  Locomotion planning for legged systems requires reasoning about suitable
contact schedules. The contact sequence and timings constitute a hybrid
dynamical system and prescribe a subset of achievable motions. State-of-the-art
approaches cast motion planning as an optimal control problem. In order to
decrease computational complexity, one common strategy separates footstep
planning from motion optimization and plans contacts using heuristics. In this
paper, we propose to learn contact schedule selection from high-level task
descriptors using Bayesian optimization. A bi-level optimization is defined in
which a Gaussian process model predicts the performance of trajectories
generated by a motion planning nonlinear program. The agent, therefore, retains
the ability to reason about suitable contact schedules, while explicit
computation of the corresponding gradients is avoided. We delineate the
algorithm in its general form and provide results for planning single-legged
hopping. Our method is capable of learning contact schedule transitions that
align with human intuition. It performs competitively against a heuristic
baseline in predicting task appropriate contact schedules.
