Ian Abraham

We present the stochastic decoupled policy gradient (SDPG), a lightweight visual reinforcement learning (RL) method that trains diverse visuomotor control policies end-to-end within a few hours on a single NVIDIA RTX 4080 GPU. SDPG estimates policy gradients via random perturbations of trajectory rollouts, requiring orders of magnitude fewer batch-rendered environments and substantially reducing compute and memory overhead. On visual MuJoCo benchmarks, SDPG consistently outperforms baseline methods in training time, memory usage, and rewards. Finally, to support future research, we introduce a suite of realistic visual robotics benchmarks spanning dexterous manipulation, challenging locomotion, and demonstrate effective sim-to-real transfer on physical hardware.

We present the stochastic decoupled policy gradient (SDPG), a lightweight visual reinforcement learning (RL) method that trains diverse visuomotor control policies end-to-end within a few hours on a single NVIDIA RTX 4080 GPU. SDPG estimates policy gradients via random perturbations of trajectory rollouts, requiring orders of magnitude fewer batch-rendered environments and substantially reducing compute and memory overhead. On visual MuJoCo benchmarks, SDPG consistently outperforms baseline methods in training time, memory usage, and rewards. Finally, to support future research, we introduce a suite of realistic visual robotics benchmarks spanning dexterous manipulation, challenging locomotion, and demonstrate effective sim-to-real transfer on physical hardware.

Reliable robotic manipulation requires control policies that can accurately represent and adapt to uncertainty arising from contact-rich interactions. Modern data-driven methods mitigate uncertainty through large-scale training and computation, and degrade significantly in performance with limited number of training samples. By contrast, classical model-based controllers are computationally efficient and reliable, but their limited ability to represent task-relevant uncertainty can hinder performance in contact-rich interactions. In this work, we propose to expand the capabilities of model-based manipulation control through more flexible uncertainty modeling that retains performance while exactly adapting to uncertainty. Our approach casts the manipulation problem as a distributionally robust control optimization and proposes a novel deterministic formulation based on Stein variational inference that preserves performance while explicitly modeling task-sensitive parameter uncertainty. As a result, the derived controllers are more aware of task sensitivities to uncertainty, yielding high reliability without compromising performance. Experimental results demonstrate up to 3$\times$ improved robustness across a range of contact-rich manipulation tasks under broad parametric uncertainty, outperforming existing model-based control methods.

Reliable robotic manipulation requires control policies that can accurately represent and adapt to uncertainty arising from contact-rich interactions. Modern data-driven methods mitigate uncertainty through large-scale training and computation, and degrade significantly in performance with limited number of training samples. By contrast, classical model-based controllers are computationally efficient and reliable, but their limited ability to represent task-relevant uncertainty can hinder performance in contact-rich interactions. In this work, we propose to expand the capabilities of model-based manipulation control through more flexible uncertainty modeling that retains performance while exactly adapting to uncertainty. Our approach casts the manipulation problem as a distributionally robust control optimization and proposes a novel deterministic formulation based on Stein variational inference that preserves performance while explicitly modeling task-sensitive parameter uncertainty. As a result, the derived controllers are more aware of task sensitivities to uncertainty, yielding high reliability without compromising performance. Experimental results demonstrate up to 3$\times$ improved robustness across a range of contact-rich manipulation tasks under broad parametric uncertainty, outperforming existing model-based control methods.

Autonomous robotic exploration in remote and extreme environments allows scientists to model complex transport phenomena and collective behaviors described by continuously deforming flow fields. Although these environments are naturally modeled as time-varying domains, most adaptive exploration methods assume static environments and fail to provide adequate coverage or satisfy any formal guarantees. This is especially the case in oceanography where autonomous underwater systems (UxS) have highly restrictive compute and payload requirements that necessitate path planning methods that yield robust data collection strategies in open-loop and underactuated settings. In this work, to address the aforementioned issues, we propose to formulate adaptive search as an ergodic coverage problem and investigate certifying coverage in the ergodic sense over evolving domains with flow-induced dynamics. We expand upon recent work demonstrating maximum mean discrepancy (MMD) as a functional ergodic metric, and derive a flow-adaptive formulation that explicitly accounts for domain evolution within the coverage objective. We show that this approach preserves ergodic coverage guarantees in ambient flows and enables effective exploration in under-actuated, and even open-loop planning settings by integrating environment dynamics. Experiments validate that our method generalizes to diverse spatiotemporal processes including ocean exploration, and tracking human and cattle movement. Physical experiments on aerial and legged robotic platforms validate our ability to obtain ergodic coverage in non-convex, flow-restricted environments while respecting robot dynamics.

Autonomous robotic exploration in remote and extreme environments allows scientists to model complex transport phenomena and collective behaviors described by continuously deforming flow fields. Although these environments are naturally modeled as time-varying domains, most adaptive exploration methods assume static environments and fail to provide adequate coverage or satisfy any formal guarantees. This is especially the case in oceanography where autonomous underwater systems (UxS) have highly restrictive compute and payload requirements that necessitate path planning methods that yield robust data collection strategies in open-loop and underactuated settings. In this work, to address the aforementioned issues, we propose to formulate adaptive search as an ergodic coverage problem and investigate certifying coverage in the ergodic sense over evolving domains with flow-induced dynamics. We expand upon recent work demonstrating maximum mean discrepancy (MMD) as a functional ergodic metric, and derive a flow-adaptive formulation that explicitly accounts for domain evolution within the coverage objective. We show that this approach preserves ergodic coverage guarantees in ambient flows and enables effective exploration in under-actuated, and even open-loop planning settings by integrating environment dynamics. Experiments validate that our method generalizes to diverse spatiotemporal processes including ocean exploration, and tracking human and cattle movement. Physical experiments on aerial and legged robotic platforms validate our ability to obtain ergodic coverage in non-convex, flow-restricted environments while respecting robot dynamics.

This paper derives an infinite-horizon ergodic controller based on kernel mean embeddings for long-duration coverage tasks on general domains. While existing kernel-based ergodic control methods provide strong coverage guarantees on general coverage domains, their practical use has been limited to sub-ergodic, finite-time horizons due to intractable computational scaling, prohibiting its use for long-duration coverage. We resolve this scaling by deriving an infinite-horizon ergodic controller equipped with an extended kernel mean embedding error visitation state that recursively records state visitation. This extended state decouples past visitation from future control synthesis and expands ergodic control to infinite-time settings. In addition, we present a variation of the controller that operates on a receding-horizon control formulation with the extended error state. We demonstrate theoretical proof of asymptotic convergence of the derived controller and show preservation of ergodic coverage guarantees for a class of 2D and 3D coverage problems.

We propose a Stein variational distributionally robust controller for nonlinear dynamical systems with latent parametric uncertainty. The method is an alternative to conservative worst-case ambiguity-set optimization with a deterministic particle-based approximation of a task-dependent uncertainty distribution, enabling the controller to concentrate on parameter sensitivities that most strongly affect closed-loop performance. Our method yields a controller that is robust to latent parameter uncertainty by coupling optimal control with Stein variational inference, and avoiding restrictive parametric assumptions on the uncertainty model while preserving computational parallelism. In contrast to classical DRO, which can sacrifice nominal performance through worst-case design, we find our approach achieves robustness by shaping the control law around relevant uncertainty that are most critical to the task objective. The proposed framework therefore reconciles robust control and variational inference in a single decision-theoretic formulation for broad classes of control systems with parameter uncertainty. We demonstrate our approach on representative control problems that empirically illustrate improved performance-robustness tradeoffs over nominal, ensemble, and classical distributionally robust baselines.

We propose a Stein variational distributionally robust controller for nonlinear dynamical systems with latent parametric uncertainty. The method is an alternative to conservative worst-case ambiguity-set optimization with a deterministic particle-based approximation of a task-dependent uncertainty distribution, enabling the controller to concentrate on parameter sensitivities that most strongly affect closed-loop performance. Our method yields a controller that is robust to latent parameter uncertainty by coupling optimal control with Stein variational inference, and avoiding restrictive parametric assumptions on the uncertainty model while preserving computational parallelism. In contrast to classical DRO, which can sacrifice nominal performance through worst-case design, we find our approach achieves robustness by shaping the control law around relevant uncertainty that are most critical to the task objective. The proposed framework therefore reconciles robust control and variational inference in a single decision-theoretic formulation for broad classes of control systems with parameter uncertainty. We demonstrate our approach on representative control problems that empirically illustrate improved performance-robustness tradeoffs over nominal, ensemble, and classical distributionally robust baselines.

This paper derives an infinite-horizon ergodic controller based on kernel mean embeddings for long-duration coverage tasks on general domains. While existing kernel-based ergodic control methods provide strong coverage guarantees on general coverage domains, their practical use has been limited to sub-ergodic, finite-time horizons due to intractable computational scaling, prohibiting its use for long-duration coverage. We resolve this scaling by deriving an infinite-horizon ergodic controller equipped with an extended kernel mean embedding error visitation state that recursively records state visitation. This extended state decouples past visitation from future control synthesis and expands ergodic control to infinite-time settings. In addition, we present a variation of the controller that operates on a receding-horizon control formulation with the extended error state. We demonstrate theoretical proof of asymptotic convergence of the derived controller and show preservation of ergodic coverage guarantees for a class of 2D and 3D coverage problems.

Koopman operator theory offers a rigorous treatment of dynamics, emerging as a robust alternative for learning-based control in robotics. By representing nonlinear dynamics as a linear, higher-dimensional operator, it provides a fresh lens for modeling complex systems. Its ability to support incremental updates and low computational cost makes it particularly appealing for real-time applications and online learning. This review delves deeply into the foundations, systematically bridging theoretical principles to practical robotic applications. We explain mathematical underpinnings, approximation approaches for inputs, data collection strategies, and lifting function design. We explore how Koopman models unify tasks like model-based control, state estimation, and motion planning. The review surveys cutting-edge research across domains ranging from aerial and legged platforms to manipulators, soft robots, and multi-agent networks. We also present advanced theoretical topics and reflect on open challenges and future research directions. To support adoption, we provide a hands-on tutorial with code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/sunnyshi0310/KoopmanRobo/tree/main</uri>.

Recent methods in ergodic coverage planning have shown promise as tools that can adapt to a wide range of geometric coverage problems with general constraints, but are highly sensitive to the numerical scaling of the problem space. The underlying challenge is that the optimization formulation becomes brittle and numerically unstable with changing scales, especially under potentially nonlinear constraints that impose dynamic restrictions, due to the kernel-based formulation. This paper proposes to address this problem via the development of a scale-agnostic and adaptive ergodic coverage optimization method based on the maximum mean discrepancy metric (MMD). Our approach allows the optimizer to solve for the scale of differential constraints while annealing the hyperparameters to best suit the problem domain and ensure physical consistency. We also derive a variation of the ergodic metric in the log space, providing additional numerical conditioning without loss of performance. We compare our approach with existing coverage planning methods and demonstrate the utility of our approach on a wide range of coverage problems.

This work addresses the problem of robot manipulation tasks under unknown dynamics, such as pick-and-place tasks under payload uncertainty, where active exploration and(/for) online parameter adaptation during task execution are essential to enable accurate model-based control. The problem is framed as dual control seeking a closed-loop optimal control problem that accounts for parameter uncertainty. We simplify the dual control problem by pre-defining the structure of the feedback policy to include an explicit adaptation mechanism. Then we propose two methods for reference trajectory generation. The first directly embeds parameter uncertainty in robust optimal control methods that minimize the expected task cost. The second method considers minimizing the so-called optimality loss, which measures the sensitivity of parameter-relevant information with respect to task performance. We observe that both approaches reason over the Fisher information as a natural side effect of their formulations, simultaneously pursuing optimal task execution. We demonstrate the effectiveness of our approaches for a pick-and-place manipulation task. We show that designing the reference trajectories whilst taking into account the control enables faster and more accurate task performance and system identification while ensuring stable and efficient control.

This paper investigates a sample-based solution to the hybrid mode control problem across non-differentiable and algorithmic hybrid modes. Our approach reasons about a set of hybrid control modes as an integer-based optimization problem where we select what mode to apply, when to switch to another mode, and the duration for which we are in a given control mode. A sample-based variation is derived to efficiently search the integer domain for optimal solutions. We find our formulation yields strong performance guarantees that can be applied to a number of robotics-related tasks. In addition, our approach is able to synthesize complex algorithms and policies to compound behaviors and achieve challenging tasks. Last, we demonstrate the effectiveness of our approach in real-world robotic examples that require reactive switching between long-term planning and high-frequency control.

In this paper, we investigate the utility of datasets and whether more data or the 'right' data is advantageous for robot learning. In particular, we are interested on quantifying the utility of contact-based data as contact holds significant information for robot learning. Our approach derives a contact-aware objective function for learning object dynamics and shape from pose and contact data. We show that the contact-aware Fisher-information metric can be used to rank and curate contact-data based on how informative data is for learning. In addition, we find that selecting a reduced dataset based on this ranking improves the learning task while also making learning a deterministic process. Interestingly, our results show that more data is not necessarily advantageous, and rather, less but informative data can accelerate learning, especially depending on the contact interactions. Last, we show how our metric can be used to provide initial guidance on data curation for contact-based robot learning.

Depth perception models have shown to be effective in several robotic vision systems such as depth completion and 3D reconstruction. However, these models have been extensively trained using non-interactive, video-based datasets with predetermined camera trajectories, which do not necessarily provide task-specific data samples to achieve competent learning. One of the key questions for downstream task-aware data acquisition is: what motion planning strategy to use? In this work, we investigate how to achieve 3D image reprojection-driven autonomous path planning to further improve supervised and unsupervised depth completion model learning. Specifically, we (i) derive a method for robot navigation based on photometric reconstruction errors, as a proxy for visiting high depth uncertainty locations, and (ii) introduce a framework for integrating motion planning systems with depth completion models, along with a new benchmark. We evaluated 4 depth models, trained on data collected by our approach and by 8 existing navigation algorithms. Experiments spanning 861 training and 118 testing environments, derived from scanning a diverse set of residential, commercial, and civic spaces from the real-world, show that our approach outperforms conventional techniques on all 4 models by an average greater than 18%.

Robotic search and rescue, exploration, and inspection require trajectory planning across a variety of domains. A popular approach to trajectory planning for these types of missions is ergodic search, which biases a trajectory to spend time in parts of the exploration domain that are believed to contain more information. Most prior work on ergodic search has been limited to searching simple surfaces, like a 2D Euclidean plane or a sphere, as they rely on projecting functions defined on the exploration domain onto analytically obtained Fourier basis functions. In this paper, we extend ergodic search to any surface that can be approximated by a triangle mesh. The basis functions are approximated through finite element methods on a triangle mesh of the domain. We formally prove that this approximation converges to the continuous case as the mesh approximation converges to the true domain. We demonstrate that on domains where analytical basis functions are available (plane, sphere), the proposed method obtains equivalent results, and while on other domains (torus, bunny, wind turbine), the approach is versatile enough to still search effectively. Lastly, we also compare with an existing ergodic search technique that can handle complex domains and show that our method results in a higher quality exploration.

We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for problems related to robotic inspection, information gathering problems, and search and rescue. These optimization schemes compel the robot to spend time in a region proportional to the expected utility of visiting that region. Current methods for ergodic trajectory optimization rely on domain-specific knowledge, e.g., a defined utility map, and well-defined spatial basis functions to produce ergodic trajectories. Here, we present a generalization of ergodic trajectory optimization based on maximum mean discrepancy that requires only samples from the search domain. We demonstrate the ability of our approach to produce coverage trajectories on a variety of problem domains including robotic inspection of objects with differential kinematics constraints and on Lie groups without having access to domain specific knowledge. Furthermore, we show favorable computational scaling compared to existing state-of-the-art methods for ergodic trajectory optimization with a trade-off between domain specific knowledge and computational scaling, thus extending the versatility of ergodic coverage on a wider application domain.

In this work, we consider the problem of multiagent informative path planning (IPP) for robots whose sensor visibility continuously changes as a consequence of a time-varying natural phenomenon. We leverage ergodic trajectory optimization (ETO), which generates paths such that the amount of time an agent spends in an area is proportional to the expected information in that area. We focus specifically on the problem of multi-agent drone search of a wildfire, where we use the time-varying environmental process of smoke diffusion to construct a sensor visibility model. This sensor visibility model is used to repeatedly calculate an expected information distribution (EID) to be used in the ETO algorithm. Our experiments show that our exploration method achieves improved information gathering over both baseline search methods and naive ergodic search formulations.

Contact dynamics hold immense amounts of information that can improve a robot's ability to characterize and learn about objects in their environment through interactions. However, collecting information-rich contact data is challenging due to its inherent sparsity and non-smooth nature, requiring an active approach to maximize the utility of contacts for learning. In this work, we investigate an optimal experimental design approach to synthesize robot behaviors that produce contact-rich data for learning. Our approach derives a contact-aware Fisher information measure that characterizes information-rich contact behaviors that improve parameter learning. We observe emergent robot behaviors that are able to excite contact interactions that efficiently learns object parameters across a range of parameter learning examples. Last, we demonstrate the utility of contact-awareness for learning parameters through contact-seeking behaviors on several robotic experiments.

In this work, we propose a computationally efficient algorithm for visual policy learning that leverages differentiable simulation and first-order analytical policy gradients. Our approach decouple the rendering process from the computation graph, enabling seamless integration with existing differentiable simulation ecosystems without the need for specialized differentiable rendering software. This decoupling not only reduces computational and memory overhead but also effectively attenuates the policy gradient norm, leading to more stable and smoother optimization. We evaluate our method on standard visual control benchmarks using modern GPU-accelerated simulation. Experiments show that our approach significantly reduces wall-clock training time and consistently outperforms all baseline methods in terms of final returns. Notably, on complex tasks such as humanoid locomotion, our method achieves a $4\times$ improvement in final return, and successfully learns a humanoid running policy within 4 hours on a single GPU.

Robotic search and rescue, exploration, and inspection require trajectory planning across a variety of domains. A popular approach to trajectory planning for these types of missions is ergodic search, which biases a trajectory to spend time in parts of the exploration domain that are believed to contain more information. Most prior work on ergodic search has been limited to searching simple surfaces, like a 2D Euclidean plane or a sphere, as they rely on projecting functions defined on the exploration domain onto analytically obtained Fourier basis functions. In this paper, we extend ergodic search to any surface that can be approximated by a triangle mesh. The basis functions are approximated through finite element methods on a triangle mesh of the domain. We formally prove that this approximation converges to the continuous case as the mesh approximation converges to the true domain. We demonstrate that on domains where analytical basis functions are available (plane, sphere), the proposed method obtains equivalent results, and while on other domains (torus, bunny, wind turbine), the approach is versatile enough to still search effectively. Lastly, we also compare with an existing ergodic search technique that can handle complex domains and show that our method results in a higher quality exploration.

The Bellman equation and its continuous-time counterpart, the Hamilton-Jacobi-Bellman (HJB) equation, serve as necessary conditions for optimality in reinforcement learning and optimal control. While the value function is known to be the unique solution to the Bellman equation in tabular settings, we demonstrate that this uniqueness fails to hold in continuous state spaces. Specifically, for linear dynamical systems, we prove the Bellman equation admits at least $\binom{2n}{n}$ solutions, where $n$ is the state dimension. Crucially, only one of these solutions yields both an optimal policy and a stable closed-loop system. We then demonstrate a common failure mode in value-based methods: convergence to unstable solutions due to the exponential imbalance between admissible and inadmissible solutions. Finally, we introduce a positive-definite neural architecture that guarantees convergence to the stable solution by construction to address this issue.

In this paper, we explore an approach to actively plan and excite contact modes in differentiable simulators as a means to tighten the sim-to-real gap. We propose an optimal experimental design approach derived from information-theoretic methods to identify and search for information-rich contact modes through the use of contact-implicit optimization. We demonstrate our approach on a robot parameter estimation problem with unknown inertial and kinematic parameters which actively seeks contacts with a nearby surface. We show that our approach improves the identification of unknown parameter estimates over experimental runs by an estimate error reduction of at least $\sim 84\%$ when compared to a random sampling baseline, with significantly higher information gains.

We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for problems related to robotic inspection, information gathering problems, and search and rescue. These optimization schemes compel the robot to spend time in a region proportional to the expected utility of visiting that region. Current methods for ergodic trajectory optimization rely on domain-specific knowledge, e.g., a defined utility map, and well-defined spatial basis functions to produce ergodic trajectories. Here, we present a generalization of ergodic trajectory optimization based on maximum mean discrepancy that requires only samples from the search domain. We demonstrate the ability of our approach to produce coverage trajectories on a variety of problem domains including robotic inspection of objects with differential kinematics constraints and on Lie groups without having access to domain specific knowledge. Furthermore, we show favorable computational scaling compared to existing state-of-the-art methods for ergodic trajectory optimization with a trade-off between domain specific knowledge and computational scaling, thus extending the versatility of ergodic coverage on a wider application domain.

Search and exploration capabilities are essential for robots to inspect hazardous areas, support scientific expeditions in extreme environments, and potentially save human lives in natural disasters. The variability of scale in these problems requires robots to reason about time alongside their dynamics and sensor capabilities to effectively assess and explore for information. Recent advances in ergodic search methods have shown promise in supporting trajectory planning for exploration in continuous, multiscale environments with dynamics consideration. However, these methods are still limited by their inability to effectively reason about and adapt the time to explore in response to their environment. This ability is crucial for adapting exploration to variable-resolution information-gathering tasks. To address this limitation, this paper poses the time-optimal ergodic search problem and investigates solutions for fast, multiscale, and adaptive robotic exploration trajectories. The problem is formulated as a minimum-time problem with an ergodic inequality constraint whose upper bound specifies the amount of coverage needed. We show the existence of optimal solutions using Pontryagin’s conditions of optimality, and we demonstrate effective, minimum-time coverage numerically through a direct transcription optimization approach. The efficacy of the approach in generating time-optimal search trajectories is demonstrated in simulation under several nonlinear dynamic constraints, and in a physical experiment using a drone in a cluttered environment. We find that constraints such as obstacle avoidance are readily integrated into our formulation, and we show through an ablation study the flexibility of search capabilities at various scales. Last, we contribute a receding-horizon formulation of time-optimal ergodic search for sensor-driven information-gathering and demonstrate improved adaptive sampling capabilities in localization tasks.

Autonomous robotic search has important applications in robotics, such as the search for signs of life after a disaster. When \emph{a priori} information is available, for example in the form of a distribution, a planner can use that distribution to guide the search. Ergodic search is one method that uses the information distribution to generate a trajectory that minimizes the ergodic metric, in that it encourages the robot to spend more time in regions with high information and proportionally less time in the remaining regions. Unfortunately, prior works in ergodic search do not perform well in complex environments with obstacles such as a building's interior or a maze. To address this, our work presents a modified ergodic metric using the Laplace-Beltrami eigenfunctions to capture map geometry and obstacle locations within the ergodic metric. Further, we introduce an approach to generate trajectories that minimize the ergodic metric while guaranteeing obstacle avoidance using measure-preserving vector fields. Finally, we leverage the divergence-free nature of these vector fields to generate collision-free trajectories for multiple agents. We demonstrate our approach via simulations with single and multi-agent systems on maps representing interior hallways and long corridors with non-uniform information distribution. In particular, we illustrate the generation of feasible trajectories in complex environments where prior methods fail.

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a linear (but higher-dimensional) operator, Koopman theory offers a fresh lens through which to understand and tackle the modeling and control of complex robotic systems. Moreover, it enables incremental updates and is computationally inexpensive, thus making it particularly appealing for real-time applications and online active learning. This review delves deeply into the foundations of Koopman operator theory and systematically builds a bridge from theoretical principles to practical robotic applications. We begin by explaining the mathematical underpinnings of the Koopman framework and discussing approximation approaches for incorporating inputs into Koopman-based modeling. Foundational considerations, such as data collection strategies as well as the design of lifting functions for effective system embedding, are also discussed. We then explore how Koopman-based models serve as a unifying tool for a range of robotics tasks, including model-based control, real-time state estimation, and motion planning. The review proceeds to a survey of cutting-edge research that demonstrates the versatility and growing impact of Koopman methods across diverse robotics sub-domains: from aerial and legged platforms to manipulators, soft-bodied systems, and multi-agent networks. A presentation of more advanced theoretical topics, necessary to push forward the overall framework, is included. Finally, we reflect on some key open challenges that remain and articulate future research directions that will shape the next phase of Koopman-inspired robotics. To support practical adoption, we provide a hands-on tutorial with executable code at https://shorturl.at/ouE59.

Exploration requires that robots reason about numerous ways to cover a space in response to dynamically changing conditions.However, in continuous domains there are potentially infinitely many options for robots to explore which can prove computationally challenging.How then should a robot efficiently optimize and choose exploration strategies to adopt?In this work, we explore this question through the use of variational inference to efficiently solve for distributions of coverage trajectories.Our approach leverages ergodic search methods to optimize coverage trajectories in continuous time and space.In order to reason about distributions of trajectories, we formulate ergodic search as a probabilistic inference problem.We propose to leverage Stein variational methods to approximate a posterior distribution over ergodic trajectories through parallel computation.As a result, it becomes possible to efficiently optimize distributions of feasible coverage trajectories for which robots can adapt exploration.We demonstrate that the proposed Stein variational ergodic search approach facilitates efficient identification of multiple coverage strategies and show online adaptation in a model-predictive control formulation.Simulated and physical experiments demonstrate adaptability and diversity in exploration strategies online.

Exploration requires that robots reason about numerous ways to cover a space in response to dynamically changing conditions. However, in continuous domains there are potentially infinitely many options for robots to explore which can prove computationally challenging. How then should a robot efficiently optimize and choose exploration strategies to adopt? In this work, we explore this question through the use of variational inference to efficiently solve for distributions of coverage trajectories. Our approach leverages ergodic search methods to optimize coverage trajectories in continuous time and space. In order to reason about distributions of trajectories, we formulate ergodic search as a probabilistic inference problem. We propose to leverage Stein variational methods to approximate a posterior distribution over ergodic trajectories through parallel computation. As a result, it becomes possible to efficiently optimize distributions of feasible coverage trajectories for which robots can adapt exploration. We demonstrate that the proposed Stein variational ergodic search approach facilitates efficient identification of multiple coverage strategies and show online adaptation in a model-predictive control formulation. Simulated and physical experiments demonstrate adaptability and diversity in exploration strategies online.

Continuous exploration without interruption is important in scenarios such as search and rescue and precision agriculture, where consistent presence is needed to detect events over large areas. Ergodic search already derives continuous trajectories in these scenarios so that a robot spends more time in areas with high information density. However, existing literature on ergodic search does not consider the robot's energy constraints, limiting how long a robot can explore. In fact, if the robots are battery-powered, it is physically not possible to continuously explore on a single battery charge. Our paper tackles this challenge, integrating ergodic search methods with energy-aware coverage. We trade off battery usage and coverage quality, maintaining uninterrupted exploration by at least one agent. Our approach derives an abstract battery model for future state-of-charge estimation and extends canonical ergodic search to ergodic search under battery constraints. Empirical data from simulations and real-world experiments demonstrate the effectiveness of our energy-aware ergodic search, which ensures continuous exploration and guarantees spatial coverage.

This systems paper presents the implementation and design of RB5, a wheeled robot for autonomous long-term exploration with fewer and cheaper sensors. Requiring just an RGB-D camera and low-power computing hardware, the system consists of an experimental platform with rocker-bogie suspension. It operates in unknown and GPS-denied environments and on indoor and outdoor terrains. The exploration consists of a methodology that extends frontier- and sampling-based exploration with a path-following vector field and a state-of-the-art SLAM algorithm. The methodology allows the robot to explore its surroundings at lower update frequencies, enabling the use of lower-performing and lower-cost hardware while still retaining good autonomous performance. The approach further consists of a methodology to interact with a remotely located human operator based on an inexpensive long-range and low-power communication technology from the internet-of-things domain (i.e., LoRa) and a customized communication protocol. The results and the feasibility analysis show the possible applications and limitations of the approach.Code—The open-source software stack is made available on the project repository webpage<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">†</sup>.

This systems paper presents the implementation and design of RB5, a wheeled robot for autonomous long-term exploration with fewer and cheaper sensors. Requiring just an RGB-D camera and low-power computing hardware, the system consists of an experimental platform with rocker-bogie suspension. It operates in unknown and GPS-denied environments and on indoor and outdoor terrains. The exploration consists of a methodology that extends frontier- and sampling-based exploration with a path-following vector field and a state-of-the-art SLAM algorithm. The methodology allows the robot to explore its surroundings at lower update frequencies, enabling the use of lower-performing and lower-cost hardware while still retaining good autonomous performance. The approach further consists of a methodology to interact with a remotely located human operator based on an inexpensive long-range and low-power communication technology from the internet-of-things domain (i.e., LoRa) and a customized communication protocol. The results and the feasibility analysis show the possible applications and limitations of the approach.

We present a method for controlling a swarm using its spectral decomposition—that is, by describing the set of trajectories of a swarm in terms of a spatial distribution throughout the operational domain—guaranteeing scale invariance with respect to the number of agents both for computation and the operator tasked with controlling the swarm. We use ergodic control, decentralized across the network, for implementation. In the DARPA OFFSET program field setting, we test this interface design for the operator using the swarm tactics and offensive mission planning (STOMP) interface—the same interface used by Raytheon BBN throughout the duration of the OFFSET program. In these tests, we demonstrate that our approach is scale-invariant—the user specification does not depend on the number of agents; it is persistent—the specification remains active until the user specifies a new command; and it is in real time—the user can interact with and interrupt the swarm at any time. Moreover, we show that the spectral/ergodic specification of swarm behavior degrades gracefully as the number of agents goes down, enabling the operator to maintain the same approach as agents become disabled or are added to the network. We demonstrate the scale-invariance and dynamic response of our system in a field-relevant simulator on a variety of tactical scenarios with up to 50 agents. We also demonstrate the dynamic response of our system in the field with a smaller team of agents. Finally, we make the code for our system available.

This paper presents maximum power point tracking improvement using model reference adaptive control (MRAC) scheme. Solar photovoltaic (PV) energy system remains one of the renewable energy applications which operate by tracking energy from the sun and converting it into useful electrical energy. However, harnessing the generated energy has been the major concern of the engineers hence the adoption of various control strategies for efficient control of the generated power. The idea is to transfer the optimal generated power to the output considering the fact that PV energy produced may have been affected by irradiation and temperature conditions. To avoid the unstable output power, there is need to deploy an efficient control scheme. Most of the conventional control techniques are not optimal to resolve power inaccuracies in the system and they have shortcomings. This work is therefore aimed at analyzing solar photovoltaic energy system using MRAC technique to investigate the control performance. The results obtained by simulation on MATLAB/Simulink software, show an average tracking efficiency of 73.41%, the rise time of 0.7093s and a duty cycle of 0.7. Moreover, MRAC operates at small gain values and the range at which MRAC can operate was found to be 0.1 &lt; 𝛤 &lt; 2.

Continuous exploration without interruption is important in scenarios such as search and rescue and precision agriculture, where consistent presence is needed to detect events over large areas. Ergodic search already derives continuous trajectories in these scenarios so that a robot spends more time in areas with high information density. However, existing literature on ergodic search does not consider the robot's energy constraints, limiting how long a robot can explore. In fact, if the robots are battery-powered, it is physically not possible to continuously explore on a single battery charge. Our paper tackles this challenge, integrating ergodic search methods with energy-aware coverage. We trade off battery usage and coverage quality, maintaining uninterrupted exploration by at least one agent. Our approach derives an abstract battery model for future state-of-charge estimation and extends canonical ergodic search to ergodic search under battery constraints. Empirical data from simulations and real-world experiments demonstrate the effectiveness of our energy-aware ergodic search, which ensures continuous exploration and guarantees spatial coverage.