978-1-4244-7815-6/10/$26.00 ©2010 IEEE ICARCV2010 A Learning Approach to Optimize Walking Cycle of a Passivity-based Biped Robot Nima Fatehi Mechatronic Group, Electrical and Computer Engineering Faculty, Islamic Azad University, Qazvin Branch Qazvin, IRAN Email: neamadeus@gmail.com Masoud Asadpour Control and Intelligent Processing Center of Excellence, Electrical Engineering Faculty, University of Tehran Tehran, IRAN Email: asadpour@ut.ac.ir Adel Akbarimajd ECE Group, Faculty of Engineering, University of Mohaghegh Ardabili Ardabil, IRAN Email: akbarimajd@uma.ac.ir Laila Majdi Mechanical Department Islamic Azad University, South Tehran Branch Tehran, IRAN Email: l.majdi@gmail.com Abstract— A learning mechanism based on Powell's optimization algorithm is proposed to optimize walking behavior of a passivity based biped robot. To this end, a passivity-based biped robot has been simulated in MSC ADAMS and a control policy inspired from humanoid walking is adopted for a stable walking of the robot. Linear controllers try to control the joints of robot in each walking phase to implement the gait proposed by the control policy. Learning is employed using Powell's optimization algorithm to adjust the control parameters so that the robot enters to an optimum limit cycle in a finite time. The fitness function is defined to evaluate the robot's optimum behavior. The results are verified by simulations in SIMULINK+ADAMS. Keywords— Biped Robot, robot simulation, Passivity based walking, Powell's method, Optimization, fitness function. I. INTRODUCTION In the recent decades there have been many interest and studies around biologically inspired locomotion systems and especially biped walking. Different approaches have been employed to develop and control biped robots including ZMP based approaches [1], passivity based walking [2,3,4] and trajectory tracking approaches [5,6]. The main challenge has been to find a best walking strategy which would be energy efficient, stable and adaptive to handle different terrain and disturbances; the features found mostly in the human walking. Due to complexity and high DOF of humanoid robots, there may be many possible gaits, but the question is how to reach the best answer. In animals, independent of the mechanical system, the best solution is learned through experience. Reinforcement learning has been used by different approaches to learn some issues in biped walking [5,7]. Neural networks also have been used by many researchers to learn the actuation of joints [8]. Sprowitz et. Al used central pattern generators and Powell's optimization method to show that a robot with an arbitrary arrangement of Yamor modules can learn to move independent of mechanical configurations [9]. Linear controllers are simple and easy to design. They are widely used for industrial and research purposes. Their main drawback is their limitation in controlling nonlinear systems, according to the fact that most physical systems have nonlinear characteristics. However some researchers have used linear controllers in nonlinear problems using a model linearized over multiple state ranges called LOLIMOT [10]. In this research we have used such idea to divide state space into some sections in each of which a linear feedback controller would be responsible to control a joint for the task defined in the gait control policy. The Powell's optimization algorithm then helps to learn the best controller parameters leading to a stable walking with the best possible energy efficiency. II. THE ROBOT MODEL The robot is simulated as a planar 2D biped with 6 joints and 7 links in MSC ADAMS. Fig. 1 shows the developed model. We tried to make our model as close as possible to passive walking systems so that it could use the natural dynamics for walking instead of actuating every joint. This has the advantage of minimizing the energy consumption and would lead to a behavior similar to human walking. The knee joints thus have been considered without any actuators and a kneecap prevents them from reverse bending. On the hip and ankle joints actuators have been used to help controlling the motion of the robot on level ground. It is assumed that these actuators are not interlocked to the joints so that they would not bypass the passive dynamics of robot and their torques are supposed to be added to the inertial and gravity forces imposed to the links. Most passivity-based biped robots use curved feet to help them reduce the energy loss of heel strike and eliminate need for an active ankle joint, but for getting closer to a human walking and for analysis of the role of heel Figure 1. MSC Adams implementation of the simulated robot 2010 11th Int. Conf. Control, Automation, Robotics and Vision Singapore, 7-10th December 2010 175