  While motion planning of locomotion for legged robots has shown great
success, motion planning for legged robots with dexterous multi-finger grasping
is not mature yet. We present an efficient motion planning framework for
simultaneously solving locomotion (e.g., centroidal dynamics), grasping (e.g.,
patch contact), and contact (e.g., gait) problems. To accelerate the planning
process, we propose distributed optimization frameworks based on Alternating
Direction Methods of Multipliers (ADMM) to solve the original large-scale
Mixed-Integer NonLinear Programming (MINLP). The resulting frameworks use
Mixed-Integer Quadratic Programming (MIQP) to solve contact and NonLinear
Programming (NLP) to solve nonlinear dynamics, which are more computationally
tractable and less sensitive to parameters. Also, we explicitly enforce patch
contact constraints from limit surfaces with micro-spine grippers. We
demonstrate our proposed framework in the hardware experiments, showing that
the multi-limbed robot is able to realize various motions including
free-climbing at a slope angle 45{\deg} with a much shorter planning time.
