  As robots move from the laboratory into the real world, motion planning will
need to account for model uncertainty and risk. For robot motions involving
intermittent contact, planning for uncertainty in contact is especially
important, as failure to successfully make and maintain contact can be
catastrophic. Here, we model uncertainty in terrain geometry and friction
characteristics, and combine a risk-sensitive objective with chance constraints
to provide a trade-off between robustness to uncertainty and constraint
satisfaction with an arbitrarily high feasibility guarantee. We evaluate our
approach in two simple examples: a push-block system for benchmarking and a
single-legged hopper. We demonstrate that chance constraints alone produce
trajectories similar to those produced using strict complementarity
constraints; however, when equipped with a robust objective, we show the chance
constraints can mediate a trade-off between robustness to uncertainty and
strict constraint satisfaction. Thus, our study may represent an important step
towards reasoning about contact uncertainty in motion planning.
