🤖 AI Summary
Traditional planning models goals as deterministic state subsets, failing to capture goal uncertainty arising from noisy perception, learning generalization, and other real-world uncertainties. Method: This paper proposes a distribution-to-distribution planning framework that directly represents both goals and current states as probability distributions, explicitly accommodating dynamic environmental uncertainty. It introduces goal distributions as fundamental planning primitives, integrates unscented transformation for nonlinear probabilistic kinematics modeling, and employs cross-entropy optimization to minimize the KL divergence between predicted and target distributions—enabling end-to-end uncertainty-aware planning. Contribution/Results: The framework unifies several classical goal cost functions as special cases. Extensive simulations demonstrate strong robustness against state disturbances, model mismatch, and data-driven goal uncertainty. Moreover, it significantly improves task success reliability under multimodal, sparse, and constrained goal distributions.
📝 Abstract
Goal spaces for planning problems are typically conceived of as subsets of the state space. It is common to select a particular goal state to plan to, and the agent monitors its progress to the goal with a distance function defined over the state space. Due to numerical imprecision, state uncertainty, and stochastic dynamics, the agent will be unable to arrive at a particular state in a verifiable manner. It is therefore common to consider a goal achieved if the agent reaches a state within a small distance threshold to the goal. This approximation fails to explicitly account for the agent's state uncertainty. Point-based goals further do not accommodate goal uncertainty that arises when goals are estimated in a data-driven way. We argue that goal distributions are a more appropriate goal representation and present a novel approach to planning under uncertainty to goal distributions. We use the unscented transform to propagate state uncertainty under stochastic dynamics and use cross-entropy method to minimize the Kullback-Leibler divergence between the current state distribution and the goal distribution. We derive reductions of our cost function to commonly used goal-reaching costs such as weighted Euclidean distance, goal set indicators, chance-constrained goal sets, and maximum expectation of reaching a goal point. We explore different combinations of goal distributions, planner distributions, and divergence to illustrate behaviors achievable in our framework.
