Orbit Characterization, Stabilization and Composition on 3D Underactuated Bipedal Walking via Hybrid Passive Linear Inverted Pendulum Model A Hybrid passive Linear Inverted Pendulum (HLIP) model is proposed for characterizing, stabilizing and composing periodic orbits for 3D underactuated bipedal walking. Specifically, Periodl (P1) and Period 2 (P2) orbits are geometrically characterized in the state space of the HLIP. Stepping controllers are designed for global stabilization of the orbits. Valid ranges of the gains and their optimality are derived. The optimal stepping controller is used to create and stabilize the walking of bipedal robots. An actuated Springloaded Inverted Pendulum (aSLIP) model and the underactuated robot Cassie are used for illustration. Both the aSLIP walking with PI or P2 orbits and the Cassie walking with all 3D compositions of the PI and P2 orbits can be smoothly generated and stabilized from a steppinginplace motion. This approach provides a perspective and a methodology towards continuous gait generation and stabilization for 3D underactuated walking robots.

Motion Decoupling and Composition via Reduced Order Model optimization for Dynamic Humanoid Walking with CLFQP based Active Force Control In this paper, 3D humanoid walking is decoupled into periodic and transitional motion, each of which is decoupled into planar walking in the sagittal and lateral plane. Reduced order models (ROMs), i.e. actuated Springloaded Inverted Pendulum (aSLIP) models and HybridLinear Inverted Pendulum (HLIP) models, are utilized for motion generation on the desired center of mass (COM) dynamics for each type of planar motion. The periodic motion is planned via point foot (underactuated) ROMs for dynamic motion with minimum ankle actuation, while the transitional motion is planned via footactuated ROMs for fast and smooth transition. Composition of the planar COM dynamics yields the desired COM dynamics in 3D, which is embedded on the humanoid via control Lyapunov function based Quadratic programs (CLFQPs). Additionally, the ground reaction force profiles of the aSLIP walking are used as desired references for ground contact forces in the CLFQPs for smooth domain transitions. The proposed framework is realized on a lowerlimb exoskeleton in simulation wherein different walking motions are achieved.