arXiv subjects

Michael Hibbard

Publications and source records attributed to Michael Hibbard.

11 recordsLinked to original sources

arXiv2025

Verifiable Mission Planning For Space Operations

Spacecraft must operate under environmental and actuator uncertainties while meeting strict safety requirements. Traditional approaches rely on scenario-based heuristics that fail to account for stochastic influences, leading to suboptimal or unsafe plans. We propose a finite-horizon, chance-constrained Markov decision process for mission planning, where states represent mission and vehicle parameters, actions correspond to operational adjustments, and temporal logic specifications encode operational reach-avoid constraints. We synthesize policies that optimize mission objectives while ensuring constraints are met with high probability. Applied to the GRACE-FO mission, the approach accounts for stochastic solar activity and uncertain thrust performance, yielding maneuver schedules that maximize scientific return and provably satisfy safety requirements. We demonstrate how Markov decision processes can be applied to space missions, enabling autonomous operation with formal guarantees.

eess.SY↗

arXiv2025

Encrypted Computation of Collision Probability for Secure Satellite Conjunction Analysis

The computation of collision probability ($\mathcal{P}_c$) is crucial for space environmentalism and sustainability by providing decision-making knowledge that can prevent collisions between anthropogenic space objects. However, the accuracy and precision of $\mathcal{P}_c$ computations is often compromised by limitations in computational resources and data availability. While significant improvements have been made in the computational aspects, the rising concerns regarding the privacy of collaborative data sharing can be a major limiting factor in the future conjunction analysis and risk assessment, especially as the space environment grows increasingly privatized, competitive, and fraught with conflicting strategic interests. This paper argues that the importance of privacy measures in space situational awareness (SSA) is underappreciated, and regulatory and compliance measures currently in place are not sufficient by themselves, presenting a significant gap. To address this gap, we introduce a novel encrypted architecture that leverages advanced cryptographic techniques, including homomorphic encryption (HE) and multi-party computation (MPC), to safeguard the privacy of entities computing space sustainability metrics, inter alia, $\mathcal{P}_c$. Our proposed protocol, Encrypted $\mathcal{P}_c$, integrates the Monte Carlo estimation algorithm with cryptographic solutions, enabling secure collision probability computation without exposing sensitive or proprietary information. This research advances secure conjunction analysis by developing a secure MPC protocol for $\mathcal{P}_c$ computation and highlights the need for innovative protocols to ensure a more secure and cooperative SSA landscape.

cs.CR↗

arXiv2024

Randomized Greedy Methods for Weak Submodular Sensor Selection with Robustness Considerations

We study a pair of budget- and performance-constrained weak-submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the standard greedy procedure which explores the entire feasible search space. We propose a pair of stochastic greedy algorithms, namely, Modified Randomized Greedy (MRG) and Dual Randomized Greedy (DRG) to approximately solve the budget- and performance-constrained problems, respectively. For both algorithms, we derive approximation guarantees that hold with high probability. We then examine the use of DRG in robust optimization problems wherein the objective is to maximize the worst-case of a number of weak submodular objectives and propose the Randomized Weak Submodular Saturation Algorithm (Random-WSSA). We further derive a high-probability guarantee for when Random-WSSA successfully constructs a robust solution. Finally, we showcase the effectiveness of these algorithms in a variety of relevant uses within the context of Earth-observing low Earth orbit satellite constellations which estimate atmospheric weather conditions and provide Earth coverage.

math.OC↗

arXiv2022

Safely: Safe Stochastic Motion Planning Under Constrained Sensing via Duality

Consider a robot operating in an uncertain environment with stochastic, dynamic obstacles. Despite the clear benefits for trajectory optimization, it is often hard to keep track of each obstacle at every time step due to sensing and hardware limitations. We introduce the Safely motion planner, a receding-horizon control framework, that simultaneously synthesizes both a trajectory for the robot to follow as well as a sensor selection strategy that prescribes trajectory-relevant obstacles to measure at each time step while respecting the sensing constraints of the robot. We perform the motion planning using sequential quadratic programming, and prescribe obstacles to sense based on the duality information associated with the convex subproblems. We guarantee safety by ensuring that the probability of the robot colliding with any of the obstacles is below a prescribed threshold at every time step of the planned robot trajectory. We demonstrate the efficacy of the Safely motion planner through software and hardware experiments.

eess.SY↗

arXiv2021

Comparing Run Time Assurance Approaches for Safe Spacecraft Docking

Run Time Assurance (RTA) systems are online safety verification techniques that filter the output of a primary controller to assure safety. RTA approaches are used in safety-critical control to intervene when a performance-driven primary controller would cause the system to violate safety constraints. This paper presents four categories of RTA approaches based on their membership to explicit or implicit monitoring and switching or optimization interventions. To validate the feasibility of each approach and compare computation time, four RTAs are defined for a three-dimensional spacecraft docking example with safety constraints on velocity.

eess.SY↗

arXiv2021

Simultaneous Perception-Action Design via Invariant Finite Belief Sets

Although perception is an increasingly dominant portion of the overall computational cost for autonomous systems, only a fraction of the information perceived is likely to be relevant to the current task. To alleviate these perception costs, we develop a novel simultaneous perception-action design framework wherein an agent senses only the task-relevant information. This formulation differs from that of a partially observable Markov decision process, since the agent is free to synthesize not only its policy for action selection but also its belief-dependent observation function. The method enables the agent to balance its perception costs with those incurred by operating in its environment. To obtain a computationally tractable solution, we approximate the value function using a novel method of invariant finite belief sets, wherein the agent acts exclusively on a finite subset of the continuous belief space. We solve the approximate problem through value iteration in which a linear program is solved individually for each belief state in the set, in each iteration. Finally, we prove that the value functions, under an assumption on their structure, converge to their continuous state-space values as the sample density increases.

cs.AI↗

arXiv2021

Entropy Maximization for Partially Observable Markov Decision Processes

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of an agent's trajectories to an outside observer while guaranteeing the completion of a task expressed by a reward function. We first prove that an agent with partial observations can achieve an entropy at most as well as an agent with perfect observations. Then, focusing on finite-state controllers (FSCs) with deterministic memory transitions, we show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of the parametric Markov chain (pMC) induced by such FSCs. This relationship allows us to recast the entropy maximization problem as a so-called parameter synthesis problem for the induced pMC. We then present an algorithm to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we illustrate the relationship between the maximum entropy, the number of memory states in the FSC, and the expected reward.

math.OC↗

arXiv2021

On Minimizing Total Discounted Cost in MDPs Subject to Reachability Constraints

We study the synthesis of a policy in a Markov decision process (MDP) following which an agent reaches a target state in the MDP while minimizing its total discounted cost. The problem combines a reachability criterion with a discounted cost criterion and naturally expresses the completion of a task with probabilistic guarantees and optimal transient performance. We first establish that an optimal policy for the considered formulation may not exist but that there always exists a near-optimal stationary policy. We additionally provide a necessary and sufficient condition for the existence of an optimal policy. We then restrict our attention to stationary deterministic policies and show that the decision problem associated with the synthesis of an optimal stationary deterministic policy is NP-complete. Finally, we provide an exact algorithm based on mixed-integer linear programming and propose an efficient approximation algorithm based on linear programming for the synthesis of an optimal stationary deterministic policy.

math.OC↗

arXiv2020

Point-Based Value Iteration and Approximately Optimal Dynamic Sensor Selection for Linear-Gaussian Processes

The problem of synthesizing an optimal sensor selection policy is pertinent to a variety of engineering applications ranging from event detection to autonomous navigation. We consider such a synthesis problem over an infinite time horizon with a discounted cost criterion. We formulate this problem in terms of a value iteration over the continuous space of covariance matrices. To obtain a computationally tractable solution, we subsequently formulate an approximate sensor selection problem, which is solvable through a point-based value iteration over a finite "mesh" of covariance matrices with a user-defined bounded trace. We provide theoretical guarantees bounding the suboptimality of the sensor selection policies synthesized through this method and provide numerical examples comparing them to known results.

eess.SY↗

arXiv2019

Minimizing the Information Leakage Regarding High-Level Task Specifications

We consider a scenario in which an autonomous agent carries out a mission in a stochastic environment while passively observed by an adversary. For the agent, minimizing the information leaked to the adversary regarding its high-level specification is critical in creating an informational advantage. We express the specification of the agent as a parametric linear temporal logic formula, measure the information leakage by the adversary's confidence in the agent's mission specification, and propose algorithms to synthesize a policy for the agent which minimizes the information leakage to the adversary. In the scenario considered, the adversary aims to infer the specification of the agent from a set of candidate specifications, each of which has an associated likelihood probability. The agent's objective is to synthesize a policy that maximizes the entropy of the adversary's likelihood distribution while satisfying its specification. We propose two approaches to solve the resulting synthesis problem. The first approach computes the exact satisfaction probabilities for each candidate specification, whereas the second approach utilizes the Fréchet inequalities to approximate them. For each approach, we formulate a mixed-integer program with a quasiconcave objective function. We solve the problem using a bisection algorithm. Finally, we compare the performance of both approaches on numerical simulations.

math.OC↗

arXiv2019

Unpredictable Planning Under Partial Observability

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of a decision-maker's trajectories while guaranteeing the completion of a task expressed by a reward function. First, we prove that a decision-maker with perfect observations can randomize its paths at least as well as a decision-maker with partial observations. Then, focusing on finite-state controllers, we recast the entropy maximization problem as a so-called parameter synthesis problem for a parametric Markov chain (pMC). We show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of this pMC. Finally, we present an algorithm, based on a nonlinear optimization problem, to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we demonstrate the proposed algorithm on motion planning scenarios.

math.OC↗