A Hierarchical Geometric Framework to Design Locomotive Gaits for Highly Articulated Robots

Motion planning for mobile robots with many degrees-of-freedom (DoF) is challenging due to their high-dimensional configuration spaces. To manage this curse of dimensionality, this paper proposes a new hierarchical framework that decomposes the system into sub-systems (based on shared capabilities of DoFs), for which we can design and coordinate motions. Instead of constructing a high-dimensional configuration space, we establish a hierarchy of two-dimensional spaces on which we can visually design gaits using geometric mechanics tools. We then coordinate motions among the two-dimensional spaces in a pairwise fashion to obtain desired robot locomotion. Further geometric analysis of the two-dimensional spaces allows us to visualize the contribution of each sub-system to the locomotion, as well as the contribution of the coordination among the sub-systems. We demonstrate our approach by designing gaits for quadrupedal robots with different morphologies, and experimentally validate our findings on a robot with a long actuated back and intermediate-sized legs.