# Towards Online Estimation of Human Joint Muscular Torque with a Lower Limb Exoskeleton Robot
## 1 Introduction
Insoles with air bladders have always been always adopted to detect foot contact state, but it is difficult to get a precise GRF, because uneven distortion during complex foot-ground contact states leads to nonlinearity. In addition, the horizontal GRF cannot be measured by the insole either, which can cause error during joint torque estimation. [PERSON] et al. [23] proposed a wearable sensing system including IMUs and GRF measurement insoles to estimate the JMT in the sagittal plane. [PERSON] et al. [24] developed a mobile force plate and motion analysis units to estimate 3D JMT. These devices are specifically designed to acquire the motion data of a human body, but are used to control an exoskeleton robot; thus, both the motion data of the user and the robot itself are required. It is unnecessary to introduce two sensing systems to measure the motion information of the user and the exoskeleton, respectively. An exoskeleton embedded sensing system has the potential to collect motion data from the user, but few have taken advantage of this. [PERSON] et al. developed Berkeley Lower Extremity Exoskeleton (BLEEX) with integrated linear position sensor and foot pressure sensors [25]. They focused on minimizing human-exoskeleton interaction forces. They did not fully investigate the estimation of JMT using those embedded sensors. Researchers also developed the manipulator based human stiffness features learning method [26]. [PERSON] et al. designed another embedded sensing system [27]. They used the positions of the exoskeleton thigh and shank, and ground reaction forces on human feet in their simplified static shank equilibrium method (SSE) to calculate the torque command to the knee joints. [PERSON] et al. developed rehabilitation exoskeletons to measure the user's JMT. In this method, the required joint torques of both the human body and the exoskeleton are calculated by inverse dynamics, respectively. The JMT is derived by removing the required joint torque of both the exoskeleton and the human limbs from the measured joint torque by torque sensors in the exoskeleton joints. The method in Ref. [28] is valid only during swing motion, and was improved in reference [29]. An insole sensor with air bladders was introduced to measure the GRF, which extends their method to the stance phase. However, the insole cannot measure the horizontal GRF. This may lead to estimation error. Besides, the influence of hip acceleration was not discussed. This work presents a novel implementation of the human lower limb JMT estimation method to devise an online JMT estimation solution that can be used to achieve active power-assist function on our prototype active power-assist lower limb exoskeleton (APAL) [30]. The main achievement of this paper is the design of an embedded sensing system and a specially designed inverse dynamics process. The sensing system is integrated in the exoskeleton structure which does not mount any sensors on the human body but obtains the motion data and interaction forces of the human body by mapping motion from the exoskeleton to a human model. Unlike traditional IDA, we solve the inverse dynamics of each human leg separately to shorten the serial chain and reduce the computational complexity. The JMT is divided into two parts which we call the mass-induced one and the FCF-induced one to avoid discontinuous dynamic equations due to different contact states of feet. The rest of the paper is organized as follows. Section 2 presents a parameterized model of the human body and specially designed inverse dynamics for estimating JMT, and then presents the embedded sensing system including trunk posture, joint motion information, and foot contact force. Section 3 demonstrates and discusses the results of the JMT estimation experiments. Finally, the conclusions of this paper are presented in Section 4.