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Abstract-This paper reports on a Gaussian belief-space planning formulation for mobile robots that includes random measurement acquisition variables that model whether or not each measurement is actually acquired. We show that maintaining the stochasticity of these variables in the planning formulation leads to a random belief covariance matrix, allowing us to consider the risk associated with the acquisition in the objective function. Inspired by modern portfolio theory and utility optimization, we design objective functions that are risk-averse, and show that risk-averse planning leads to decisions made by the robot that are desirable when operating under uncertainty. We show the benefit of this approach using simulations of a planar robot traversing an uncertain environment and of an underwater robot searching for loopclosure actions while performing visual SLAM.

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