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

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