Optimal decision-making presents a significant challenge for autonomous systems operating in uncertain, stochastic and time-varying environments. Environmental variability over time can significantly impact the system's optimal decision making strategy for mission completion. To model such environments, our work combines the previous notion of Time-Varying Markov Decision Processes (TVMDP) with partial observability and introduces Time-Varying Partially Observable Markov Decision Processes (TV-POMDP). We propose a two-pronged approach to accurately estimate and plan within the TV-POMDP: 1) Memory Prioritized State Estimation (MPSE), which leverages weighted memory to provide more accurate time-varying transition estimates; and 2) an MPSE-integrated planning strategy that optimizes long-term rewards while accounting for temporal constraint. We validate the proposed framework and algorithms using simulations and hardware, with robots exploring a partially observable, time-varying environments. Our results demonstrate superior performance over standard methods, highlighting the framework's effectiveness in stochastic, uncertain, time-varying domains.

The exploration of ocean worlds stands as a pivotal element in humanity's exploration of our solar system, encompassing critical research objectives including the quest for potential signs of life and the comprehensive understanding of conditions fostering habitability [1], [2], [3]. Robotic exploration missions are essential for the exploration of potentially habitable ocean worlds. Past lander and rover missions including the Mars exploration program [4] and the Perseverance rover mission [5] are human-in-the-loop systems with expert teams on Earth supervising the terrain sampling process and controlling them based on the collected data. However, unlike Mars missions, many of the ocean world missions, including the Europa Lander mission concept [6], are anticipated to have short durations, on the order of tens of days, due to the intensity of the radiation environment, adverse thermal conditions, low availability of solar energy, and using battery as the sole power source. The limited mission duration combined with the long communication delays between Earth and the ocean worlds necessitates a high degree of autonomy for the lander's success [7]. The Europa lander's primary objectives include collecting terrain samples for in situ analysis of surface and sub-surface materials. Autonomy in terrain sampling missions is challenging due to the high degree of uncertainty in the surface topology at the landing site, terrain material properties, composition, and appearance. Constraints on the number of samples that can be analyzed in-situ, coupled with the risk of system failures, further limits the extent of exploration [8].

Autonomous lander missions on extraterrestrial bodies will need to sample granular material while coping with domain shift, no matter how well a sampling strategy is tuned on Earth. This paper proposes an adaptive scooping strategy that uses deep Gaussian process method trained with meta-learning to learn on-line from very limited experience on the target terrains. It introduces a novel meta-training approach, Deep Meta-Learning with Controlled Deployment Gaps (CoDeGa), that explicitly trains the deep kernel to predict scooping volume robustly under large domain shifts. Employed in a Bayesian Optimization sequential decision-making framework, the proposed method allows the robot to use vision and very little on-line experience to achieve high-quality scooping actions on out-of-distribution terrains, significantly outperforming non-adaptive methods proposed in the excavation literature as well as other state-of-the-art meta-learning methods. Moreover, a dataset of 6,700 executed scoops collected on a diverse set of materials, terrain topography, and compositions is made available for future research in granular material manipulation and meta-learning.

Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with independent dynamics, this paper presents an algorithm to find the optimal policy for a multi-component budget-constrained POMDP. We first introduce a budgeted-POMDP model (b-POMDP) which enables us to find the optimal policy for a POMDP while adhering to budget constraints. Next, we prove that the value function or maximal collected reward for a b-POMDP is a concave function of the budget for the finite horizon case. Our second contribution is an algorithm to calculate the optimal policy for a multi-component budget-constrained POMDP by finding the optimal budget split among the individual component POMDPs. The optimal budget split is posed as a welfare maximization problem and the solution is computed by exploiting the concave nature of the value function. We illustrate the effectiveness of the proposed algorithm by proposing a maintenance and inspection policy for a group of real-world infrastructure components with different deterioration dynamics, inspection and maintenance costs. We show that the proposed algorithm vastly outperforms the policy currently used in practice.

We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model dynamics of an agents that operates under resource constraints in a stochastic environment. The presented algorithms work in time polynomial with respect to the representation of the model and they synthesize strategies ensuring that a given set of goal states will be reached (once or infinitely many times) with probability 1 without resource exhaustion. In particular, when the amount of resource becomes too low to safely continue in the mission, the strategy changes course of the agent towards one of a designated set of reload states where the agent replenishes the resource to full capacity; with sufficient amount of resource, the agent attempts to fulfill the mission again. We also present two heuristics that attempt to reduce expected time that the agent needs to fulfill the given mission, a parameter important in practical planning. The presented algorithms were implemented and numerical examples demonstrate (i) the effectiveness (in terms of computation time) of the planning approach based on consumption Markov decision processes and (ii) the positive impact of the two heuristics on planning in a realistic example.

We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes the continual exploration of different paths in an MDP while ensuring the satisfaction of a temporal logic specification. We first show that the maximum entropy of an MDP can be finite, infinite or unbounded. We provide necessary and sufficient conditions under which the maximum entropy of an MDP is finite, infinite or unbounded. We then present an algorithm to synthesize a policy that maximizes the entropy of an MDP. The proposed algorithm is based on a convex optimization problem and runs in time polynomial in the size of the MDP. We also show that maximizing the entropy of an MDP is equivalent to maximizing the entropy of the paths that reach a certain set of states in the MDP. Finally, we extend the algorithm to an MDP subject to a temporal logic specification. In numerical examples, we demonstrate the proposed method on different motion planning scenarios and illustrate that as the restrictions imposed on the paths by a specification increase, the maximum entropy decreases, which in turn, increases the predictability of paths.

In this paper, we consider an adversarial scenario where one agent seeks to achieve an objective and its adversary seeks to learn the agent's intentions and prevent the agent from achieving its objective. The agent has an incentive to try to deceive the adversary about its intentions, while at the same time working to achieve its objective. The primary contribution of this paper is to introduce a mathematically rigorous framework for the notion of deception within the context of optimal control. The central notion introduced in the paper is that of a belief-induced reward: a reward dependent not only on the agent's state and action, but also adversary's beliefs. Design of an optimal deceptive strategy then becomes a question of optimal control design on the product of the agent's state space and the adversary's belief space. The proposed framework allows for deception to be defined in an arbitrary control system endowed with a reward function, as well as with additional specifications limiting the agent's control policy. In addition to defining deception, we discuss design of optimally deceptive strategies under uncertainties in agent's knowledge about the adversary's learning process. In the latter part of the paper, we focus on a setting where the agent's behavior is governed by a Markov decision process, and show that the design of optimally deceptive strategies under lack of knowledge about the adversary naturally reduces to previously discussed problems in control design on partially observable or uncertain Markov decision processes. Finally, we present two examples of deceptive strategies: a "cops and robbers" scenario and an example where an agent may use camouflage while moving. We show that optimally deceptive strategies in such examples follow the intuitive idea of how to deceive an adversary in the above settings.