###### Abstract
Force/torque sensors [11] could measure this torque, but it significantly adds to device cost. In the case of an LLRR for a developing country's market, the costs of the sensors would be prohibitive. Moreover, these sensors add complexity and weight to the device unless miniaturized custom-made force/torque sensors are used [12]. Other approaches require using additional pressure sensors [13], Foot Contact Forces (FCFs) [14], or ground reaction forces (GRFs) [15]. Moreover, several approaches use Surface Electromyography (sEMG) sensors and signal processing techniques to estimate the human-robot interaction torque. However, using sEMG signals adds additional procedures and costs. In addition, they are also subject to variabilities inherent to the sEMG signal acquisition [16, 17, 18]. In addition, other studies report only the tests for a one-Degree-of-Freedom (DOF) LLRR, such as the estimation of ankle dynamic joint torque by a neuromusculoskeletal solver-informed Neural Network (NN) model [19]. These methods do not take into account the coupled dynamics of multiple joints. [PERSON] et al. [12] reported an Inverse Dynamics (ID) and Nonlinear Disturbance Observer (NDO) method to estimate the human-robot interaction torque without using additional sensors. As a result, their methods can produce accurate estimations. However, they rely on a precise model. Therefore, they reported the need to extend their methods for the cases when there are uncertainties. [PERSON] et al. [20] evaluated the behavior of three methods to control the angular position of an exoskeleton for knee assistance. They reported the controllers' effectiveness and showed that a model reference adaptive control (MRAC) strategy based on an NDO obtained better performance than the others. Therefore, NDO-based methods are promising for human-robot interaction torque estimation when there are uncertainties. A multi-DOF LLRR is a nonlinear system with coupled dynamics [21], which is subject to parametric uncertainties and external perturbations, e.g., there are uncertainties in the Body Segment Inertial Parameters (BSIPs) such as segment masses, Center of Mass (CoM), and inertias. Therefore, it is difficult to obtain an exact model of the system [22, 23]. Moreover, according to [PERSON] et al. [24], the dynamics of the human-robot system change from subject to subject. Additionally, it changes for one subject during the progress of their rehabilitation, i.e., between sessions. In cadaver studies, it is simple to locate the CoM by determining the center of balance of the segment [25]. However, the cross-sectional area and length profile are required to compute the CoM in vivo accurately, obtained using complex imaging systems. Therefore, several models are used to estimate the BSIPs indirectly. The models reported by [PERSON] et al. [26] and [PERSON] et al. [27] contain each body segment weight and length as the percentage of total body weight and height, respectively. Moreover, the CoM location is given as a percentage of the segment length. Both methods may be helpful to obtain a BSIPs rough estimate. However, each body segment has a unique bone, muscle, fat, and other tissues combination [25]. Therefore, the density of a segment is not uniform, and models such as the reported by [PERSON] et al. [26], and [PERSON] et al. [27] do not accurately model the LLRR with the user. Thus, developing a human-robot interaction torque estimation method is challenging to perform the isotonic rehabilitation exercises with the LLRR. Furthermore, subjects with partial lower limb amputations are not included in the aforementioned models. Therefore, it is even more challenging to compute their BSIPs. Moreover, adding a prosthesis to their limbs would also modify the BSIPs values in an unknown manner, adding uncertainties to the model. The estimation problem concerns the use of the dynamic model of an LLRR to estimate the human-robot interaction torque \(\hat{\mathbf{\tau}}_{int}\) despite BSIPs uncertainties.