Joint sensor fault detection and recovery based on virtual sensor for walking legged robots 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—This paper presents a novel method for joint sensor faults detection and faulty signal reconstruction. It uses the Virtual Joint Sensor (VJS). The model structure of the VJS consists of two interconnected models: The simple Linear Inverted Pendulum Model (LIPM) and the robot leg kinematics model (LKM). Kalman filter based on LIPM estimates the Center of Mass (CoM) position of the biped. The LKM uses the estimated CoM position to calculate the joints angles. A faulty signal model is formed to detect the faults, based on an adaptive threshold, and recovers the signal using the VJS outputs. The sensor abrupt, incipient, and frozen output faults are studied and tested. The validity of the proposed method was confirmed by simulations on 3D dynamics model of the humanoid robot SURALP while walking on a flat terrain. Index Terms— Sensor faults, virtual sensor, inertial measurement unit (IMU), fault detection, Kalman filter, ZMP. I. INTRODUCTION The interest in the humanoid walking stability has increased dramatically and attracted a great attention of many researchers. The joint encoder-sensors that are assembled at the legs-joints have a significant effect on the stability of the robot. Due to faulty readings, the robot may lose its stability causing a human, robot, or environmental damage. A fault can be defined as an unpermitted deviation of the variable from its acceptable behavior. The faults are divided into abrupt (step-like) fault, incipient (drift-like) fault, and intermittent fault based on their timing dependency [1]. The faults can be additive or multiplicative with respect to the system model. Sensor faults [2] may lead to a malfunction or system failure. Thus it is a necessity to design a fault detection and isolation (FDI) scheme. This FDI is used to monitor and estimate the faults in real time. The FDI methods are either model-free or model-based methods. The model-free FDI methods [3, 4] depend on the system features without using the system model. However, they don’t reconstruct the faulty signals. The model-based FDI methods [1] utilize the system dynamic model. This model operates in parallel to the real system, they have the same input and their outputs are used to form the residual [1, 5-10]. The faulty signal can be reconstructed and its performance depends on the quality of the model [11]. However, obtaining the dynamic model for complicated systems such as the humanoid robot is a challenge. This challenge is due to the many degrees of freedom, coupling effects, nonlinear dynamics, and parameter and environment uncertainty [12]. Therefore, it is recommended to use software sensors or virtual sensors [13]. Virtual sensors are based on simple mathematical models. They increase the measurement redundancy and reliability in the system. Furthermore, they can be used for the fault detection and signal recovery as in this paper. In this work, a novel method for detecting the joint encoder abrupt, incipient, and frozen output faults is proposed. It also recovers the faulty signal based on the VJS. This method consists of two steps: the VJS step and the fault detection and recovery step as in Fig. 1. In the first step, the VJS estimates the joints angles. It is based on the estimated position of the robot CoM ˆ c and the inverse kinematic model for each leg of the robot. The CoM position is estimated by using the LIPM [14] where the body (trunk) is modeled as a lumped mass at the CoM and moves only horizontally. Using the CoM position, the joint angles θ  are estimated using the leg inverse kinematics. In the second step, a state space model for the measured angles meas θ from the sensors is formed including the fault η . The faults are detected and the true angle θ is reconstructed for all the joints simultaneously by using Kalman filter and threshold. In this work, the effect of the fault on the closed loop control system is not studied. The faults are detected and the true signals are reconstructed in an open loop fashion. Also, the terrain is assumed to be flat. The rest of the paper is organized as follows: Section 2 describes the virtual joint sensor. Section 3 introduces the fault detection and signal reconstruction method. Section 4 introduces the calculation of the threshold. Section 5 and section 6 show the results and the conclusion respectively. ＹＷＸＭＱＭＴＷＹＹＭＲＳＹＸＭＴＯＱＴＯＤＳＱＮＰＰ＠ﾩＲＰＱＴ＠ｉｅｅｅ ＱＲＱＰ