Analysis results and tools for the control of planar bipedal gaits using hybrid zero dynamics

New analysis and tools are presented that extend the hybrid zero dynamics (HZD) framework for the control of planar bipedal walkers. Results include (i) analysis of walking on a slope, (ii) analysis of dynamic (decoupling matrix) singularities, and (iii) an alternative method for choosing virtual constraints. A key application of the new tools is the design of controllers that render a passive bipedal gait robust to disturbances without the use of full actuation-while still requiring zero control effort at steady-state. The new tools can also be used to design controllers for gaits having an arbitrary steady-state torque profile. Five examples are given that illustrate these and other results.