MEXGEN: An Effective and Efficient Information Gain Approximation for Information Gathering Path Planning

TL;DR

The paper tackles online information gathering under uncertainty within a POMDP framework, where planning must maximize information-informed rewards over a horizon. It introduces MexGen, a measurement-prediction method that computes a single predicted measurement by averaging $M$ samples of the measurement function $h(\mathbf{x})$ with $\mathbf{x} \sim B_t$, i.e., $\hat{z} = \dfrac{1}{M} \sum_{i=1}^M h(\mathbf{x}^{(i)})$, enabling efficient estimation of information gain. A key theoretical result shows $\mathrm{MSE}(\text{PIM}) + \varepsilon \ge E[\mathrm{MSE}(\text{MexGen})]$ with $\varepsilon = \dfrac{1}{M} \sigma^2$, proving MexGen reduces measurement-prediction error, particularly for nonlinear or multimodal beliefs. Extensive simulations and field experiments with an onboard quadrotor validate improved planning performance and substantial run-time savings over MC and PIM, demonstrating practical impact for autonomous sensing tasks.

Abstract

Autonomous robots for gathering information on objects of interest has numerous real-world applications because of they improve efficiency, performance and safety. Realizing autonomy demands online planning algorithms to solve sequential decision making problems under uncertainty; because, objects of interest are often dynamic, object state, such as location is not directly observable and are obtained from noisy measurements. Such planning problems are notoriously difficult due to the combinatorial nature of predicting the future to make optimal decisions. For information theoretic planning algorithms, we develop a computationally efficient and effective approximation for the difficult problem of predicting the likely sensor measurements from uncertain belief states}. The approach more accurately predicts information gain from information gathering actions. Our theoretical analysis proves the proposed formulation achieves a lower prediction error than the current efficient-method. We demonstrate improved performance gains in radio-source tracking and localization problems using extensive simulated and field experiments with a multirotor aerial robot.

Figures (8)

• Figure 1: Trajectory heat maps from field experiments. We compared the current efficient method (PIM) and a computationally expensive method (MC-8) for computing information gain from possible future measurements with ours for a radio source localization task. Trajectory planning decisions, i.e. information gathering actions, are more effective with ours---resulting in a $40$% reduction in mission completion times in the best case (vs. PIM, the next best method) and visibly shorter paths leading to consistently localizing the closest object and navigating to reduce the uncertainty of the next object (see $\S$\ref{['sec:field']}). The demonstration video is at: https://youtu.be/XrsCC6MkaB4
• Figure 2: Consider an agent with an onboard sensor for acquiring noisy range measurements tasked with tracking the position an object of interest (e.g. radio source). At time $t=0$, the agent evaluates Action 2's reward out of three possible actions over a look ahead horizon of $t=1$. The red contours depict the belief state probability density. In True, we update the belief state with a measurement from the ground truth object position at $t=1$ for comparison. PIM and MexGen tiles show the Updated Belief Stategiven the predicted range measurement generated at $t=1$. Now, PIM, the existing computationally efficient approximation, incorrectly predicts an unrealistic measurement from an estimated future estate of an object. The result is an over confident future object belief state that is significantly different from the Truth. In contrast, MexGen uses the expected measurement and updates the belief state to predict the future state; this result compares well with the True state at $t=1$ in contrast to PIM and leads to a better approximation of information gain from Action 2.
• Figure 3: Agent and object path extracts in the object following experiments ($\square$: represent the starting positions; $\triangle$: represent the ending positions).
• Figure 4: Object following results showing estimation error and uncertainty of estimates (position components of the covariance matrix) as Tr(Cov) from 50 unique initial states $\times$ 30 MC simulations per method. The median values are plotted at each time step for: \ref{['fig:follow_static']} Random Walk, \ref{['fig:follow_cv']} Constant Velocity, \ref{['fig:follow_cv_ift']} CV-IFT, and \ref{['fig:follow_cv_ift_mm']} CV-IFT with mismatched filter (the hard estimation problem setting). More effective planning decisions with our MexGen method yield improved tracking accuracy and lower uncertainty over time.
• Figure 5: Agent and object path extracts in the multi-object tracking and localisation experiments ($\square$: the starting positions; $\triangle$: ending positions).

Theorems & Definitions (1)

• Lemma 1