  To dynamically traverse challenging terrain, legged robots need to
continually perceive and reason about upcoming features, adjust the locations
and timings of future footfalls and leverage momentum strategically. We present
a pipeline that enables flexibly-parametrized trajectories for perceptive and
dynamic quadruped locomotion to be optimized in an online, receding-horizon
manner. The initial guess passed to the optimizer affects the computation
needed to achieve convergence and the quality of the solution. We consider two
methods for generating good guesses. The first is a heuristic initializer which
provides a simple guess and requires significant optimization but is
nonetheless suitable for adaptation to upcoming terrain. We demonstrate
experiments using the ANYmal C quadruped, with fully onboard sensing and
computation, to cross obstacles at moderate speeds using this technique. Our
second approach uses latent-mode trajectory regression (LMTR) to imitate expert
data - while avoiding invalid interpolations between distinct behaviors - such
that minimal optimization is needed. This enables high-speed motions that make
more expansive use of the robot's capabilities. We demonstrate it on flat
ground with the real robot and provide numerical trials that progress toward
deployment on terrain. These results illustrate a paradigm for advancing beyond
short-horizon dynamic reactions, toward the type of intuitive and adaptive
locomotion planning exhibited by animals and humans.
