Belief Roadmaps with Uncertain Landmark Evanescence

TL;DR

This work addresses navigation under map-based uncertainty when landmarks may disappear, introducing landmark evanescence as a core challenge. It extends Belief Roadmaps by adopting a Gaussian mixture belief over robot pose and landmark presence (LEPD), with efficient process/measurement updates that accommodate evanescence and a pruning scheme to keep computation tractable. The BRULE framework, including BRULE-Expected, demonstrates that a bounded, mixture-based belief can achieve high-quality plans in simulations and on a real Spot robot, outperforming optimistic BRMs and handling correlated landmark presence. The results indicate the method's practical value for robust localization-aware navigation in dynamic environments and point to future work on richer environment evolution and occlusion modeling.

Abstract

We would like a robot to navigate to a goal location while minimizing state uncertainty. To aid the robot in this endeavor, maps provide a prior belief over the location of objects and regions of interest. To localize itself within the map, a robot identifies mapped landmarks using its sensors. However, as the time between map creation and robot deployment increases, portions of the map can become stale, and landmarks, once believed to be permanent, may disappear. We refer to the propensity of a landmark to disappear as landmark evanescence. Reasoning about landmark evanescence during path planning, and the associated impact on localization accuracy, requires analyzing the presence or absence of each landmark, leading to an exponential number of possible outcomes of a given motion plan. To address this complexity, we develop BRULE, an extension of the Belief Roadmap. During planning, we replace the belief over future robot poses with a Gaussian mixture which is able to capture the effects of landmark evanescence. Furthermore, we show that belief updates can be made efficient, and that maintaining a random subset of mixture components is sufficient to find high quality solutions. We demonstrate performance in simulated and real-world experiments. Software is available at https://bit.ly/BRULE.

Figures (5)

• Figure 1: A robot, uncertain of its own position, must navigate to the goal. There is a direct path, in orange, from the start to the goal location. However this path does not contain any landmarks, so the robot's position uncertainty becomes large. The green and blue paths have evanescent landmarks that may or may not be present, leading to many possible position estimates and uncertainties along these paths. An upper bound on the number of uncertainties is exponential in the number of landmarks in the environment, which is untenable, even in simple environments. In this work, we show how to tractably plan with landmark evanescence.
• Figure 2: Four example environments are shown above. The roadmap nodes and edges are shown in dark gray and green respectively. The colored dots are landmarks. All landmarks of the same color are correlated and are independent of differently colored landmarks, except for the environment in the top left where all landmarks are independent.
• Figure 3: In the left plot, a box plot of the regret is shown across the maximum number of particles maintained by BRULE and the number of samples for BRULE-E. Performance tends to improve as the number of samples used increases. In the right plot, we see the run time associated with each of the methods. We see that as the size of the planners increases, BRULE has comparable performance to BRULE-E with a greatly reduced runtime.
• Figure 4: On the left, the test environment for real world experiments using a Boston Dynamics Spot. A mutex distribution is prescribed for landmarks 6 and 9. All other landmarks are marked absent. On the right, six executions of each plan computed by the two methods are shown. Three trials have the landmark 6 present and three trials have the landmark 9 present. Due to the mutex correlation, BRULE-E fails to recover the path that visits both landmarks. However, BRULE reasons about the correlation and determines that a longer path minimizes uncertainty at the goal.
• Figure 5: The crosstrack error from the nominal path for each planner. The more informative path discovered by BRULE yields a tighter spread of executions.