Mesh-Based Methods for Robust and Agile Dynamic Gaits

In this paper, we propose and analyze mesh-based tools to control bounding motions of an 8 degree-of-freedom planar quadruped model with limited footholds on terrain. There are two complementary goals in our presentation. First, we aim to clarify potential advantages and diadvantages of our mesh-based approach in planning agile motions for a legged system. A key advantage is the ability to map our reachable states and their feasible transitions, given a relatively highdimensional nonlinear dynamics system for which traditional meshing techniques would be impractical. A suspected disadvantage is that meshing has finite resolution, and robustness of mesh-based results should correspondingly be considered. Our second goal is to discuss proposed definitions and metrics for agility. In particular, we present initial guidelines for quantifying and thereby improving specific metrics that correlate to good performance in a long jump task. We find that our mesh-based policies predict future dynamics for plans up to about a 5-step horizon. To quantify agility, we focus on two intuitive aspects: control of forward motion (speed) and control of foothold placement. Our results provide evidence that the ability to decouple these goals to perform a long jump follow a complex and non-intuitive structure, and that our mesh-based approach is well suited for such agile motion planning tasks.