MEAM Ph.D. Thesis Defense: “Real-Time Perception and Mixed-Integer Footstep Control for Underactuated Bipedal Walking on Rough Terrain”

The promise of bipedal robots is to go where people go, serving as surrogates for human labor in dangerous, unstructured environments. For the most part, this promise remains unrealized. The primary challenge for controlling bipedal locomotion is underactuation. Standing on a single leg limits control authority, requiring appropriate foot placement to generate or absorb momentum and maintain balance. Rough terrain exacerbates this challenge by introducing restrictions on where the robot can step. These restrictions must be identified from onboard sensing modalities and accounted for in the footstep plan, all while meeting the strict real-time requirements of feedback control. In this thesis, we examine systems, modeling choices, and algorithms for solving this problem, ultimately enabling dynamic bipedal walking over previously unseen discontinuous terrain.

Conventional approaches decouple the problem of walking over rough terrain into separate modules for footstep planning and motion control, limiting walking speed and online adaptability. The beginning of this thesis introduces a new model-predictive-control-style footstep planner which eliminates this decomposition. We jointly optimize over the robot’s dynamics and discrete choice of stepping surface in real time to stabilize underactuated walking over constrained footholds.

Our footstep controller depends on approximating the safe terrain as a union of convex planar polygon “stepping stones”. In order to generate such an approximation from onboard sensors in real time, we propose novel safe terrain segmentation and convex decomposition algorithms. Our segmentation approach avoids the common design choice of plane segmentation, which we argue makes segmentation algorithms slower and less reliable. Instead, we classify terrain as safe based only on local features, yielding a segmentation which is both fast to compute and temporally consistent. We present full stack perceptive locomotion experiments on the underactuated biped Cassie, leveraging our novel footstep controller and perception pipeline to walk over previously unseen discontinuous terrain.

Finally, we present an exploratory study of a cascaded-fidelity model predictive footstep controller, which combines elements of our first footstep planner with whole-body model predictive control in order to navigate even more challenging terrains.