Motion Planning for Legged and Humanoid Robots a Dissertation Submitted to the Department of Computer Science and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Legged vehicles have attracted interest for many high-mobility applications, such as military troop support and logistics in rocky, steep, and forested terrain, scientific exploration of cliffs, mountains, and volcanoes on earth and other planets, and search and rescue. Humanoid robots have additional applications in homes and offices as personal assistants. But planning and controlling their motion is difficult, because dozens of joints must be coordinated to maintain balance while executing a task. It is particularly difficult in extremely uneven, steep, or cluttered terrain — precisely where legs are an advantage. I present a legged locomotion planner that reasons with the physical and operational constraints in the vehicle’s high dimensional configuration space, producing motions that are guaranteed to avoid collision and remain balanced. This planner works on a variety of terrain, ranging from flat ground to steep and rocky cliff faces, and is applied to three very different robots: NASA’s six-legged lunar vehicle ATHLETE, AIST Japan’s biped humanoid robot HRP-2, and Stanford’s four-limbed rock climbing robot Capuchin. The planner consists of two parts: first, a graph search to find a sequence of contacts to make and break, and second, the planning of single-step motions between successive contacts using a probabilistic roadmap planner (PRM). I prove that a “fuzzy search”, where PRM planning is interleaved between candidate steps, has theoretical completeness properties, and a running time not strongly affected by configuration space dimension. The planner can also produce natural-looking motions given a small number of “motion primitives”, high-quality example motions that bias