Decision Region Determination for Touch Based Localization

Many robotic systems deal with uncertainty by performing a sequence of information gathering actions. Unfortunately, it is not only NP-hard to solve optimally, but also NP-hard to approximate better than logarithmically [3]. Instead, many successful systems perform a shallow online search, optimizing for a specified metric on the resulting belief distributions. One often used metric, known as information gain, maximizes the expected decrease in Shannon entropy [2, 5, 1, 18, 6, 4, 12, 9, 15]. Shannon entropy measures the amount of uncertainty in a distribution. Thus, minimizing this is useful if the objective is to remove all uncertainty. In our prior work, we formulate a similar metric for manipulation, with the goal of finding the location of an object from an uncertainty distribution over pose. Notably, we prove our metric produces nearoptimal sequences when selecting actions greedily, whereas optimizing Shannon entropy may not [13]. In many robotics problems, you don’t need to reduce uncertainty completely you simply need to reduce it enough to accomplish your task. Optimizing for a taskdriven criteria directly enables the system to utilize fewer information gathering actions than reducing all uncertainty. For example, Hsiao [11] found that optimizing for probability of success outperformed optimizing for reducing Shannon entropy. In decision theory, value of information (VoI) [10] is a commonly used metric which attempts to capture this idea. In our current and ongoing work, we formulate an objective for task-driven uncertainty reduction. We design metrics which are adaptive submodular [7], rendering the greedily policy with this metric near-optimal. We present the formalization of this idea for touch based localization, and an algorithm with near-optimality bounds published recently [14]. Additionally, we present our newly developed formulation, which is significantly faster to compute.