Calculating the Inverse Kinematic (IK) equations is a complex problem due to the nonlinearity of these equations. Choosing the end effector orientation affects the reach of the target location. The Forward Kinematics (FK) of Humanoid Robotic Legs (HRL) is determined by using DenavitHartenberg (DH) method. The HRL has two legs with five Degrees of Freedom (DoF) each. The paper proposes using a Particle Swarm Optimization (PSO) algorithm to optimize the best orientation angle of the end effector of HRL. The selected orientation angle is used to solve the IK equations to reach the target location with minimum error. The performance of the proposed method is measured by six scenarios with different simulated positions of the legs. The proposed method is compared with procedures that used different optimization algorithms such as Genetic Algorithm (GA), Differential Evolution (DE), and Invasive Weed Optimization (IWO). The Root Mean Square Error (RMSE) and computation time are used as comparison measures. The proposed method gives the best results among others, and it reaches the target location with an average RMSE of 10-12 with 2.5 seconds average computation time.
