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This work explores an innovative algorithm designed to enhance the mobility of underactuated bipedal robots across challenging terrains, especially when navigating through spaces with constrained opportunities for foot support, like steps or stairs. By combining ankle torque with a refined angular momentum-based linear inverted pendulum model (ALIP), our method allows variability in the robot's center of mass height. We employ a dual-strategy controller that merges virtual constraints for precise motion regulation across essential degrees of freedom with an ALIP-centric model predictive control (MPC) framework, aimed at enforcing gait stability. The effectiveness of our feedback design is demonstrated through its application on the Cassie bipedal robot, which features 20 degrees of freedom. Key to our implementation is the development of tailored nominal trajectories and an optimized MPC that reduces the execution time to under 500 microseconds--and, hence, is compatible with Cassie's controller update frequency. This paper not only showcases the successful hardware deployment but also demonstrates a new capability, a bipedal robot using a moving walkway. 

A new control paradigm using angular momentum and foot placement as state variables in the linear inverted pendulum model has expanded the realm of possibilities for the control of bipedal robots. This new paradigm, known as the ALIP model, has shown effectiveness in cases where a robot's center of mass height can be assumed to be constant or near constant as well as in cases where there are no non-kinematic restrictions on foot placement. Walking up and down stairs violates both of these assumptions, where center of mass height varies significantly within a step and the geometry of the stairs restrict the effectiveness of foot placement. In this paper, we explore a variation of the ALIP model that allows the length of the virtual pendulum formed by the robot's stance foot and center of mass to follow smooth trajectories during a step. We couple this model with a control strategy constructed from a novel combination of virtual constraint-based control and a model predictive control algorithm to stabilize a stair climbing gait that does not soley rely on foot placement. Simulations on a 20-degree of freedom model of the Cassie biped in the SimMechanics simulation environment show that the controller is able to achieve periodic gait.