Pitching dynamics are an important component of the dynamics of legged locomotion. We develop an energy-open pitching stabilization model to achieve full asymptotic stability of locomotion. This model is called the pitched-actuated Spring-Loaded Inverted Pendulum (pitched-actuated SLIP) model. It extends the conservative SLIP model to include a trunk as well as net nonzero hip torque and leg damping. The hip torque is governed by a proportional and derivative controller which uses only the angle between body and leg as feedback during stance. During the swing phase of the leg, inertial frame feedback is used to reset the leg to a fixed angle in space. The use of body-frame feedback in stance is thought to be relevant to biology and robotic control, as time delays and uncertainty in inertial frame feedback could be challenging in stance. Further, this method of control during stance could be implemented in a neural feedforward manner using antagonistic pairs of muscle or muscle-like actuators around the hip joint. This model of pitching dynamics exhibits full asymptotic stability over a range of model parameters. Further, derivative control significantly impacts disturbance mitigation. Periodic locomotion solutions of the model with large energy cost tend to be unstable. Whereas, the most energy efficient locomotion solutions found tend to be within the stable region of the parameter space. The correlation between energy efficiency and stability found in this model may have significant implications for locomotion with pitching.

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