  Online control design using a high-fidelity, full-order model for a bipedal
robot can be challenging due to the size of the state space of the model. A
commonly adopted solution to overcome this challenge is to approximate the
full-order model (anchor) with a simplified, reduced-order model (template),
while performing control synthesis. Unfortunately it is challenging to make
formal guarantees about the safety of an anchor model using a controller
designed in an online fashion using a template model. To address this problem,
this paper proposes a method to generate safety-preserving controllers for
anchor models by performing reachability analysis on template models while
bounding the modeling error. This paper describes how this reachable set can be
incorporated into a Model Predictive Control framework to select controllers
that result in safe walking on the anchor model in an online fashion. The
method is illustrated on a 5-link RABBIT model, and is shown to allow the robot
to walk safely while utilizing controllers designed in an online fashion.
