2015 15th Interational Conference on Control, Automation and Systems (ICCAS 2015) Oct. 13-16, 2015 in BEXCO, Busan, Korea Modeling and Dynamic Analysis of the Biped Robot Muhammad Rameez l and Dr. Liaquat Ali Khan 2 * 1 Department ofMechatronics Engineering, Air University Islamabad, Pakistan (rameez994@hotmail.com) 2 Department of Mechanical Engineering, Muhammad Ali Jinnah University Islamabad, Pakistan (kliaguat@rocketmail. com) Abstract: Biped robots have several degrees of feedom (DOF) composed of many articulated links connected together by joint which ends up in a complex structure and diffcult to make it mimic human like locomotion gait which is dynamic in nature and at the same time stable in the sense of not falling by. This paper presents dynamic equations of motion and its Matlab simulation of joints position. These dynamic equations are derived by starting with the kinematics which includes forward kinematics (FK) derived by using the Denavit-Hartenberg notation and inverse kinematics (IK) and then solving the dynamics of the biped robot. Two well-known methods for solving the dynamic of the robot are Newton-Euler formulation and Euler-Lagrangian formulation. This work uses the Euler-Lagrange formulation as it is a fancy formulation technique for solving dynamics instead of fnding all the forces, velocities using Newton-Euler formulation. Keywords: Biped robot, Denavit-Hartenberg parameters, Forward kinematics, Dynamic equations 1. INTRODUCTION Robots are today's interesting topic due to their abilities to performed repetitive and difcult tasks untiringly with high accuracy in any environment which is hard for humans to interact within. In the feld of robotics, study and development of mobile robots which include wheeled and legged robots has attracted researchers and scientists due to their higher degree of mobility that can move around in the environments with the ability to accomplish the tasks sensing and avoiding the obstacles as well. Furthermore, the development of legged locomotion robots has received more attention due to their higher degree of feedom which enhances its mobility (especially in climbing up and down the stairs) over the wheeled robots. Many researchers have contributed their work in the feld of biped robots locomotion on design, modeling kinematics and dynamics, gait synthesis and control of the legged locomotion with stability analysis [3] [5] [6]. In all these contributions dynamic modeling forms the basis for biped robot locomotion. Modeling of the biped robot starts with the forward kinematics that deals with the position and orientation of the end effector, which is derived by using the Denavit-Hartenberg (DH) convention. Inverse kinematics is solved in order to determine the joint angles for given desired point. Afer determining the kinematics the next step is to solve the dynamics of the model by either using the formulation of Newton-Euler or Euler-Lagrange [1] [2]. C. Herandez-Santos et al [5] in their work presented the modeling by starting with the kinematics and dynamics of the biped robot and the torque required for the joints is computed by the Euler Lagrange approach. 978-89-93215-09-0/15/$31.00 @rCROS 1149 This paper presents the dynamic modeling and simulation of the dynamic equation using Matlab®. The dynamic equations of motion are derived using the Lagrangian formulation [1] [2] which is an energy based approach. This is an extension of the previous works in which design and forward kinematics of the biped robot were presented [4]. 2. FORWARD KINEMATICS Forward kinematics is the study of determining the position and orientation of the end-effector with respect to a fxed coordinate reference fame. This section will give a brief overview of the work done previously. In the previous work [4] forward kinematics was done using the Denavit-Hartenberg (DH) convention. Denavit-Hartenberg notation is defned by four parameters which are pre-defned before determining the transformation matrices. Figure 1 shows the schematics of the biped robot used. l. Xs Fig. I Biped robot schematic [4]