This paper addresses a multi-objective optimization problem for robotic manipulator motion planning

focusing on minimizing end-effector positioning error and energy consumption while optimizing both joint angle trajectories and mobile base paths. We propose a computational framework integrating forward kinematics modeling with a hybrid optimization strategy that combines nonlinear programming

particle swarm optimization

deep/breadth-first search

and genetic algorithms. The method first optimizes joint trajectories under kinematic constraints

then determines optimal base positioning and shortest feasible routes while avoiding obstacles and finally extends to multi-target task planning through genetic algorithm–based sequence optimization. Experimental results demonstrate that the proposed approach achieves high positioning accuracy with significantly reduced energy consumption

while maintaining robust adaptability to diverse task configurations. This work provides a generalizable solution for intelligent robotic path planning and multi-objective decision optimization.