A Probabilistic Framework for Constrained Manipulations and Task and Motion Planning under Uncertainty

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 pro le 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.