  This paper presents a hierarchical control strategy based on hybrid systems
theory, nonlinear control, and safety-critical systems to enable cooperative
locomotion of robotic guide dogs and visually impaired people. We address
high-dimensional and complex hybrid dynamical models that represent
collaborative locomotion. At the high level of the control scheme, local and
nonlinear baseline controllers, based on the virtual constraints approach, are
designed to induce exponentially stable dynamic gaits. The baseline controller
for the leash is assumed to be a nonlinear controller that keeps the human in a
safe distance from the dog while following it. At the lower level, a real-time
quadratic programming (QP) is solved for modifying the baseline controllers of
the robot as well as the leash to avoid obstacles. In particular, the QP
framework is set up based on control barrier functions (CBFs) to compute
optimal control inputs that guarantee safety while being close to the baseline
controllers. The stability of the complex periodic gaits is investigated
through the Poincare return map. To demonstrate the power of the analytical
foundation, the control algorithms are transferred into an extensive numerical
simulation of a complex model that represents cooperative locomotion of a
quadrupedal robot, referred to as Vision 60, and a human model. The complex
model has 16 continuous-time domains with 60 state variables and 20 control
inputs.
