In order to explore the balance in legged locomotion, we are studying systems that hop and run on one springy leg. Pre vious work has shown that relatively simple algorithms can achieve balance on one leg for the special case of a system that is constrained mechanically to operate in a plane ( Rai bert, in press; Raibert and Brown, in press). Here we general ize the approach to a three-dimensional ( 3D) one-legged machine that runs and balances on an open floor without physical support. We decompose control of the machine into three separate parts: one part that controls forward running velocity, one part that controls attitude of the body, and a third part that controls hopping height. Experiments with a physical 3D one-legged hopping machine showed that this control scheme, while simple to implement, is powerful enough to permit hopping in place, running at a desired rate, and travel along a simple path. These algorithms that control locomotion in 3D are direct generalizations of those in 2D, with surprisingly little additional complication.

Simple L O C O~O~~O I I algorithms provide balance for machines that run on one leg. The generalization uf these one-leg algorithms for control of machines with several legs is explored. The generalization is quite simple when multilegged systems run with gaits that use the support legs one at a time. For these gaits the ~n e-l e g algorithms can be used b o control multilegged running. The cortcept of a virtual leg is introduced to further extend the approach to gaits that use the legs in pairs, such as the trot, the pace, and the bound. These quadruped running gaits map into gaits that use one virtual leg for support at a rime, for which the one-leg algorithms can provide control. This approach was used in laboratory experiments to control a quadruped machine that runs with a trotting gait.

Online learning and controller adaptation will be an essential component for legged robots in the next few years as they begin to leave the laboratory setting and join our world. I present the first example of a learning system which is able to quickly and reliably acquire a robust feedback control policy for 3D dynamic bipedal walking from a blank slate using only trials implemented on the physical robot. The robot begins walking within a minute and learning converges in approximately 20 minutes. The learning works quickly enough that the robot is able to continually adapt to the terrain as it walks. This success can be attributed in part to the mechanics of our robot, which is capable of stable walking down a small ramp even when the computer is turned off.In this thesis, I analyze the dynamics of passive dynamic walking, starting with reduced planar models and working up to experiments on our real robot. I describe, in detail, the actor-critic reinforcement learning algorithm that is implemented on the return map dynamics of the biped. Finally, I address issues of scaling and controller augmentation using tools from optimal control theory and a simulation of a planar one-leg hopping robot. These learning results provide a starting point for the production of robust and energy efficient walking and running robots that work well initially, and continue to improve with experience.Thesis Supervisor: