Dynamic Modeling and State Estimation of Cable-Conduit Actuation During Interaction With Nonpassive Environments

Remote actuation solutions such as cable-conduit transmissions are beneficial in wearable robotics to reduce dynamic loading on distal joints. However, these systems often introduce high reflected impedance or require rigid sensors for force control that hinder their integration in wearables. Low impedance and ease of integration could be both obtained by combining distributed cable strain sensing with dynamic modeling to estimate output force and position. In this article, we present a new computational model to analyze the dynamics of cable-conduit systems. The model features bidirectional propagation of motion within the transmission, which allows for simulation of human-interacting systems, where either or both the human and the robot can be force or position sources. Moreover, we present a new method for rapidly solving for the system of equations based on iterative linearization of the system of nonlinear equations. The model and the solution method are validated in a physical prototype through experiments involving physical interaction with a human subject. Finally, we develop methods for model-based estimation of cable tension given measurements from multiple noisy strain sensors embedded in the transmission, and quantify the accuracy achievable via different methods as a function of the number and location of sensors. Results demonstrate that the model accurately predicts behavior observed in the prototype. Moreover, the newly developed iterative linearization solution method allows a 100-fold increase of computation speed compared to a standard solver. Finally, we demonstrate that cable tension can be estimated with increasing accuracy when increasing the number of sensors, but accuracy decreases if the output portion of the transmission is not instrumented.