A Momentum-Based Foot Placement Strategy for Stable Postural Control of Robotic Spring-Mass Running with Point Feet

A long-standing argument in model-based control of locomotion is about the level of complexity that a model should have to define a behavior such as running. Even though goldilocks model based on biomechanical evidence is often sought, it is unclear what complexity level qualifies to be such a model. This dilemma deepens further for bipedal robotic running with point feet, since these robots are underactuated, while tracking center-of-mass (COM) trajectories defined by the spring-loaded inverted pendulum (SLIP) model of running allocates all control inputs, leaving angular coordinates of the robot's trunk uncontrolled. Existing work in the literature approach this problem either by trading off COM trajectories against upright trunk posture during stance or by adopting more detailed models that include effects of trunk angular dynamics. In this paper, we present a new approach based on modifying foot placement targets of the SLIP model. Theoretical analysis and numerical results show that the proposed approach outperforms these traditional strategies.