Modeling a Biped Robot on Matlab/SimMechanics Marlon Fernando Velásquez-Lobo, Juan Manuel Ramirez-Cortés, José de Jesus Rangel-Magdaleno Electronics Department Instituto Nacional de Astrofísica, Óptica y Electrónica Tonantzintla Puebla, México mvelasquez@inaoep.mx, jmramirez@ieee.org, jrangel@inaoep.mx José Luis Vázquez-González Computing, Electronics and Mechatronics Department Universidad de las Américas Puebla Cholula Puebla, México josel.vazquez@udlap.mx Abstract — This paper presents a methodology for modeling a biped robot on Matlab/SimMechanics, which supports mathematical model development with time and effort savings. The model used for the biped robot simulation consists of 5-links which are connected through revolute joins. The identical legs have knee joints between the shank and thigh parts, and a rigid body forms the torso. Furthermore, modeling of ground contact forces is described. A PD controller is used on a linear model in state variable form in order to simulate the dynamic of the system. Results obtained from the dynamic simulation are presented. Keywords—Biped robot, SimMechanics, modeling, torque. I. INTRODUCTION In the last decades there has been a growing interest in the research community with the ultimate goal to come up with walking biped robots emulating human displacement. The interest is motivated by a number of reasons based on the ability of biped robots to navigate in rugged terrains or irregular environments where wheeled robots cannot move [1,2]. A number of possible applications in diverse fields are continuously emerging: replacement of humans in hazardous works such as rescue operations [3], military operations, disaster scenarios [4], or restoration movement in people with disabilities such as dynamically controlled prosthetics [5] and rehabilitation robotics [6]. The research progress, however, has been relatively limited because of the complexity of legged robot dynamics, which grows with the number of links and degrees of freedom (DoF) [7,8]. Generally the dynamic model of biped robots is obtained through the Lagrange energy model, however, it must be noted that the computational complexity of the Lagrange equations is Oሺn ୯ ଷ ሻ, where n ୯ represents the number of DoF of the mechanical system [9]. Lengthy formulations are therefore to be expected, so that they can define a three-dimensional system where the number of DoF is greater than twelve [10]. Usually, a Simulink model is represented by algebraic and differential equations that predict the future state of a system with the current state [11]. A SimMechanics-based tool is described in this paper as a design aid during the system modeling process. A SimMechanics model is a representation of the physical structure of a machine, specified through some variables such as mass, geometry and kinematic relations between its components. SimMechanics converts this representation into an equivalent mathematical model [12], which saves time and effort during the development of the mathematical model. This paper presents a methodology for creating a model of a 5-link biped robot, with a proportional-integral-derivative (PID) control performed to track a desired trajectory. II. MODEL OF BIPED ROBOT USING SIMMECHANICS SimMechanics is a block diagram modeling environment for modeling and simulating mechanical systems using the standard Newtonian dynamics of forces and torques [12]. SimMechanics simulates translational and rotational motion in three dimensions, and includes a suite of tools to specify bodies, mass properties, possible motions, kinematic constraints, coordinate systems, and the means of initiating and measuring motions. The steps involved in SimMechanics in order to build and run a model representation of a machine are listed as follows: • Specify body inertial properties, degrees of freedom, and constraints, along with coordinate systems attached to bodies to measure positions and velocities. • Set up sensors and actuators to record and initiate body motions, as well as apply forces/torques. • Start the simulation, calling the Simulink solvers to find the motions of the system, while maintaining any imposed constraints. • Visualize the machine while building the model and animate the simulation while running, using the Handle Graphics or virtual reality-based visualization tool. Modeling a biped robot can be divided into three parts: the links, the actuator or servo and modeling of the ground contact forces. In this work, the biped robot consists of 5-links which are connected through revolute joins (one rotational DoF). The identical legs have knee joint between the shank and thigh parts, and one rigid body forms the torso. Fig. 1 shows the model structure. Fig. 2 shows the block diagram of the biped robot. Three subsystems can be identified, both legs and torso, and the reference signal for each joint. These subsystems are described in the following section 978-1-4673-6155-2/13/$31.00 © 2013 IEEE 203