Robot object manipulation in real-world environments is challenging because robot operation must be robust to a range of sensing, estimation, and actuation uncertainties to avoid potentially unsafe and costly mistakes that are a barrier to their adoption. In this paper, we propose a flexible and generalisable physics-informed causal Bayesian network (CBN) based framework for a robot to probabilistically reason about candidate manipulation actions, to enable robot decision-making robust to arbitrary robot system uncertainties -- the first of its kind to use a probabilistic programming language implementation. Using experiments in high-fidelity Gazebo simulation of an exemplar block stacking task, we demonstrate our framework's ability to: (1) predict manipulation outcomes with high accuracy (Pred Acc: 88.6%); and, (2) perform greedy next-best action selection with 94.2% task success rate. We also demonstrate our framework's suitability for real-world robot systems with a domestic robot. Thus, we show that by combining probabilistic causal modelling with physics simulations, we can make robot manipulation more robust to system uncertainties and hence more feasible for real-world applications. Further, our generalised reasoning framework can be used and extended for future robotics and causality research.
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