Evolution of Biped Walking Using Truncated Fourier Series and Particle Swarm Optimization Nima Shafii 1 , Siavash Aslani 1 ,Omid Mohamad Nezami 1 , Saeed Shiry 2 1 Mechatronics Research Laboratoy (MRL), Department of Computer and Electerical Engineering, Qazvin Islamic Azad University, Qazvin, Iran {shafii, saslani, mohamadnezami}@mrl.ir 2 Computer Engineering Department, Amirkabir University, Tehran, Iran shiry@ce.aut.ac.ir Abstract. Controlling a biped robot with a high degree of freedom to achieve stable and straight movement patterns is a complex problem. With growing computational power of computer hardware, high resolution real time simulation of such robot models has become more and more applicable. This paper presents a novel approach to Generate Bipedal gait for humanoid locomotion. This approach is based on modified Truncated Fourier Series (TFS) for generating angular trajectories. It is also the first time that Particle Swarm Optimization (PSO) is used to find the best angular trajectory and optimize TFS. This method has been implemented on Simulated NAO robot in Robocup 3D soccer simulation environment (rcssserver3d). To overcome inherent noise of the simulator we applied a Resampling algorithm which could lead the robustness in nondeterministic environments. Experimental results show that PSO optimizes TFS faster and better than GA to generate straighter and faster humanoid locomotion. Keywords: Bipedal Locomotion; Particle Swarm Optimization; Truncated Fourier series 1 Introduction In recent years, bipedal locomotion, especially "bipedal walking" has been one of the interesting research topics in multi disciplinary topic. Bipedal walking as a very complex motion, involves most of humanoid joints including its sensors and actuators. Many researchers have focused on this topic and a lot of approaches have been presented. But so far no method exists that can walk a robot as stable as human's do. There are two major approaches in bipedal walking researches; model-based and model free approaches. In model-based approach the designer first derives model of the robot and then builds a controller for the model. Two well known methods in this approach are "Zero Moment Point"[1] (ZMP) and "Inverted Pendulum"[2]. In model-free approach, which is also called "Dynamics Based", it is common to make use of the sensory information and associate it with motions. No physical model is used in this method that eases the implementation of the skills. There are three