Safe Execution of Temporally Flexible Plans for Bipedal Walking Devices

Plans with temporal flexibility have been used to allow discrete systems to adapt to disturbances that occur while the plan is being executed. To control more complex devices, such as bipedal walking machines, we must extend this execution paradigm to the control of hybrid (discrete/continuous) systems. Systems of this type are difficult to control for two reasons: 1) their high dimensionality and nonlinearity make control complex, even under nominal circumstances; and 2) operation of such systems in unstructured environments requires robustness to significant disturbances. We introduce a novel approach to hybrid temporally flexible plan execution that achieves robustness by transforming the high-dimensional system into a set of lowdimensional, weakly-coupled systems. This allows us to apply concepts previously developed for robust plan execution under uncertainty for discrete systems. We accomplish this decoupling using three components: 1) a feedback linearizing controller which provides basic decoupling of variables, 2) a hybrid plan dispatcher, which utilizes plan flexibility to adjust control settings for individual decoupled variables, and 3) plan compilation, which computes bounds for the dispatcher’s adjustments to control settings that satisfy plan requirements. We show the interaction of these components in the control of a bipedal