  Dynamic locomotion in rough terrain requires accurate foot placement,
collision avoidance, and planning of the underactuated dynamics of the system.
Reliably optimizing for such motions and interactions in the presence of
imperfect and often incomplete perceptive information is challenging. We
present a complete perception, planning, and control pipeline, that can
optimize motions for all degrees of freedom of the robot in real-time. To
mitigate the numerical challenges posed by the terrain a sequence of convex
inequality constraints is extracted as local approximations of foothold
feasibility and embedded into an online model predictive controller.
Steppability classification, plane segmentation, and a signed distance field
are precomputed per elevation map to minimize the computational effort during
the optimization. A combination of multiple-shooting, real-time iteration, and
a filter-based line-search are used to solve the formulated problem reliably
and at high rate. We validate the proposed method in scenarios with gaps,
slopes, and stepping stones in simulation and experimentally on the ANYmal
quadruped platform, resulting in state-of-the-art dynamic climbing.
