Sensitivity of balancing in legged systems under torque constraint variations

The balancing capabilities of a legged system can be influenced by several properties of the system itself, for instance, the strength of joint motors in a robot or muscle strength in living systems. In this work, the changes in the balancing capabilities of a legged system are evaluated as the joint actuator torque limits of the system change. The legged system is modeled with an inverted pendulum model with an actuated ankle and a finite foot size. The effect of variations of the ankle torque limits on the system balance stability is quantified through the local properties of Lagrange multipliers in optimization theory and are validated through numerical experiments. With the proposed method, the information on the balance stability boundary of a legged system is used to predict the balance stability characteristics of the system with altered joint torque limits, hence providing quantifiable guidelines to the design of such systems.