  We present a motion planning algorithm with probabilistic guarantees for
limbed robots with stochastic gripping forces. Planners based on deterministic
models with a worst-case uncertainty can be conservative and inflexible to
consider the stochastic behavior of the contact, especially when a gripper is
installed. Our proposed planner enables the robot to simultaneously plan its
pose and contact force trajectories while considering the risk associated with
the gripping forces. Our planner is formulated as a nonlinear programming
problem with chance constraints, which allows the robot to generate a variety
of motions based on different risk bounds. To model the gripping forces as
random variables, we employ Gaussian Process regression. We validate our
proposed motion planning algorithm on an 11.5 kg six-limbed robot for two-wall
climbing. Our results show that our proposed planner generates various
trajectories (e.g., avoiding low friction terrain under the low risk bound,
choosing an unstable but faster gait under the high risk bound) by changing the
probability of risk based on various specifications.
