Inequality-Type Zhang Equivalency of Great-Than-or-Equal-to (GTOET) Sign in Matrix-Vector, Matrix, and Integral Situations Applied to Obstacle Avoidance

In this paper, the concept of Zhang equivalency (ZE) and equality-type ZE are revisited. On the basis of equality-type ZE, we introduce the inequality-type ZE of great-than-or-equal-to (GTOET) sign and thus propose the order-1, order-2, and order-3 general formulas of the inequality-type ZE of GTOET sign. Furthermore, we investigate the inequality-type ZE of GTOET sign in three different and appealing situations, including matrix-vector situation, matrix situation, and integral situation. Besides, the corresponding formulas are presented. The distance between a certain object and an obstacle can be considered as the point-to-point distance, and thus the obstacle avoidance scheme is described as an inequality. Inspired by that thought, we apply the inequality-type ZE of GTOET sign to the matrix-form obstacle avoidance.