Informative Path Planning to Explore and Map Unknown Planetary Surfaces with Gaussian Processes

Some environments remain largely unexplored, like unvisited planetary surfaces or regions of the ocean. Many of the destinations we are interested in have never been explored and thus, there is no a priori knowledge to leverage. Instead, a vehicle must sample upon arrival, process this data, and either send this information back to a teleoperator or autonomously decide where to go next. Teleoperation is suboptimal in that human intuition can be imprecise and cannot be mathematically guaranteed to yield an optimal result. Given a surface environment, a mobile agent will map the distribution of a scalar variable without any prior information, with a degree of confidence of model convergence, and while minimizing distance traveled. Science-blind approaches to covering a surface area include a predefined path with waypoints for a vehicle to locomote in an “open-loop” policy, like the Boustrephedon or Spiral patterns. Information theoretic approaches iteratively gather information to feed back into a model or policy, which then updates with a waypoint to visit next. Gaussian processes have been popularly incorporated into active learning exploration strategies due to their ability to incorporate information into a parameter-free model and quantify a confidence metric with every model prediction. We evaluate the performance of this informative path planning algorithm in mapping an environment on three different surfaces: parabola, Townsend, and hydration value across a lunar crater from LAMP data. The Gaussian process model was tasked to learn these relationships across these specific surfaces to investigate the efficacy of the learner and policy on a noiseless vs noisy surface, a convex vs a nonconvex surface, and a smooth well-behaved function vs an unknown real function. We quantify model variance, model root-mean-squared error, distance, and surface global minimum identification of the various methods in exploring a range of surfaces with no a priori knowledge. The results show that the information-driven methods significantly outperform naive exploration methods in minimizing model error and distance with potential of convergence.