZND) method, and the motion scheme is then given. Secondly, by using ZND and Lagrange-multiplier methods, a continuous-time (CT) model for real-time solving the problem is established. In order to realize on digital computers, we use a ten-instant Zhang time discretization (abbreviated as ZTD) general formula with the fifth-order precision to discretize the model, and a special algorithm with high precision is derived, developed and analyzed. Finally, five discrete-time ZND (DTZND) algorithms are further acquired by adopting this ten-instant ZTD formula and other ZTD formulas, and the corresponding theoretical analyses are given. Computer experiment results numerically verify the online effectiveness and correctness of the developed five DTZND algorithms.