Soon-Jo Chung

Lu Gan, Connor Lee, Soon-Jo Chung

This work presents a new method for unsupervised thermal image classification and semantic segmentation by transferring knowledge from the RGB domain using a multi-domain attention network. Our method does not require any thermal annotations or co-registered RGB-thermal pairs, enabling robots to perform visual tasks at night and in adverse weather conditions without incurring additional costs of data labeling and registration. Current unsupervised domain adaptation methods look to align global images or features across domains. However, when the domain shift is significantly larger for cross-modal data, not all features can be transferred. We solve this problem by using a shared backbone network that promotes generalization, and domain-specific attention that reduces negative transfer by attending to domain-invariant and easily-transferable features. Our approach outperforms the state-of-the-art RGB-to-thermal adaptation method in classification benchmarks, and is successfully applied to thermal river scene segmentation using only synthetic RGB images. Our code is made publicly available at https://github.com/ganlumomo/thermal-uda-attention.

Michael O'Connell, Guanya Shi, Xichen Shi et al.

Executing safe and precise flight maneuvers in dynamic high-speed winds is important for the ongoing commoditization of uninhabited aerial vehicles (UAVs). However, because the relationship between various wind conditions and its effect on aircraft maneuverability is not well understood, it is challenging to design effective robot controllers using traditional control design methods. We present Neural-Fly, a learning-based approach that allows rapid online adaptation by incorporating pretrained representations through deep learning. Neural-Fly builds on two key observations that aerodynamics in different wind conditions share a common representation and that the wind-specific part lies in a low-dimensional space. To that end, Neural-Fly uses a proposed learning algorithm, domain adversarially invariant meta-learning (DAIML), to learn the shared representation, only using 12 minutes of flight data. With the learned representation as a basis, Neural-Fly then uses a composite adaptation law to update a set of linear coefficients for mixing the basis elements. When evaluated under challenging wind conditions generated with the Caltech Real Weather Wind Tunnel, with wind speeds up to 43.6 kilometers/hour (12.1 meters/second), Neural-Fly achieves precise flight control with substantially smaller tracking error than state-of-the-art nonlinear and adaptive controllers. In addition to strong empirical performance, the exponential stability of Neural-Fly results in robustness guarantees. Last, our control design extrapolates to unseen wind conditions, is shown to be effective for outdoor flights with only onboard sensors, and can transfer across drones with minimal performance degradation.

Connor Lee, Jonathan Gustafsson Frennert, Lu Gan et al.

We present a new method to adapt an RGB-trained water segmentation network to target-domain aerial thermal imagery using online self-supervision by leveraging texture and motion cues as supervisory signals. This new thermal capability enables current autonomous aerial robots operating in near-shore environments to perform tasks such as visual navigation, bathymetry, and flow tracking at night. Our method overcomes the problem of scarce and difficult-to-obtain near-shore thermal data that prevents the application of conventional supervised and unsupervised methods. In this work, we curate the first aerial thermal near-shore dataset, show that our approach outperforms fully-supervised segmentation models trained on limited target-domain thermal data, and demonstrate real-time capabilities onboard an Nvidia Jetson embedded computing platform. Code and datasets used in this work will be available at: https://github.com/connorlee77/uav-thermal-water-segmentation.

Hiroyasu Tsukamoto, Soon-Jo Chung, Jean-Jacques E. Slotine

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit the systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is, therefore, to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.

Saptarshi Bandyopadhyay, Soon-Jo Chung

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.

Sri Aditya Deevi, Connor Lee, Lu Gan et al.

Multimodal deep sensor fusion has the potential to enable autonomous vehicles to visually understand their surrounding environments in all weather conditions. However, existing deep sensor fusion methods usually employ convoluted architectures with intermingled multimodal features, requiring large coregistered multimodal datasets for training. In this work, we present an efficient and modular RGB-X fusion network that can leverage and fuse pretrained single-modal models via scene-specific fusion modules, thereby enabling joint input-adaptive network architectures to be created using small, coregistered multimodal datasets. Our experiments demonstrate the superiority of our method compared to existing works on RGB-thermal and RGB-gated datasets, performing fusion using only a small amount of additional parameters. Our code is available at https://github.com/dsriaditya999/RGBXFusion.

Benjamin P. S. Donitz, Declan Mages, Hiroyasu Tsukamoto et al.

Interstellar objects (ISOs) represent a compelling and under-explored category of celestial bodies, providing physical laboratories to understand the formation of our solar system and probe the composition and properties of material formed in exoplanetary systems. In this work, we investigate existing approaches to designing successful flyby missions to ISOs, including a deep learning-driven guidance and control algorithm for ISOs traveling at velocities over 60 km/s. We have generated spacecraft trajectories to a series of synthetic representative ISOs, simulating a ground campaign to observe the target and resolve its state, thereby determining the cruise and close approach delta-Vs required for the encounter. We discuss the accessibility of and mission design to ISOs with varying characteristics, with special focuses on 1) state covariance estimation throughout the cruise, 2) handoffs from traditional navigation approaches to novel autonomous navigation for fast flyby regimes, and 3) overall recommendations about preparing for the future in situ exploration of these targets. The lessons learned also apply to the fast flyby of other small bodies, e.g., long-period comets and potentially hazardous asteroids, which also require tactical responses with similar characteristics.

Hiroyasu Tsukamoto, Benjamin Rivière, Changrak Choi et al.

The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the analytical form of our CaRT safety filter formally ensures safe maneuvers of nonlinear multi-agent systems, optimally with minimal deviation from the learning-based policy. Second, in off-nominal settings, the analytical form of our CaRT robust filter optimally tracks the certified safe trajectory, generated by the previous layer in the hierarchy, the CaRT safety filter. We show using contraction theory that CaRT guarantees safety and the exponential boundedness of the trajectory tracking error, even under the presence of deterministic and stochastic disturbance. Also, the hierarchical nature of CaRT enables enhancing its robustness for safety just by its superior tracking to the certified safe trajectory, thereby making it suitable for off-nominal scenarios with large disturbances. This is a major distinction from conventional safety function-driven approaches, where the robustness originates from the stability of a safe set, which could pull the system over-conservatively to the interior of the safe set. Our log-barrier formulation in CaRT allows for its distributed implementation in multi-agent settings. We demonstrate the effectiveness of CaRT in several examples of nonlinear motion planning and control problems, including optimal, multi-spacecraft reconfiguration.

Masahiro Ono, Daniel Selva, Morgan L. Cable et al.

The surface and subsurface of worlds beyond Mars remain largely unexplored. Yet these worlds hold keys to fundamental questions in planetary science - from potentially habitable subsurface oceans on icy moons to ancient records preserved in Kuiper Belt objects. NASA's success in Mars exploration was achieved through incrementalism: 22 progressively sophisticated missions over decades. This paradigm, which we call Planetary Exploration 2.0 (PE 2.0), is untenable for the outer Solar System, where cruise times of a decade or more make iterative missions infeasible. We propose Planetary Exploration 3.0 (PE 3.0): a paradigm in which unvisited worlds are explored by a single or a few missions with radically adaptive space systems. A PE 3.0 mission conducts both initial exploratory science and follow-on hypothesis-driven science based on its own in situ data returns, evolving spacecraft capabilities to work resiliently in previously unseen environments. The key enabler of PE 3.0 is software-defined space systems (SDSSs) - systems that can adapt their functions at all levels through software updates. This paper presents findings from a Keck Institute for Space Studies (KISS) workshop on PE 3.0, covering: (1) PE 3.0 systems engineering including science definition, architecture, design methods, and verification & validation; (2) software-defined space system technologies including reconfigurable hardware, multi-functionality, and modularity; (3) onboard intelligence including autonomous science, navigation, controls, and embodied AI; and (4) three PE 3.0 mission concepts: a Neptune/Triton smart flyby, an ocean world explorer, and an Oort cloud reconnaissance mission.

Hiroyasu Tsukamoto, Soon-Jo Chung, Yashwanth Kumar Nakka et al.

Interstellar objects (ISOs) are likely representatives of primitive materials invaluable in understanding exoplanetary star systems. Due to their poorly constrained orbits with generally high inclinations and relative velocities, however, exploring ISOs with conventional human-in-the-loop approaches is significantly challenging. This paper presents Neural-Rendezvous -- a deep learning-based guidance and control framework for encountering fast-moving objects, including ISOs, robustly, accurately, and autonomously in real time. It uses pointwise minimum norm tracking control on top of a guidance policy modeled by a spectrally-normalized deep neural network, where its hyperparameters are tuned with a loss function directly penalizing the MPC state trajectory tracking error. We show that Neural-Rendezvous provides a high probability exponential bound on the expected spacecraft delivery error, the proof of which leverages stochastic incremental stability analysis. In particular, it is used to construct a non-negative function with a supermartingale property, explicitly accounting for the ISO state uncertainty and the local nature of nonlinear state estimation guarantees. In numerical simulations, Neural-Rendezvous is demonstrated to satisfy the expected error bound for 100 ISO candidates. This performance is also empirically validated using our spacecraft simulator and in high-conflict and distributed UAV swarm reconfiguration with up to 20 UAVs.

Connor Lee, Matthew Anderson, Nikhil Raganathan et al.

We present the first publicly-available RGB-thermal dataset designed for aerial robotics operating in natural environments. Our dataset captures a variety of terrain across the United States, including rivers, lakes, coastlines, deserts, and forests, and consists of synchronized RGB, thermal, global positioning, and inertial data. We provide semantic segmentation annotations for 10 classes commonly encountered in natural settings in order to drive the development of perception algorithms robust to adverse weather and nighttime conditions. Using this dataset, we propose new and challenging benchmarks for thermal and RGB-thermal (RGB-T) semantic segmentation, RGB-T image translation, and motion tracking. We present extensive results using state-of-the-art methods and highlight the challenges posed by temporal and geographical domain shifts in our data. The dataset and accompanying code is available at https://github.com/aerorobotics/caltech-aerial-rgbt-dataset.

Connor Lee, Saraswati Soedarmadji, Matthew Anderson et al.

We present a new method to automatically generate semantic segmentation annotations for thermal imagery captured from an aerial vehicle by utilizing satellite-derived data products alongside onboard global positioning and attitude estimates. This new capability overcomes the challenge of developing thermal semantic perception algorithms for field robots due to the lack of annotated thermal field datasets and the time and costs of manual annotation, enabling precise and rapid annotation of thermal data from field collection efforts at a massively-parallelizable scale. By incorporating a thermal-conditioned refinement step with visual foundation models, our approach can produce highly-precise semantic segmentation labels using low-resolution satellite land cover data for little-to-no cost. It achieves 98.5% of the performance from using costly high-resolution options and demonstrates between 70-160% improvement over popular zero-shot semantic segmentation methods based on large vision-language models currently used for generating annotations for RGB imagery. Code will be available at: https://github.com/connorlee77/aerial-auto-segment.

Hannah Grauer, Elena-Sorina Lupu, Connor Lee et al.

Space debris and inactive satellites pose a threat to the safety and integrity of operational spacecraft and motivate the need for space situational awareness techniques. These uncooperative targets create a challenging tracking and detection problem due to a lack of prior knowledge of their features, trajectories, or even existence. Recent advancements in computer vision models can be used to improve upon existing methods for tracking such uncooperative targets to make them more robust and reliable to the wide-ranging nature of the target. This paper introduces an autonomous detection model designed to identify and monitor these objects using learning and computer vision. The autonomous detection method aims to identify and accurately track the uncooperative targets in varied circumstances, including different camera spectral sensitivities, lighting, and backgrounds. Our method adapts to the relative distance between the observing spacecraft and the target, and different detection strategies are adjusted based on distance. At larger distances, we utilize You Only Look Once (YOLOv8), a multitask Convolutional Neural Network (CNN), for zero-shot and domain-specific single-shot real time detection of the target. At shorter distances, we use knowledge distillation to combine visual foundation models with a lightweight fast segmentation CNN (Fast-SCNN) to segment the spacecraft components with low storage requirements and fast inference times, and to enable weight updates from earth and possible onboard training. Lastly, we test our method on a custom dataset simulating the unique conditions encountered in space, as well as a publicly-available dataset.

Vrushabh Zinage, Narek Harutyunyan, Eric Verheyden et al.

Legged locomotion in unstructured environments demands not only high-performance control policies but also formal guarantees to ensure robustness under perturbations. Control methods often require carefully designed reference trajectories, which are challenging to construct in high-dimensional, contact-rich systems such as quadruped robots. In contrast, Reinforcement Learning (RL) directly learns policies that implicitly generate motion, and uniquely benefits from access to privileged information, such as full state and dynamics during training, that is not available at deployment. We present ContractionPPO, a framework for certified robust planning and control of legged robots by augmenting Proximal Policy Optimization (PPO) RL with a state-dependent contraction metric layer. This approach enables the policy to maximize performance while simultaneously producing a contraction metric that certifies incremental exponential stability of the simulated closed-loop system. The metric is parameterized as a Lipschitz neural network and trained jointly with the policy, either in parallel or as an auxiliary head of the PPO backbone. While the contraction metric is not deployed during real-world execution, we derive upper bounds on the worst-case contraction rate and show that these bounds ensure the learned contraction metric generalizes from simulation to real-world deployment. Our hardware experiments on quadruped locomotion demonstrate that ContractionPPO enables robust, certifiably stable control even under strong external perturbations.

Mahdi Taheri, Haeyoon Han, Soon-Jo Chung et al.

This paper develops a fault detection and identification (FDI) method for nonlinear control-affine systems under simultaneous actuator and sensor faults. We adopt a geometric approach to study the isolability of faults in the sense of the principal angles between subspaces corresponding to each actuator and sensor fault. As for the fault identification, a hybrid estimator that consists of a Luenberger-like observer with contraction guarantees is developed. Moreover, neural networks are embedded in the mentioned observer to estimate actuator and sensor faults. Considering that the training dataset for neural networks cannot be representative of every fault scenario, the last layer of each network is adapted using mirror descent-based laws. The mirror descent-based adaptive laws impose isolability conditions for fault channels and do not assume a quadratic parameter estimation space to consider the geometry of the fault subspaces. A Lyapunov-based analysis establishes that the state and parameter estimation errors are uniformly ultimately bounded. The effectiveness of our proposed FDI method is illustrated on the 3-axis attitude control system of a spacecraft.

Joshua D. Ibrahim, Mahdi Taheri, Soon-Jo Chung et al.

This paper focuses on data-driven fault detection, identification, and recovery (FDIR) for nonlinear control-affine systems under actuator faults. We create a unified framework in the space of probability densities, rather than on individual trajectories, using fault-indexed Perron--Frobenius (PF) operators to predict the evolution of state distributions under different fault profiles. By leveraging the probability-flow representation of the Fokker--Planck equation, we construct deterministic PF operators that reproduce exact stochastic marginals, define forward reachable density families, and establish certifiable 2-Wasserstein bounds on the divergence between fault-driven and nominal density evolutions. These provide quantitative conditions for the detectability and identifiability of various faults. The fault-indexed operators are learned from trajectory data via flow map matching (FMM), and we demonstrate that the observable FMM residual directly bounds the approximation error of the operator in the 2-Wasserstein metric. Additionally, we co-train a contraction certificate that bounds the gap between the learned operator family, the actual fault-driven density flow, and the nominal dynamics. The operator library is then used online for continuous fault parameter fitting over a continuous parameter space to generalize the learned operators to out-of-distribution (OOD) scenarios. To carry out the recovery control, we employ reachable density propagation and Gaussian mixture covariance steering. The proposed framework is validated on a 10-state spacecraft attitude-control system with four reaction wheels.

Joshua D. Ibrahim, Mahdi Taheri, Soon-Jo Chung et al.

Fault detection and identification (FDI) is critical for maintaining the safety and reliability of systems subject to actuator and sensor faults. In this paper, the problem of FDI for nonlinear control-affine systems under simultaneous actuator and sensor faults is studied. We model fault signatures through the evolution of the probability density flow along the trajectory and characterize detectability using the 2-Wasserstein metric. In order to introduce quantifiable guarantees for fault detectability based on system parameters and fault magnitudes, we derive upper bounds on the distributional separation between nominal and faulty dynamics. The latter is achieved through a stochastic contraction analysis of probability distributions in the 2-Wasserstein metric. A data-driven FDI method is developed by means of a conditional flow-matching scheme that learns neural vector fields governing density propagation under different fault profiles. To generalize the data-driven FDI method across continuous fault magnitudes, Gaussian bridge interpolation and Feature-wise Linear Modulation (FiLM) conditioning are incorporated. The effectiveness of our proposed method is illustrated on a spacecraft attitude control system, and its performance is compared with an augmented Extended Kalman Filter (EKF) baseline. The results confirm that trajectory-based distributional analysis provides improved discrimination between fault scenarios and enables reliable data-driven FDI with a lower false alarm rate compared with the augmented EKF.

Geeling Chau, Yujin An, Ahamed Raffey Iqbal et al.

A major goal in neuroscience is to discover neural data representations that generalize. This goal is challenged by variability along recording sessions (e.g. environment), subjects (e.g. varying neural structures), and sensors (e.g. sensor noise), among others. Recent work has begun to address generalization across sessions and subjects, but few study robustness to sensor failure which is highly prevalent in neuroscience experiments. In order to address these generalizability dimensions we first collect our own electroencephalography dataset with numerous sessions, subjects, and sensors, then study two time series models: EEGNet (Lawhern et al., 2018) and TOTEM (Talukder et al., 2024). EEGNet is a widely used convolutional neural network, while TOTEM is a discrete time series tokenizer and transformer model. We find that TOTEM outperforms or matches EEGNet across all generalizability cases. Finally through analysis of TOTEM's latent codebook we observe that tokenization enables generalization.

Xingxing Zuo, Nikhil Ranganathan, Connor Lee et al.

Monocular depth estimation (MDE) from thermal images is a crucial technology for robotic systems operating in challenging conditions such as fog, smoke, and low light. The limited availability of labeled thermal data constrains the generalization capabilities of thermal MDE models compared to foundational RGB MDE models, which benefit from datasets of millions of images across diverse scenarios. To address this challenge, we introduce a novel pipeline that enhances thermal MDE through knowledge distillation from a versatile RGB MDE model. Our approach features a confidence-aware distillation method that utilizes the predicted confidence of the RGB MDE to selectively strengthen the thermal MDE model, capitalizing on the strengths of the RGB model while mitigating its weaknesses. Our method significantly improves the accuracy of the thermal MDE, independent of the availability of labeled depth supervision, and greatly expands its applicability to new scenarios. In our experiments on new scenarios without labeled depth, the proposed confidence-aware distillation method reduces the absolute relative error of thermal MDE by 22.88\% compared to the baseline without distillation.

James Ragan, Fred Y. Hadaegh, Soon-Jo Chung

Monte Carlo Tree Search is a popular method for solving decision making problems. Faster implementations allow for more simulations within the same wall clock time, directly improving search performance. To this end, we present an alternative array-based implementation of the classic Upper Confidence bounds applied to Trees algorithm. Our method preserves the logic of the original algorithm, but eliminates the need for branch prediction, enabling faster performance on pipelined processors, and up to a factor of 2.8 times better scaling with search depth in our numerical simulations.

Arion Zimmermann, Soon-Jo Chung, Fred Hadaegh

The accurate state estimation of unknown bodies in space is a critical challenge with applications ranging from the tracking of space debris to the shape estimation of small bodies. A necessary enabler to this capability is to find and track features on a continuous stream of images. Existing methods, such as SIFT, ORB and AKAZE, achieve real-time but inaccurate pose estimates, whereas modern deep learning methods yield higher quality features at the cost of more demanding computational resources which might not be available on space-qualified hardware. Additionally, both classical and data-driven methods are not robust to the highly opaque self-cast shadows on the object of interest. We show that, as the target body rotates, these shadows may lead to large biases in the resulting pose estimates. For these objects, a bias in the real-time pose estimation algorithm may mislead the spacecraft's state estimator and cause a mission failure, especially if the body undergoes a chaotic tumbling motion. We present COFFEE, the Celestial Occlusion Fast FEature Extractor, a real-time pose estimation framework for asteroids designed to leverage prior information on the sun phase angle given by sun-tracking sensors commonly available onboard spacecraft. By associating salient contours to their projected shadows, a sparse set of features are detected, invariant to the motion of the shadows. A Sparse Neural Network followed by an attention-based Graph Neural Network feature matching model are then jointly trained to provide a set of correspondences between successive frames. The resulting pose estimation pipeline is found to be bias-free, more accurate than classical pose estimation pipelines and an order of magnitude faster than other state-of-the-art deep learning pipelines on synthetic data as well as on renderings of the tumbling asteroid Apophis.

Daniel Neamati, Yashwanth Kumar Nakka, Soon-Jo Chung

Accurate gravity field models are essential for safe proximity operations around small bodies. State-of-the-art techniques use spherical harmonics or high-fidelity polyhedron shape models. Unfortunately, these techniques can become inaccurate near the surface of the small body or have high computational costs, especially for binary or heterogeneous small bodies. New learning-based techniques do not encode a predefined structure and are more versatile. In exchange for versatility, learning-based techniques can be less robust outside the training data domain. In deployment, the spacecraft trajectory is the primary source of dynamics data. Therefore, the training data domain should include spacecraft trajectories to accurately evaluate the learned model's safety and robustness. We have developed a novel method for learning-based gravity models that directly uses the spacecraft's past trajectories. We further introduce a method to evaluate the safety and robustness of learning-based techniques via comparing accuracy within and outside of the training domain. We demonstrate this safety and robustness method for two learning-based frameworks: Gaussian processes and neural networks. Along with the detailed analysis provided, we empirically establish the need for robustness verification of learned gravity models when used for proximity operations.

Hiroyasu Tsukamoto, Soon-Jo Chung, Jean-Jacques Slotine et al.

This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient condition for incremental exponential stability of non-autonomous nonlinear system trajectories. Its innovation lies in providing formal robustness guarantees for learning-based control frameworks, utilizing contraction theory as an analytical tool to study the nonlinear stability of learned systems via convex optimization. In particular, we rigorously show in this paper that, by regarding modeling errors of the learning schemes as external disturbances, the NCM control is capable of obtaining an explicit bound on the distance between a time-varying target trajectory and perturbed solution trajectories, which exponentially decreases with time even under the presence of deterministic and stochastic perturbation. These useful features permit simultaneous synthesis of a contraction metric and associated control law by a neural network, thereby enabling real-time computable and probably robust learning-based control for general control-affine nonlinear systems.

Hiroyasu Tsukamoto, Soon-Jo Chung, Jean-Jacques E. Slotine

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit the systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is, therefore, to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.

Guanya Shi, Kamyar Azizzadenesheli, Michael O'Connell et al.

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation, in inverted pendulum and 6-DoF drone control tasks under varying wind conditions.

Yashwanth Kumar Nakka, Soon-Jo Chung

We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of \emph{deterministic} nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem using sequential convex programming for trajectory generation and control. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC. We also present the predictor-corrector extension (gPC-SCP$^\mathrm{PC}$) for real-time motion trajectory generation in the presence of stochastic uncertainty. In the gPC-SCP$^\mathrm{PC}$ method, we first predict the uncertainty using the gPC method and then optimize the motion plan to accommodate the uncertainty. We empirically demonstrate the efficacy of the gPC-SCP and the gPC-SCP$^\mathrm{PC}$ methods for the following two test cases: 1) collision checking under uncertainty in actuation and physical parameters and 2) collision checking with stochastic obstacle model for 3DOF and 6DOF robotic systems. We validate the effectiveness of the gPC-SCP method on the 3DOF robotic spacecraft testbed.

Benjamin Rivière, Soon-Jo Chung

We present H-TD2: Hybrid Temporal Difference Learning for Taxi Dispatch, a model-free, adaptive decision-making algorithm to coordinate a large fleet of automated taxis in a dynamic urban environment to minimize expected customer waiting times. Our scalable algorithm exploits the natural transportation network company topology by switching between two behaviors: distributed temporal-difference learning computed locally at each taxi and infrequent centralized Bellman updates computed at the dispatch center. We derive a regret bound and design the trigger condition between the two behaviors to explicitly control the trade-off between computational complexity and the individual taxi policy's bounded sub-optimality; this advances the state of the art by enabling distributed operation with bounded-suboptimality. Additionally, unlike recent reinforcement learning dispatch methods, this policy estimation is adaptive and robust to out-of-training domain events. This result is enabled by a two-step modelling approach: the policy is learned on an agent-agnostic, cell-based Markov Decision Process and individual taxis are coordinated using the learned policy in a distributed game-theoretic task assignment. We validate our algorithm against a receding horizon control baseline in a Gridworld environment with a simulated customer dataset, where the proposed solution decreases average customer waiting time by 50% over a wide range of parameters. We also validate in a Chicago city environment with real customer requests from the Chicago taxi public dataset where the proposed solution decreases average customer waiting time by 26% over irregular customer distributions during a 2016 Major League Baseball World Series game.

Benjamin Riviere, Wolfgang Hoenig, Matthew Anderson et al.

We present a self-improving, Neural Tree Expansion (NTE) method for multi-robot online planning in non-cooperative environments, where each robot attempts to maximize its cumulative reward while interacting with other self-interested robots. Our algorithm adapts the centralized, perfect information, discrete-action space method from AlphaZero to a decentralized, partial information, continuous action space setting for multi-robot applications. Our method has three interacting components: (i) a centralized, perfect-information "expert" Monte Carlo Tree Search (MCTS) with large computation resources that provides expert demonstrations, (ii) a decentralized, partial-information "learner" MCTS with small computation resources that runs in real-time and provides self-play examples, and (iii) policy & value neural networks that are trained with the expert demonstrations and bias both the expert and the learner tree growth. Our numerical experiments demonstrate Neural Tree Expansion's computational advantage by finding better solutions than a MCTS with 20 times more resources. The resulting policies are dynamically sophisticated, demonstrate coordination between robots, and play the Reach-Target-Avoid differential game significantly better than the state-of-the-art control-theoretic baseline for multi-robot, double-integrator systems. Our hardware experiments on an aerial swarm demonstrate the computational advantage of Neural Tree Expansion, enabling online planning at 20Hz with effective policies in complex scenarios.

Hiroyasu Tsukamoto, Soon-Jo Chung, Jean-Jacques Slotine

Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametrization, called adaptive Neural Contraction Metric (aNCM). The aNCM approximates real-time optimization for computing a differential Lyapunov function and a corresponding stabilizing adaptive control law by using a Deep Neural Network (DNN). The use of DNNs permits real-time implementation of the control law and broad applicability to a variety of nonlinear systems with parametric and nonparametric uncertainties. We show using contraction theory that the aNCM ensures exponential boundedness of the distance between the target and controlled trajectories in the presence of parametric uncertainties of the model, learning errors caused by aNCM approximation, and external disturbances. Its superiority to the existing robust and adaptive control methods is demonstrated using a cart-pole balancing model.

Michael O'Connell, Guanya Shi, Xichen Shi et al.

Realtime model learning proves challenging for complex dynamical systems, such as drones flying in variable wind conditions. Machine learning technique such as deep neural networks have high representation power but is often too slow to update onboard. On the other hand, adaptive control relies on simple linear parameter models can update as fast as the feedback control loop. We propose an online composite adaptation method that treats outputs from a deep neural network as a set of basis functions capable of representing different wind conditions. To help with training, meta-learning techniques are used to optimize the network output useful for adaptation. We validate our approach by flying a drone in an open air wind tunnel under varying wind conditions and along challenging trajectories. We compare the result with other adaptive controller with different basis function sets and show improvement over tracking and prediction errors.

Hiroyasu Tsukamoto, Soon-Jo Chung

This paper presents Learning-based Autonomous Guidance with RObustness and Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear motion planners with formal robustness and stability guarantees, by designing a differential Lyapunov function using contraction theory. LAG-ROS utilizes a neural network to model a robust tracking controller independently of a target trajectory, for which we show that the Euclidean distance between the target and controlled trajectories is exponentially bounded linearly in the learning error, even under the existence of bounded external disturbances. We also present a convex optimization approach that minimizes the steady-state bound of the tracking error to construct the robust control law for neural network training. In numerical simulations, it is demonstrated that the proposed method indeed possesses superior properties of robustness and nonlinear stability resulting from contraction theory, whilst retaining the computational efficiency of existing learning-based motion planners.

Guanya Shi, Wolfgang Hönig, Xichen Shi et al.

We present Neural-Swarm2, a learning-based method for motion planning and control that allows heterogeneous multirotors in a swarm to safely fly in close proximity. Such operation for drones is challenging due to complex aerodynamic interaction forces, such as downwash generated by nearby drones and ground effect. Conventional planning and control methods neglect capturing these interaction forces, resulting in sparse swarm configuration during flight. Our approach combines a physics-based nominal dynamics model with learned Deep Neural Networks (DNNs) with strong Lipschitz properties. We make use of two techniques to accurately predict the aerodynamic interactions between heterogeneous multirotors: i) spectral normalization for stability and generalization guarantees of unseen data and ii) heterogeneous deep sets for supporting any number of heterogeneous neighbors in a permutation-invariant manner without reducing expressiveness. The learned residual dynamics benefit both the proposed interaction-aware multi-robot motion planning and the nonlinear tracking control design because the learned interaction forces reduce the modelling errors. Experimental results demonstrate that Neural-Swarm2 is able to generalize to larger swarms beyond training cases and significantly outperforms a baseline nonlinear tracking controller with up to three times reduction in worst-case tracking errors.

Hiroyasu Tsukamoto, Soon-Jo Chung, Jean-Jacques E. Slotine

We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The NSCM framework allows autonomous agents to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic neural contraction metric, as illustrated in simulation results.

Hiroyasu Tsukamoto, Soon-Jo Chung

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global approximation of an optimal contraction metric, the existence of which is a necessary and sufficient condition for exponential stability of nonlinear systems. The optimality stems from the fact that the contraction metrics sampled offline are the solutions of a convex optimization problem to minimize an upper bound of the steady-state Euclidean distance between perturbed and unperturbed system trajectories. We demonstrate how to exploit NCMs to design an online optimal estimator and controller for nonlinear systems with bounded disturbances utilizing their duality. The performance of our framework is illustrated through Lorenz oscillator state estimation and spacecraft optimal motion planning problems.

Hiroyasu Tsukamoto, Soon-Jo Chung

This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is non-convex, its equivalent convex formulation is proposed utilizing state-dependent coefficient parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L2-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H-infinity, and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.

Yashwanth Kumar Nakka, Anqi Liu, Guanya Shi et al.

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an \underline{Info}rmation-cost \underline{S}tochastic \underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.

Xichen Shi, Patrick Spieler, Ellande Tang et al.

Fixed-wing vertical take-off and landing (VTOL) aircraft pose a unique control challenge that stems from complex aerodynamic interactions between wings and rotors. Thus, accurate estimation of external forces is indispensable for achieving high performance flight. In this paper, we present a composite adaptive nonlinear tracking controller for a fixed-wing VTOL. The method employs online adaptation of linear force models, and generates accurate estimation for wing and rotor forces in real-time based on information from a three-dimensional airflow sensor. The controller is implemented on a custom-built fixed-wing VTOL, which shows improved velocity tracking and force prediction during the transition stage from hover to forward flight, compared to baseline flight controllers.

Guanya Shi, Wolfgang Hönig, Yisong Yue et al.

In this paper, we present Neural-Swarm, a nonlinear decentralized stable controller for close-proximity flight of multirotor swarms. Close-proximity control is challenging due to the complex aerodynamic interaction effects between multirotors, such as downwash from higher vehicles to lower ones. Conventional methods often fail to properly capture these interaction effects, resulting in controllers that must maintain large safety distances between vehicles, and thus are not capable of close-proximity flight. Our approach combines a nominal dynamics model with a regularized permutation-invariant Deep Neural Network (DNN) that accurately learns the high-order multi-vehicle interactions. We design a stable nonlinear tracking controller using the learned model. Experimental results demonstrate that the proposed controller significantly outperforms a baseline nonlinear tracking controller with up to four times smaller worst-case height tracking errors. We also empirically demonstrate the ability of our learned model to generalize to larger swarm sizes.

Benjamin Rivière, Wolfgang Hoenig, Yisong Yue et al.

We present GLAS: Global-to-Local Autonomy Synthesis, a provably-safe, automated distributed policy generation for multi-robot motion planning. Our approach combines the advantage of centralized planning of avoiding local minima with the advantage of decentralized controllers of scalability and distributed computation. In particular, our synthesized policies only require relative state information of nearby neighbors and obstacles, and compute a provably-safe action. Our approach has three major components: i) we generate demonstration trajectories using a global planner and extract local observations from them, ii) we use deep imitation learning to learn a decentralized policy that can run efficiently online, and iii) we introduce a novel differentiable safety module to ensure collision-free operation, thereby allowing for end-to-end policy training. Our numerical experiments demonstrate that our policies have a 20% higher success rate than optimal reciprocal collision avoidance, ORCA, across a wide range of robot and obstacle densities. We demonstrate our method on an aerial swarm, executing the policy on low-end microcontrollers in real-time.

Guanya Shi, Yiheng Lin, Soon-Jo Chung et al.

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems.

Anqi Liu, Guanya Shi, Soon-Jo Chung et al.

We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from operating in an environment, in order to learn to achieve a challenging control goal (e.g., an agile maneuver close to a boundary). A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect informative data and reduce uncertainty, thereby achieving both improved controller safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We derive generalization bounds for learning, and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform the conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior.

Guanya Shi, Xichen Shi, Michael O'Connell et al.

Precise near-ground trajectory control is difficult for multi-rotor drones, due to the complex aerodynamic effects caused by interactions between multi-rotor airflow and the environment. Conventional control methods often fail to properly account for these complex effects and fall short in accomplishing smooth landing. In this paper, we present a novel deep-learning-based robust nonlinear controller (Neural Lander) that improves control performance of a quadrotor during landing. Our approach combines a nominal dynamics model with a Deep Neural Network (DNN) that learns high-order interactions. We apply spectral normalization (SN) to constrain the Lipschitz constant of the DNN. Leveraging this Lipschitz property, we design a nonlinear feedback linearization controller using the learned model and prove system stability with disturbance rejection. To the best of our knowledge, this is the first DNN-based nonlinear feedback controller with stability guarantees that can utilize arbitrarily large neural nets. Experimental results demonstrate that the proposed controller significantly outperforms a Baseline Nonlinear Tracking Controller in both landing and cross-table trajectory tracking cases. We also empirically show that the DNN generalizes well to unseen data outside the training domain.

Jingjin Yu, Soon-Jo Chung, Petros G. Voulgaris

We study the problem of multi-robot target assignment to minimize the total distance traveled by the robots until they all reach an equal number of static targets. In the first half of the paper, we present a necessary and sufficient condition under which true distance optimality can be achieved for robots with limited communication and target-sensing ranges. Moreover, we provide an explicit, non-asymptotic formula for computing the number of robots needed to achieve distance optimality in terms of the robots' communication and target-sensing ranges with arbitrary guaranteed probabilities. The same bounds are also shown to be asymptotically tight. In the second half of the paper, we present suboptimal strategies for use when the number of robots cannot be chosen freely. Assuming first that all targets are known to all robots, we employ a hierarchical communication model in which robots communicate only with other robots in the same partitioned region. This hierarchical communication model leads to constant approximations of true distance-optimal solutions under mild assumptions. We then revisit the limited communication and sensing models. By combining simple rendezvous-based strategies with a hierarchical communication model, we obtain decentralized hierarchical strategies that achieve constant approximation ratios with respect to true distance optimality. Results of simulation show that the approximation ratio is as low as 1.4.