Heterogeneous Bayesian decentralized data fusion captures the set of problems in which two or more robots must combine probability density functions over non-equal, but overlapping sets of random variables. In the context of multi-robot dynamic systems, this enables robots to take a “divide and conquer” approach to reason and share data over complementary tasks instead of over the full joint state space. For example, in a target tracking application, this allows robots to track different subsets of targets and share data on only common targets. This paper presents a system by which robots can each use a local factor graph to represent relevant partitions of a complex global joint probability distribution, thus allowing them to avoid reasoning over the entirety of a more complex model and saving communication as well as computation costs. From a theoretical point of view, this paper makes contributions by casting the heterogeneous decentralized fusion problem in terms of factor graphs, analyzing the challenges that arise due to dynamic filtering, and then developing a new conservative filtering algorithm that ensures statistical correctness. From a practical point of view, we show how this system can be used to represent different multi-robot applications and then test it with simulations and hardware experiments to validate and demonstrate its statistical conservativeness, applicability, and robustness to real-world challenges.

Partially Observable Markov Decision Processes (POMDPs) provide a structured framework for decision-making under uncertainty, but their application requires efficient belief updates. Sequential Importance Resampling Particle Filters (SIRPF), also known as Bootstrap Particle Filters, are commonly used as belief updaters in large approximate POMDP solvers, but they face challenges such as particle deprivation and high computational costs as the system's state dimension grows. To address these issues, this study introduces Rao-Blackwellized POMDP (RB-POMDP) approximate solvers and outlines generic methods to apply Rao-Blackwellization in both belief updates and online planning. We compare the performance of SIRPF and Rao-Blackwellized Particle Filters (RBPF) in a simulated localization problem where an agent navigates toward a target in a GPS-denied environment using POMCPOW and RB-POMCPOW planners. Our results not only confirm that RBPFs maintain efficient belief approximations over time with fewer particles, but, more surprisingly, RBPFs combined with quadrature-based integration improve planning quality significantly compared to SIRPF-based planning under the same computational limits.

We consider the uncertain multi-robot motion planning (MRMP) problem with cooperative localization (CL-MRMP), under both motion and measurement noise, where each robot can act as a sensor for its nearby teammates. We formalize CL-MRMP as a chance-constrained motion planning problem, and propose a safety-guaranteed algorithm that explicitly accounts for robot-robot correlations. Our approach extends a sampling-based planner to solve CL-MRMP while preserving probabilistic completeness. To improve efficiency, we introduce novel biasing techniques. We evaluate our method across diverse benchmarks, demonstrating its effectiveness in generating motion plans, with significant performance gains from biasing strategies.

How can intelligent machines assess their competency to complete a task? This question has come into focus for autonomous systems that algorithmically make decisions under uncertainty. We argue that machine self-confidence—a form of meta-reasoning based on self-assessments of system knowledge about the state of the world, itself, and ability to reason about and execute tasks—leads to many computable and useful competency indicators for such agents. This article presents our body of work, so far, on this concept in the form of the Factorized Machine Self-Confidence (FaMSeC) framework, which holistically considers several major factors driving competency in algorithmic decision-making: outcome assessment, solver quality, model quality, alignment quality, and past experience. In FaMSeC, self-confidence indicators are derived via “problem-solving statistics” embedded in Markov Decision Process solvers and related approaches. These statistics come from evaluating probabilistic exceedance margins in relation to certain outcomes and associated competency standards specified by an evaluator. Once designed, and evaluated, the statistics can be easily incorporated into autonomous agents and serve as indicators of competency. We include detailed descriptions and examples for Markov Decision Process agents and show how outcome assessment and solver quality factors can be found for a range of tasking contexts through novel use of meta-utility functions, behavior simulations, and surrogate prediction models. Numerical evaluations are performed to demonstrate that FaMSeC indicators perform as desired (references to human subject studies beyond the scope of this article are provided).

When a robot autonomously performs a complex task, it frequently must balance competing objectives while maintaining safety. This becomes more difficult in uncertain environments with stochastic outcomes. Enhancing transparency in the robot's behavior and aligning with user preferences are also crucial. This paper introduces a novel framework for multi-objective reinforcement learning that ensures safe task execution, optimizes trade-offs between objectives, and adheres to user preferences. The framework has two main layers: a multi-objective task planner and a high-level selector. The planning layer generates a set of optimal trade-off plans that guarantee satisfaction of a temporal logic task. The selector uses active inference to decide which generated plan best complies with user preferences and aids learning. Operating iteratively, the framework updates a parameterized learning model based on collected data. Case studies and benchmarks on both manipulation and mobile robots show that our framework outperforms other methods and (i) learns multiple optimal trade-offs, (ii) adheres to a user preference, and (iii) allows the user to adjust the balance between (i) and (ii).

Autonomous selection of optimal options for data collection from multiple alternatives is challenging in uncertain environments. When secondary information about options is accessible, such problems can be framed as contextual multi-armed bandits (CMABs). Neuro-inspired active inference has gained interest for its ability to balance exploration and exploitation using the expected free energy objective function. Unlike previous studies that showed the effectiveness of active inference based strategy for CMABs using synthetic data, this study aims to apply active inference to realistic scenarios, using a simulated mineralogical survey site selection problem. Hyperspectral data from AVIRIS-NG at Cuprite, Nevada, serves as contextual information for predicting outcome probabilities, while geologists' mineral labels represent outcomes. Monte Carlo simulations assess the robustness of active inference against changing expert preferences. Results show active inference requires fewer iterations than standard bandit approaches with real-world noisy and biased data, and performs better when outcome preferences vary online by adapting the selection strategy to align with expert shifts.

In uncertain and dynamic environments, decentralized data fusion (DDF) techniques have been widely used to estimate the states and the uncertainty levels over large mission spaces in a robust and scalable way. In data fusion frameworks using distributed sensor networks, undetected sensor failures can degrade the quality of fusion results of the entire system. Therefore, DDF methods which are robust to inconsistent data are needed. In this paper, a fault-tolerant Bayesian DDF method using Gaussian mixture models is developed. The probability of agent reliability states, which represent consistency of local estimates that agents share with their neighbors, are modeled as weights of mixture models and estimated together with the target process. The target process and reliability states are updated in a decentralized Bayesian way, exploiting the properties of Gaussian mixture models. To prevent the hypothesis explosion problem of Gaussian mixture models, a mixture compression method considering the physical meaning of mixture weights is utilized. A numerical simulation on a 2D dynamic target tracking problem is presented to verify performance of the suggested algorithm and compared with existing DDF methods. It is shown that the suggested algorithm gives more compact fusion results compared to existing fault-tolerant DDF method.

Current methods of deploying robots that operate in dynamic, uncertain environments, such as Uncrewed Aerial Systems in search & rescue missions, require nearly continuous human supervision for vehicle guidance and operation. These methods do not consider high-level mission context resulting in cumbersome manual operation or inefficient exhaustive search patterns. We present a human-centered autonomous frame-work that infers geospatial mission context through dynamic feature sets, which then guides a probabilistic target search planner. Operators provide a set of diverse inputs, including priority definition, spatial semantic information about ad-hoc geographical areas, and reference waypoints, which are probabilistically fused with geographical database information and condensed into a geospatial distribution representing an operator’s preferences over an area. An online, POMDP-based planner, optimized for target searching, is augmented with this reward map to generate an operator-constrained policy. Our results, simulated based on input from five professional rescuers, display effective task mental model alignment, 18% more victim finds, and 15 times more efficient guidance plans then current operational methods.

Giving autonomous agents the ability to forecast their own outcomes and uncertainty will allow them to communicate their competencies and be used more safely. We accomplish this by using a learned world model of the agent system to forecast full agent trajectories over long time horizons. Real world systems involve significant sources of both aleatoric and epistemic uncertainty that compound and interact over time in the trajectory forecasts. We develop a deep generative world model that quantifies aleatoric uncertainty while incorporating the effects of epistemic uncertainty during the learning process. We show on two reinforcement learning problems that our uncertainty model produces calibrated outcome uncertainty estimates over the full trajectory horizon.

We consider the problem of motion and communication planning under uncertainty with limited information from a remote sensor network. Because the remote sensors are power and bandwidth limited, we use event-triggered (ET) estimation to manage communication costs. We introduce a fast and efficient sampling-based planner which computes motion plans coupled with ET communication strategies that minimize communication costs, while satisfying constraints on the probability of reaching the goal region and the point-wise probability of collision. We derive a novel method for offline propagation of the expected state distribution, and corresponding bounds on this distribution. These bounds are used to evaluate the chance constraints in the algorithm. Case studies establish the validity of our approach and demonstrate computational efficiency and asymptotic optimality of the planner.

In autonomous robotic decision-making under uncertainty, the tradeoff between exploitation and exploration of available options must be considered. If secondary information associated with options can be utilized, such decision-making problems can often be formulated as contextual multi-armed bandits (CMABs). In this study, we apply active inference, which has been actively studied in the field of neuroscience in recent years, as an alternative action selection strategy for CMABs. Unlike conventional action selection strategies, it is possible to rigorously evaluate the uncertainty of each option when calculating the expected free energy (EFE) associated with the decision agent's probabilistic model, as derived from the free-energy principle. We specifically address the case where a categorical observation likelihood function is used, such that EFE values are analytically intractable. We introduce new approximation methods for computing the EFE based on variational and Laplace approximations. Extensive simulation study results demonstrate that, compared to other strategies, active inference generally requires far fewer iterations to identify optimal options and generally achieves superior cumulative regret, for relatively low extra computational cost.

The factor graph decentralized data fusion (FG-DDF) framework was developed for the analysis and exploitation of conditional independence in heterogeneous Bayesian decentralized fusion problems, in which robots update and fuse pdfs over different, but overlapping subsets of random states. This allows robots to efficiently use smaller probabilistic models and sparse message passing to accurately and scalably fuse relevant local parts of a larger global joint state pdf while accounting for data dependencies between robots. Whereas prior work required limiting assumptions about network connectivity and model linearity, this paper relaxes these to explore the applicability and robustness of FG-DDF in more general settings. We develop a new heterogeneous fusion rule which generalizes the homogeneous covariance intersection algorithm for such cases and test it in multi-robot tracking and localization scenarios with non-linear motion/observation models under communication dropouts. Simulation and hardware experiments show that, in practice, the FG-DDF continues to provide consistent filtered estimates under these more practical operating conditions, while reducing computation and communication costs by more than 99%, thus enabling the design of scalable real-world multi-robot systems.

The ability of autonomous robots to model, communicate, and act on semantic “soft data” remains challenging. The human-assisted robotic planning and sensing (HARPS) framework is presented for active semantic sensing and planning in human–robot teams to address these gaps by formally combining the benefits of online sampling-based partially observable Markov decision process policies, multimodal human–robot interaction, and Bayesian data fusion. HARPS lets humans impose model structure and extend the range of soft data by sketching and labeling new semantic features in uncertain environments. Dynamic model updating lets robotic agents actively query humans for novel and relevant semantic data, thereby improving model and state beliefs for improved online planning. Simulations of a unmanned aerial vehicle-enabled target search in a large-scale partially structured environment show significant improvements in time and beliefs required for interception versus conventional planning with robot-only sensing. A human subject study in the same environment shows an average doubling in dynamic target capture rate compared to the lone robot case and highlights the robustness of HARPS over a range of user characteristics and interaction modalities.

In Bayesian peer-to-peer decentralized data fusion, the underlying distributions held locally by autonomous agents are frequently assumed to be over the same set of variables (homogeneous). This requires each agent to process and communicate the full global joint distribution, and thus, leads to high computation and communication costs irrespective of relevancy to specific local objectives. This work formulates and studies heterogeneous decentralized fusion problems, defined as the set of problems in which either the communicated or the processed distributions describe different, but overlapping, random states of interest that are subsets of a larger full global joint state. We exploit the conditional independence structure of such problems and provide a rigorous derivation of novel exact and approximate conditionally factorized heterogeneous fusion rules. We further develop a new version of the homogeneous channel filter algorithm to enable conservative heterogeneous fusion for smoothing and filtering scenarios in dynamic problems. Numerical examples show more than 99.5% potential communication reduction for heterogeneous channel filter fusion, and a multitarget tracking simulation shows that these methods provide consistent estimates while remaining computationally scalable.

Humans cannot always be treated as oracles for collaborative sensing. Robots, thus, need to maintain beliefs over unknown world states when receiving semantic data from humans, as well as account for possible discrepancies between the human-provided data and these beliefs. To this end, this article introduces the problem of semantic data association (SDA) in relation to conventional data association problems for sensor fusion. It then develops a novel probabilistic semantic data association (PSDA) algorithm to rigorously address SDA in general settings, unlike previous work on semantic data fusion, which developed heuristic techniques for specific settings. PSDA is further incorporated into a recursive hybrid Bayesian data fusion scheme that uses Gaussian mixture priors for object states and softmax functions for semantic human sensor data likelihoods. Simulations of a multiobject search task show that PSDA enables robust collaborative state estimation under a wide range of conditions where semantic human sensor data can be erroneous or contain significant reference ambiguities.

For autonomous agents to act as trustworthy partners to human users, they must be able to reliably communicate their competency for the tasks they are asked to perform. Towards this objective, we develop probabilistic world models based on deep generative modelling that allow for the simulation of agent trajectories and accurate calculation of tasking outcome probabilities. By combining the strengths of conditional variational autoencoders with recurrent neural networks, the deep generative world model can probabilistically forecast trajectories over long horizons to task completion. We show how these forecasted trajectories can be used to calculate outcome probability distributions, which enable the precise assessment of agent competency for specific tasks and initial settings.

Human-robot teams are expected to accomplish complex tasks in high-risk and uncertain environments. In domains such as space exploration or search & rescue, a human operator may not be a robotics expert, but will need to establish a baseline understanding of the robot's capabilities with respect to a given task in order to appropriately utilize and rely on the robot. This willingness to rely, also known as trust, is based partly on the operator's belief in the robot's task proficiency. If trust is too high, the operator may unknowingly push the robot beyond its capabilities. If trust is too low, the operator may not utilize it when they otherwise could have, wasting precious time and resources. In this work, we discuss results from an online human-subjects study investigating how a robot communicated report of its task proficiency with respect to an operator's expectations affects trust and performance in a navigation task. Our results show that communication of a robot self-assessment helped operators understand when reliance on the robot was appropriate given the task and conditions. This led to improvements in task performance, informed choices of autonomy level, and increased trust.

This paper presents a method for Bayesian multi-robot peer-to-peer data fusion where any pair of autonomous robots hold non-identical, but overlapping parts of a global joint probability distribution, representing real world inference tasks (e.g., mapping, tracking). It is shown that in dynamic stochastic systems, filtering, which corresponds to marginalization of past variables, results in direct and hidden dependencies between variables not mutually monitored by the robots, which might lead to an overconfident fused estimate. The paper makes both theoretical and practical contributions by providing (i) a rigorous analysis of the origin of the dependencies and (ii) a conservative filtering algorithm for heterogeneous data fusion in dynamic systems that can be integrated with existing fusion algorithms. This work uses factor graphs as both the analysis tool and the inference engine. Each robot in the network maintains a local factor graph and communicates only relevant parts of it (a sub-graph) to its neighboring robot. We discuss the applicability to various multi-robot robotic applications and demonstrate the performance using a multi-robot multi-target tracking simulation, showing that the proposed algorithm produces conservative estimates at each robot.

This paper presents a method for target localization and tracking in clutter using Bayesian fusion of vision and Radio Frequency (RF) sensors used aboard a small Unmanned Aircraft System (sUAS). Sensor fusion is used to ensure tracking robustness and reliability in case of camera occlusion or RF signal interference. Camera data is processed using an off-the-shelf algorithm that detects possible objects of interest in a given image frame, and the true RF emitting target needs to be identified from among these if it is present. These data sources, as well as the unknown motion of the target, lead to a heavily non-linear non-Gaussian target state uncertainties, which are not amenable to typical data association methods for tracking. A probabilistic model is thus first rigorously developed to relate conditional dependencies between target movements, RF data and visual object detections. A modified particle filter is then developed to simultaneously reason over target states and RF emitter association hypothesis labels for visual object detections. Truth model simulations are presented to compare and validate the effectiveness of the RF + visual data fusion filter.

When registering 3-D point clouds it is expected that some points in one cloud do not have corresponding points in the other cloud. These non-correspondences are likely to occur near one another, as surface regions visible from one sensor pose are obscured or out of frame for another. In this work, a hidden Markov random field model is used to capture this prior within the framework of the iterative closest point algorithm. The EM algorithm is used to estimate the distribution parameters and learn the hidden component memberships. Experiments are presented demonstrating that this method outperforms several other outlier rejection methods when the point clouds have low or moderate overlap.

In search applications, autonomous unmanned vehicles must be able to efficiently reacquire and localize mobile targets that can remain out of view for long periods of time in large spaces. As such, all available information sources must be actively leveraged - including imprecise but readily available semantic observations provided by humans. To achieve this, this work develops and validates a novel collaborative human-machine sensing solution for dynamic target search. Our approach uses continuous partially observable Markov decision process (CPOMDP) planning to generate vehicle trajectories that optimally exploit imperfect detection data from onboard sensors, as well as semantic natural language observations that can be specifically requested from human sensors. The key innovation is a scalable hierarchical Gaussian mixture model formulation for efficiently solving CPOMDPs with semantic observations in continuous dynamic state spaces. The approach is demonstrated and validated with a real human-robot team engaged in dynamic indoor target search and capture scenarios on a custom testbed.

Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman filter model parameters, e.g. process noise covariance, pre-whitening filter models for non-white noise, etc. Conventional optimization techniques for tuning can get stuck in poor local minima and can be expensive to implement with real sensor data. To address these issues, a new “black box” Bayesian optimization strategy is developed for automatically tuning Kalman filters. In this approach, performance is characterized by one of two stochastic objective functions: normalized estimation error squared (NEES) when ground truth state models are available, or the normalized innovation error squared (NIS) when only sensor data is available. By intelligently sampling the parameter space to both learn and exploit a nonparametric Gaussian process surrogate function for the NEESINIS costs, Bayesian optimization can efficiently identify multiple local minima and provide uncertainty quantification on its results.

This note considers softmax parameter estimation when little/no labeled training data is available, but a priori information about the relative geometry of class label log-odds boundaries is available. It is shown that “data-free” softmax model synthesis corresponds to solving a linear system of parameter equations, wherein desired dominant class log-odds boundaries are encoded via convex polytopes that decompose the input feature space. When solvable, the linear equations yield closed-form softmax parameter solution families using class boundary polytope specifications only. This allows softmax parameter learning to be implemented without expensive brute force data sampling and numerical optimization. The linear equations can also be adapted to constrained maximum likelihood estimation in data-sparse settings. Since solutions may also fail to exist for the linear parameter equations derived from certain polytope specifications, it is thus also shown that there exist probabilistic classification problems over m convexly separable classes for which the log-odds boundaries cannot be learned using an m-class softmax model.

This paper examines the problem of distributed path planning for a mobile sensor network comprised of communication-aware robots performing general information gathering missions. Mutual information is derived for distributed sensing over packet erasure channels that model multi-hop communication. We model distributed path planning as a non-cooperative game and derive utility functions that are optimized locally by each robot. Each robot computes the control input in a distributed manner that results in a combined action that can be bounded by the optimal centralized result by utilizing sub-modularity in certain cases. It is shown that when the communication model includes multi-hop communication to expand the coverage of the sensor network, the property of sub-modularity is lost. We further show that the additional global knowledge required for the local computation of utility functions can be learned by simple consensus approaches. Finally, we discuss a sampling approach to approximate the proposed utility functions in order to reduce the associated computational requirements.

A terrain mapping model is proposed using a generalized Markov random field (MRF) representation. Unlike previous work, the proposed MRF can fully represent uncertainties due to sensor pose and measurement errors, as well as data association errors in a single model. Additionally, neither homoscedasticity nor a predefined shape of the likelihood distribution is assumed. The flexibility of an MRF model allows spatial height correlations to be incorporated. The ability to include spatial correlations not only improves the accuracy through the benefits of Bayesian prior modeling, but also serves as a basis for terrain property characterization. Maximum likelihood solutions of terrain roughness are derived. Benefits of the proposed model are demonstrated experimentally on indoor and outdoor datasets. Results show that the MRF model leads to lower height estimation errors. In addition, the capability of estimating non-Gaussian height distributions allows the information about individual terrain features to be preserved. Finally, the model is able to accurately estimate the roughness of the terrain, which is beneficial for edge detection of obstacles and nontraversible terrain regions.

This paper considers Bayesian data fusion of conventional robot sensor information with ambiguous human-generated categorical information about continuous world states of interest. First, it is shown that such soft information can be generally modeled via hybrid continuous-to-discrete likelihoods that are based on the softmax function. A new hybrid fusion procedure, called variational Bayesian importance sampling (VBIS), is then introduced to combine the strengths of variational Bayes approximations and fast Monte Carlo methods to produce reliable posterior estimates for Gaussian priors and softmax likelihoods. VBIS is then extended to more general fusion problems that involve complex Gaussian mixture (GM) priors and multimodal softmax likelihoods, leading to accurate GM approximations of highly non-Gaussian fusion posteriors for a wide range of robot sensor data and soft human data. Experiments for hardware-based multitarget search missions with a cooperative human-autonomous robot team show that humans can serve as highly informative sensors through proper data modeling and fusion, and that VBIS provides reliable and scalable Bayesian fusion estimates via GMs.

A new method is presented for fusing conventional continuous sensor observations with discrete multi-categorical state-dependent information, which can be furnished by humans in many cooperative human-robot interaction problems. The hybrid likelihood function for mapping between continuous hidden states and categorical observations are specified via softmax models. Although softmax models avoid discretization of continuous states, they are challenging to implement for real-time data fusion since they are not analytically integrable. An approximation based on variational Bayesian (VB) methods is presented here to obtain fast closed-form Gaussian solutions to the desired posteriors in cases where the hidden continuous states have Gaussian pdfs. A joint human-robot target localization example illustrates the properties and utility of the VB hybrid fusion strategy, which also applies more generally to inference in hybrid Bayesian networks and mixture models.