In a world designed for legs, quadrupeds, bipeds, and humanoids have the
opportunity to impact emerging robotics applications from logistics, to
agriculture, to home assistance. The goal of this survey is to cover the recent
progress toward these applications that has been driven by model-based
optimization for the real-time generation and control of movement. The majority
of the research community has converged on the idea of generating locomotion
control laws by solving an optimal control problem (OCP) in either a
model-based or data-driven manner. However, solving the most general of these
problems online remains intractable due to complexities from intermittent
unidirectional contacts with the environment, and from the many degrees of
freedom of legged robots. This survey covers methods that have been pursued to
make these OCPs computationally tractable, with specific focus on how
environmental contacts are treated, how the model can be simplified, and how
these choices affect the numerical solution methods employed. The survey
focuses on model-based optimization, covering its recent use in a stand alone
fashion, and suggesting avenues for combination with learning-based
formulations to further accelerate progress in this growing field.Comment: submitted for initial review; comments welcom