An LMI Approach to Controller Design for Balancing over Slackline

Balancing over a tight rope or slackline is a challenging task as the stabilizing moments must be internally generated by moving the arms. In this study, we use a two-segment biomechanical model of the subject to investigate postural stability and control during the balancing task on slackline. The assumed model has three degree of freedom (DoF), including slackline displacement, body orientation, and the arm rotation that also generates the stabilizing torque. We assume vestibular sensing of the body rotation rate and emulate a neural estimator in the brain that reconstructs the missing state variables. We employ linear matrix inequality (LMI) framework to design the controller-estimator to stabilize the proposed biomechanical model. The nonlinear model is then simulated to ensure postural stability during the execution of balancing task over slackline.