Robots operating in complex and unknown environments frequently require geometric-semantic representations of the environment to safely perform their tasks. While inferring the environment, they must account for many possible scenarios when planning future actions. Since objects' class types are discrete and the robot's self-pose and the objects' poses are continuous, the environment can be represented by a hybrid discrete-continuous belief which is updated according to models and incoming data. Prior probabilities and observation models representing the environment can be learned from data using deep learning algorithms. Such models often couple environmental semantic and geometric properties. As a result, semantic variables are interconnected, causing semantic state space dimensionality to increase exponentially. In this paper, we consider planning under uncertainty using partially observable Markov decision processes (POMDPs) with hybrid semantic-geometric beliefs. The models and priors consider the coupling between semantic and geometric variables. Within POMDP, we introduce the concept of semantically aware safety. Obtaining representative samples of the theoretical hybrid belief, required for estimating the value function, is very challenging. As a key contribution, we develop a novel form of the hybrid belief and leverage it to sample representative samples. We show that under certain conditions, the value function and probability of safety can be calculated efficiently with an explicit expectation over all possible semantic mappings. Our simulations show that our estimates of the objective function and probability of safety achieve similar levels of accuracy compared to estimators that run exhaustively on the entire semantic state-space using samples from the theoretical hybrid belief. Nevertheless, the complexity of our estimators is polynomial rather than exponential.

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