Zachary Sunberg

Himanshu Gupta, Bradley Hayes, Zachary Sunberg

This paper presents a hybrid online Partially Observable Markov Decision Process (POMDP) planning system that addresses the problem of autonomous navigation in the presence of multi-modal uncertainty introduced by other agents in the environment. As a particular example, we consider the problem of autonomous navigation in dense crowds of pedestrians and among obstacles. Popular approaches to this problem first generate a path using a complete planner (e.g., Hybrid A*) with ad-hoc assumptions about uncertainty, then use online tree-based POMDP solvers to reason about uncertainty with control over a limited aspect of the problem (i.e. speed along the path). We present a more capable and responsive real-time approach enabling the POMDP planner to control more degrees of freedom (e.g., both speed AND heading) to achieve more flexible and efficient solutions. This modification greatly extends the region of the state space that the POMDP planner must reason over, significantly increasing the importance of finding effective roll-out policies within the limited computational budget that real time control affords. Our key insight is to use multi-query motion planning techniques (e.g., Probabilistic Roadmaps or Fast Marching Method) as priors for rapidly generating efficient roll-out policies for every state that the POMDP planning tree might reach during its limited horizon search. Our proposed approach generates trajectories that are safe and significantly more efficient than the previous approach, even in densely crowded dynamic environments with long planning horizons.

Benjamin Kraske, Qi Heng Ho, Federico Rossi et al.

Policies for Partially Observable Markov Decision Processes (POMDPs) are often designed using a nominal system model. In practice, this model can deviate from the true system during deployment due to factors such as calibration drift or sensor degradation, leading to unexpected performance degradation. This work studies policy robustness against deviations in the POMDP observation model. We introduce the Policy Observation Robustness Problem: to determine the maximum tolerable deviation in a POMDP's observation model that guarantees the policy's value remains above a specified threshold. We analyze two variants: the sticky variant, where deviations are dependent on state and actions, and the non-sticky variant, where they can be history-dependent. We show that the Policy Observation Robustness Problem can be formulated as a bi-level optimization problem in which the inner optimization is monotonic in the size of the observation deviation. This enables efficient solutions using root-finding algorithms in the outer optimization. For the non-sticky variant, we show that when policies are represented with finite-state controllers (FSCs) it is sufficient to consider observations which depend on nodes in the FSC rather than full histories. We present Robust Interval Search, an algorithm with soundness and convergence guarantees, for both the sticky and non-sticky variants. We show this algorithm has polynomial time complexity in the non-sticky variant and at most exponential time complexity in the sticky variant. We provide experimental results validating and demonstrating the scalability of implementations of Robust Interval Search to POMDP problems with tens of thousands of states. We also provide case studies from robotics and operations research which demonstrate the practical utility of the problem and algorithms.

Zakariya Laouar, Qi Heng Ho, Zachary Sunberg

Partially observable Markov decision processes (POMDPs) offer a principled formalism for planning under state and transition uncertainty. Despite advances made towards solving large POMDPs, obtaining performant policies under limited planning time remains a major challenge due to the curse of dimensionality and the curse of history. For many POMDP problems, the value of information (VOI) - the expected performance gain from reasoning about observations - varies over the belief space. We introduce a dynamic programming framework that exploits this structure by conditionally processing observations based on the value of information at each belief. Building on this framework, we propose Value of Information Monte Carlo planning (VOIMCP), a Monte Carlo Tree Search algorithm that allocates computational effort more efficiently by selectively disregarding observation information when the VOI is low, avoiding unnecessary branching of observations. We provide theoretical guarantees on the near-optimality of our VOI reasoning framework and derive non-asymptotic convergence bounds for VOIMCP. Simulation evaluations demonstrate that VOIMCP outperforms baselines on several POMDP benchmarks.

Himanshu Gupta, Paul Motter, Aritra Chakrabarty et al.

Solving multi-robot motion planning (MRMP) requires generating collision-free kinodynamically feasible trajectories for multiple interacting robots. We introduce Kinodynamic Translation-Invariant Edge Bundles or KiTE-Extend, a planner-agnostic action selection mechanism for sampling-based kinodynamic motion planning. KiTE-Extend uses a library of trajectory segments computed offline to guide action selection during online planning, improving the ability of existing planners to identify feasible motion segments without altering state propagation, collision checking, or cost evaluation, and without changing their theoretical guarantees. While KiTE-Extend can modestly improve single-agent planners, its benefits are most clear in the multi-agent setting, where it is able to explore more effectively and significantly improve planning through the dense spatiotemporal constraints introduced by robot-robot interaction. Through experiments on multiple kinodynamic systems and environments, we show that KiTE-Extend reduces planning time and improves scalability across the three most common MRMP paradigms: centralized, prioritized, and conflict-based.

Benjamin Kraske, Zakariya Laouar, Zachary Sunberg

As humans come to rely on autonomous systems more, ensuring the transparency of such systems is important to their continued adoption. Explainable Artificial Intelligence (XAI) aims to reduce confusion and foster trust in systems by providing explanations of agent behavior. Partially observable Markov decision processes (POMDPs) provide a flexible framework capable of reasoning over transition and state uncertainty, while also being amenable to explanation. This work investigates the use of user-provided counterfactuals to generate contrastive explanations of POMDP policies. Feature expectations are used as a means of contrasting the performance of these policies. We demonstrate our approach in a Search and Rescue (SAR) setting. We analyze and discuss the associated challenges through two case studies.

John Mern, Anil Yildiz, Zachary Sunberg et al.

Online solvers for partially observable Markov decision processes have difficulty scaling to problems with large action spaces. Monte Carlo tree search with progressive widening attempts to improve scaling by sampling from the action space to construct a policy search tree. The performance of progressive widening search is dependent upon the action sampling policy, often requiring problem-specific samplers. In this work, we present a general method for efficient action sampling based on Bayesian optimization. The proposed method uses a Gaussian process to model a belief over the action-value function and selects the action that will maximize the expected improvement in the optimal action value. We implement the proposed approach in a new online tree search algorithm called Bayesian Optimized Monte Carlo Planning (BOMCP). Several experiments show that BOMCP is better able to scale to large action space POMDPs than existing state-of-the-art tree search solvers.

Zachary Sunberg, Mykel Kochenderfer

This work examines the hypothesis that partially observable Markov decision process (POMDP) planning with human driver internal states can significantly improve both safety and efficiency in autonomous freeway driving. We evaluate this hypothesis in a simulated scenario where an autonomous car must safely perform three lane changes in rapid succession. Approximate POMDP solutions are obtained through the partially observable Monte Carlo planning with observation widening (POMCPOW) algorithm. This approach outperforms over-confident and conservative MDP baselines and matches or outperforms QMDP. Relative to the MDP baselines, POMCPOW typically cuts the rate of unsafe situations in half or increases the success rate by 50%.

Zachary Sunberg, Mykel Kochenderfer

Online solvers for partially observable Markov decision processes have been applied to problems with large discrete state spaces, but continuous state, action, and observation spaces remain a challenge. This paper begins by investigating double progressive widening (DPW) as a solution to this challenge. However, we prove that this modification alone is not sufficient because the belief representations in the search tree collapse to a single particle causing the algorithm to converge to a policy that is suboptimal regardless of the computation time. This paper proposes and evaluates two new algorithms, POMCPOW and PFT-DPW, that overcome this deficiency by using weighted particle filtering. Simulation results show that these modifications allow the algorithms to be successful where previous approaches fail.

Zachary Sunberg, Mykel Kochenderfer

Online solvers for partially observable Markov decision processes have been applied to problems with large discrete state spaces, but continuous state, action, and observation spaces remain a challenge. This paper begins by investigating double progressive widening (DPW) as a solution to this challenge. However, we prove that this modification alone is not sufficient because the belief representations in the search tree collapse to a single particle causing the algorithm to converge to a policy that is suboptimal regardless of the computation time. This paper proposes and evaluates two new algorithms, POMCPOW and PFT-DPW, that overcome this deficiency by using weighted particle filtering. Simulation results show that these modifications allow the algorithms to be successful where previous approaches fail.

Patrick Slade, Preston Culbertson, Zachary Sunberg et al.

Robots performing manipulation tasks must operate under uncertainty about both their pose and the dynamics of the system. In order to remain robust to modeling error and shifts in payload dynamics, agents must simultaneously perform estimation and control tasks. However, the optimal estimation actions are often not the optimal actions for accomplishing the control tasks, and thus agents trade between exploration and exploitation. This work frames the problem as a Bayes-adaptive Markov decision process and solves it online using Monte Carlo tree search and an extended Kalman filter to handle Gaussian process noise and parameter uncertainty in a continuous space. MCTS selects control actions to reduce model uncertainty and reach the goal state nearly optimally. Certainty equivalent model predictive control is used as a benchmark to compare performance in simulations with varying process noise and parameter uncertainty.

Zachary Sunberg, Christopher Ho, Mykel Kochenderfer

Safe interaction with human drivers is one of the primary challenges for autonomous vehicles. In order to plan driving maneuvers effectively, the vehicle's control system must infer and predict how humans will behave based on their latent internal state (e.g., intentions and aggressiveness). This research uses a simple model for human behavior with unknown parameters that make up the internal states of the traffic participants and presents a method for quantifying the value of estimating these states and planning with their uncertainty explicitly modeled. An upper performance bound is established by an omniscient Monte Carlo Tree Search (MCTS) planner that has perfect knowledge of the internal states. A baseline lower bound is established by planning with MCTS assuming that all drivers have the same internal state. MCTS variants are then used to solve a partially observable Markov decision process (POMDP) that models the internal state uncertainty to determine whether inferring the internal state offers an advantage over the baseline. Applying this method to a freeway lane changing scenario reveals that there is a significant performance gap between the upper bound and baseline. POMDP planning techniques come close to closing this gap, especially when important hidden model parameters are correlated with measurable parameters.