Center of Mass States and Disturbance Estimation for a Walking Biped Iyad Hashlamon Faculty of Engineering and Natural Sciences Sabanci University Tuzla, Istanbul, Turkey hashlamon@sabanciuniv.edu Kemalettin Erbatur Faculty of Engineering and Natural Sciences Sabanci University Tuzla, Istanbul, Turkey erbatur@sabanciuniv.edu Abstract— An on-line assessment of the balance of the robot requires information of the state variables of the robot dynamics and measurement data about the environmental interaction forces. However, modeling errors, external forces and hard to measure states pose difficulties to the control systems. This paper presents a method of using the motion information to estimate the center of mass (CoM) states and the disturbance of walking humanoid robot. The motion is acquired from the inertial measurement unit (IMU) and forward kinematics only. Kalman filter and disturbance observer are employed, Kalman filter is used for the states and disturbance estimation, and the disturbance observer is used to decompose the disturbance into modeling error and acceleration error based on the frequency band. The disturbance is modeled mathematically in terms of previous CoM and Zero moment point (ZMP) states rather than augmenting it in the system states. The ZMP is estimated using the quadratic programming method to solve the constraint dynamic equations of the humanoid robot in translational motion. A biped robot model of 12-degrees-of-freedom (DOF) is used in the full-dynamics 3-D simulations for the estimation validation. The results indicate that the presented estimation method is successful and promising. Index Terms—Humanoid robot, Disturbance Observer, Kalman filter, state estimation. I. INTRODUCTION The control of the Humanoid robots walking and stability is a challenging task which requires the availability of various feedback variables. The use of expensive and numerous sensors on board could be regarded as a solution. However, cost, external disturbances, unmodeled dynamics, sensor noise and sensor dynamics pose difficulties for measurement systems which are crucial for feedback control in this area. Disturbance and Center of mass (CoM) states information play an important role in the control and stability of humanoids. The disturbance, in terms of modeling error and acceleration error, may affect the control algorithms adversely. CoM states are used in the stability criteria, directly [1-4] or through the inertial and gravity forces [1] [2]. The difficulties in the measurement systems motivate the use of intelligent techniques for the estimation of the state variables and disturbances. Systematic estimation is based on models. Bipeds balance is usually studied using simplified models. A simple model is the Linear Inverted Pendulum Model LIPM [3] where the body (trunk) is modeled as a lumped mass at the Center of Mass (CoM) and moves only horizontally. This model is convenient since it can be written in discrete state space representation. Thus, the linear methods of estimation can be implemented. Controlling the biped CoM dynamics [4] requires the zero moment point (ZMP) trajectory, the knowledge of the CoM states and the disturbance. The ZMP can be calculated by estimating the reaction forces and their location using constraint optimization [5]. The constraints are due to the leg in contact, friction and support polygon [6]. The CoM states are estimated based on process and measurement models. The models change according to the used sensors and the states. The disturbance may have significant effects of the system. It can be estimated by modeling it as an augmented step disturbance state in the system model [7] or by using a Disturbance observer [8]. In [9], the CoM position and velocity states are estimated. The augmented state principle is used to estimate the disturbance. The measurement model includes position and force measurements. The disturbance observer reported in [10] is used to estimate the external force using inertial sensors and foot force sensors. The ZMP disturbance observer in [11, 12] decomposes the ZMP error into position error and acceleration error based on the frequency band, however it doesn’t consider the CoM states In this paper, different from [9], The disturbance and the CoM position, velocity, and acceleration states of a walking biped are estimated without force or position sensors, and the disturbance is modeled mathematically as a function of the previous known ZMP, position and acceleration states. This estimation is based on the readings of the IMU and the kinematics of the robot legs through the assembled joint- encoders. The discrete model of the LIPM dynamic equations is obtained to form the process model of the linear state space representation with the ZMP as the input, and the acceleration as the output model. The input ZMP is estimated using the quadratic programming method to solve the constraint dynamic equations of the humanoid robot in translational motion. Kalman filter is used in its basic linear structure for the estimation, the acceleration from IMU serves as the ＹＷＸＭＱＭＴＶＷＳＭＱＳＸＷＭＲＯＱＳＯＤＳＱＮＰＰ＠ﾩＲＰＱＳ＠ｉｅｅｅ ＲＴＸ