Three-Dimensional Biased Proportional Navigation Guidance Based on Spatial Rotation of Predicted Final Velocity

This study presents the design of three-dimensional biased proportional navigation guidance laws for arrival at a stationary target along desired direction based on spatial rotation predicted final velocity vector. The focus is full constructive derivation using vector-form expressions without introducing local representation such as Euler angles or quaternions. proposed approach synthesises bias command in form an angular vector through realisation predictive control philosophy, which has been unexplored setting. avoids heuristic choices and approximations process hence overcomes limitation earlier studies. provides theoretical practical advantages including rigour derivation, clear geometric understandings about problem provided by identification most effective velocity, independence from selection fixed coordinate system, avoidance singularities representations, more direct trajectory shaping, simple implementation.