Zhang equivalency of inequation-to-inequation type for constraints of redundant manipulators

In solving specific problems, physical laws and mathematical theorems directly express the con-nections between variables with equations/inequations. At times, it could be extremely hard or not viable to solve these equations/inequations directly. The PE (principle of equivalence) is a commonly applied pragmatic method across multiple fields. PE transforms the initial equa-tions/inequations into simplified equivalent equations/inequations that are more manageable to solve, allowing researchers to achieve their objectives. The problem-solving process in many fields benefits from the use of PE. Recently, the ZE (Zhang equivalency) framework has surfaced as a promising approach for addressing time-dependent optimization problems. This ZEF (ZE frame-work) consolidates constraints at different tiers, demonstrating its capacity for the solving of time-dependent optimization problems. To broaden the application of ZEF in time-dependent op-timization problems, specifically in the domain of motion planning for redundant manipulators, the authors systematically investigate the ZEF-I2I (ZEF of the inequation-to-inequation) type. The study concentrates on transforming constraints (i.e., joint constraints and obstacles avoidance depicted in different tiers) into consolidated constraints backed by rigorous mathematical deriva-tions. The effectiveness and applicability of the ZEF-I2I are verified through two optimization motion planning schemes, which consolidate constraints in the velocity-tier and acceleration-tier. Schemes are required to accomplish the goal of repetitive motion planning within constraints. The firstly presented optimization motion planning schemes are then reformulated as two time -dependent quadratic programming problems. Simulative experiments conducted on the basis of a six-joint redundant manipulator confirm the outstanding effectiveness of the firstly presented ZEF-I2I in achieving the goal of motion planning within constraints.