  Logic-Geometric Programming (LGP) is a powerful motion and manipulation
planning framework, which represents hierarchical structure using logic rules
that describe discrete aspects of problems, e.g., touch, grasp, hit, or push,
and solves the resulting smooth trajectory optimization. The expressive power
of logic allows LGP for handling complex, large-scale sequential manipulation
and tool-use planning problems. In this paper, we extend the LGP formulation to
stochastic domains. Based on the control-inference duality, we interpret LGP in
a stochastic domain as fitting a mixture of Gaussians to the posterior path
distribution, where each logic profile defines a single Gaussian path
distribution. The proposed framework enables a robot to prioritize various
interaction modes and to acquire interesting behaviors such as contact
exploitation for uncertainty reduction, eventually providing a composite
control scheme that is reactive to disturbance. The supplementary video can be
found at https://youtu.be/CEaJdVlSZyo
