Reactive Task Planner Synthesis of Multi-Contact Dynamic Locomotion in Constrained Environments

Contact-based decision and planning methods are increasingly being sought for task execution in humanoid robots. Formal methods for verification and synthesis have not been yet incorporated into the motion planning sequence to generate complex mobility behaviors in legged humanoid robots. This study takes a step toward formally synthesizing a high-level reactive task planner for unified legged and armed locomotion in constrained environments. We formulate a two-player temporal logic game between the contact planner and its possibly adversarial environment. The resulting discrete planner satisfies the given task specifications expressed as a fragment of temporal logic and is executed by a low-level phase-space planner. We devise a set of low-level locomotion modes based on centroidal momentum dynamics. Provable correctness of the low-level execution of the synthesized discrete planner is guaranteed through the socalled simulation relations. Simulations of dynamic locomotion in constrained environments support the effectiveness of the outlined hierarchical planner protocol.