  This study proposes a hierarchically integrated framework for safe task and
motion planning (TAMP) of bipedal locomotion in a partially observable
environment with dynamic obstacles and uneven terrain. The high-level task
planner employs linear temporal logic (LTL) for a reactive game synthesis
between the robot and its environment and provides a formal guarantee on
navigation safety and task completion. To address environmental partial
observability, a belief abstraction is employed at the high-level navigation
planner to estimate the dynamic obstacles' location. Accordingly, a synthesized
action planner sends a set of locomotion actions to the middle-level motion
planner, while incorporating safe locomotion specifications extracted from
safety theorems based on a reduced-order model (ROM) of the locomotion process.
The motion planner employs the ROM to design safety criteria and a sampling
algorithm to generate non-periodic motion plans that accurately track
high-level actions. At the low level, a foot placement controller based on an
angular-momentum linear inverted pendulum model is implemented and integrated
with an ankle-actuated passivity-based controller for full-body trajectory
tracking. To address external perturbations, this study also investigates safe
sequential composition of the keyframe locomotion state and achieves robust
transitions against external perturbations through reachability analysis. The
overall TAMP framework is validated with extensive simulations and hardware
experiments on bipedal walking robots Cassie and Digit designed by Agility
Robotics.
