Panagiotis Tsiotras

Yue Guan, Daigo Shishika, Jason R. Marden et al. · gatech

This work introduces the dynamic Defender-Attacker Blotto (dDAB) game, extending the classical static Blotto game to a dynamic resource allocation setting over graphs. In the dDAB game, a defender is required to maintain numerical superiority against attacker resources across a set of key nodes in a connected graph. The engagement unfolds as a discrete-time game, where each player reallocates its resources in turn, with resources allowed to move at most one hop per time step. The primary goal is to determine the necessary and sufficient amount of defender resources required to guarantee sustained defense, along with the corresponding strategies. To address the central challenge arising from graph-constrained resource reallocation, we conduct a reachability analysis, starting with simplified settings where attacker resources act as a single cohesive group. We then extend the framework to allow attacker resources to split and merge arbitrarily, and construct defender strategies using superposition principles. A set-based dynamic programming algorithm is developed to compute the optimal strategies, as well as the minimum amount of defender resources to ensure successful defense. The effectiveness of our approach is demonstrated through numerical simulations and hardware experiments on the Georgia Tech Robotarium platform.

Travis Driver, Katherine Skinner, Mehregan Dor et al.

Missions to small celestial bodies rely heavily on optical feature tracking for characterization of and relative navigation around the target body. While deep learning has led to great advancements in feature detection and description, training and validating data-driven models for space applications is challenging due to the limited availability of large-scale, annotated datasets. This paper introduces AstroVision, a large-scale dataset comprised of 115,970 densely annotated, real images of 16 different small bodies captured during past and ongoing missions. We leverage AstroVision to develop a set of standardized benchmarks and conduct an exhaustive evaluation of both handcrafted and data-driven feature detection and description methods. Next, we employ AstroVision for end-to-end training of a state-of-the-art, deep feature detection and description network and demonstrate improved performance on multiple benchmarks. The full benchmarking pipeline and the dataset will be made publicly available to facilitate the advancement of computer vision algorithms for space applications.

Joshua Pilipovsky, Vignesh Sivaramakrishnan, Meeko M. K. Oishi et al.

Verifying the input-output relationships of a neural network so as to achieve some desired performance specification is a difficult, yet important, problem due to the growing ubiquity of neural nets in many engineering applications. We use ideas from probability theory in the frequency domain to provide probabilistic verification guarantees for ReLU neural networks. Specifically, we interpret a (deep) feedforward neural network as a discrete dynamical system over a finite horizon that shapes distributions of initial states, and use characteristic functions to propagate the distribution of the input data through the network. Using the inverse Fourier transform, we obtain the corresponding cumulative distribution function of the output set, which can be used to check if the network is performing as expected given any random point from the input set. The proposed approach does not require distributions to have well-defined moments or moment generating functions. We demonstrate our proposed approach on two examples, and compare its performance to related approaches.

Mehregan Dor, Travis Driver, Kenneth Getzandanner et al.

We propose AstroSLAM, a standalone vision-based solution for autonomous online navigation around an unknown target small celestial body. AstroSLAM is predicated on the formulation of the SLAM problem as an incrementally growing factor graph, facilitated by the use of the GTSAM library and the iSAM2 engine. By combining sensor fusion with orbital motion priors, we achieve improved performance over a baseline SLAM solution. We incorporate orbital motion constraints into the factor graph by devising a novel relative dynamics factor, which links the relative pose of the spacecraft to the problem of predicting trajectories stemming from the motion of the spacecraft in the vicinity of the small body. We demonstrate the excellent performance of AstroSLAM using both real legacy mission imagery and trajectory data courtesy of NASA's Planetary Data System, as well as real in-lab imagery data generated on a 3 degree-of-freedom spacecraft simulator test-bed.

Andrey Pak, Hemanth Manjunatha, Dimitar Filev et al.

Autonomous driving has received a lot of attention in the automotive industry and is often seen as the future of transportation. Passenger vehicles equipped with a wide array of sensors (e.g., cameras, front-facing radars, LiDARs, and IMUs) capable of continuous perception of the environment are becoming increasingly prevalent. These sensors provide a stream of high-dimensional, temporally correlated data that is essential for reliable autonomous driving. An autonomous driving system should effectively use the information collected from the various sensors in order to form an abstract description of the world and maintain situational awareness. Deep learning models, such as autoencoders, can be used for that purpose, as they can learn compact latent representations from a stream of incoming data. However, most autoencoder models process the data independently, without assuming any temporal interdependencies. Thus, there is a need for deep learning models that explicitly consider the temporal dependence of the data in their architecture. This work proposes CARNet, a Combined dynAmic autoencodeR NETwork architecture that utilizes an autoencoder combined with a recurrent neural network to learn the current latent representation and, in addition, also predict future latent representations in the context of autonomous driving. We demonstrate the efficacy of the proposed model in both imitation and reinforcement learning settings using both simulated and real datasets. Our results show that the proposed model outperforms the baseline state-of-the-art model, while having significantly fewer trainable parameters.

Dongliang Zheng, Panagiotis Tsiotras

In this work, we propose the Informed Batch Belief Trees (IBBT) algorithm for motion planning under motion and sensing uncertainties. The original stochastic motion planning problem is divided into a deterministic motion planning problem and a graph search problem. We solve the deterministic planning problem using sampling-based methods such as PRM or RRG to construct a graph of nominal trajectories. Then, an informed cost-to-go heuristic for the original problem is computed based on the nominal trajectory graph. Finally, we grow a belief tree by searching over the graph using the proposed heuristic. IBBT interleaves between batch state sampling, nominal trajectory graph construction, heuristic computing, and search over the graph to find belief space motion plans. IBBT is an anytime, incremental algorithm. With an increasing number of batches of samples added to the graph, the algorithm finds motion plans that converge to the optimal one. IBBT is efficient by reusing results between sequential iterations. The belief tree searching is an ordered search guided by an informed heuristic. We test IBBT in different planning environments. Our numerical investigation confirms that IBBT finds non-trivial motion plans and is faster compared with previous similar methods.

Daniel T. Larsson, Dipankar Maity, Panagiotis Tsiotras

In this chapter, an integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, environment abstractions for resource-constrained autonomous agents is presented. The formulation leverages concepts from information-theoretic signal compression, specifically, the information bottleneck (IB) method, to pose an abstraction problem as an optimal encoder search over the space of multi-resolution trees. The abstractions emerge in a task-relevant manner as a function of agent information-processing constraints. We detail our formulation, and show how hierarchical tree structures, signal encoders, and information-theoretic methods for signal compression can be unified under a common theme. A discussion delineating the benefits and drawbacks of our formulation is presented, as well as a detailed explanation how our approach can be interpreted within the context of generating abstractions for resource-constrained autonomous systems. It is shown that the resulting information-theoretic abstraction problem over the space of multi-resolution trees can be formulated as a integer linear programming (ILP) problem. We demonstrate the approach on a number of examples, and provide a discussion detailing the differences of the proposed framework compared to existing methods. Lastly, we consider a linear program relaxation of the ILP problem, thereby demonstrating that multi-resolution information-theoretic tree abstractions can be obtained by solving a convex program.

George Rapakoulias, Fengjiao Liu, Panagiotis Tsiotras

In this work, we revisit the discrete-time Schrödinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian policies that transport the initial distribution to the final distribution, and are expressed as mixtures of elementary component-to-component optimal policies. We then study the policy optimization within this feasible set in the context of discrete-time SBs and density-steering problems, respectively. We show that for minimum-effort density-steering problems, the proposed policy achieves the same control cost as existing approaches in the literature. For discrete-time SB problems, the proposed policy yields a cost smaller than or equal to that in the literature, resulting in a less conservative approximation. Finally, we study the continuous-time limit of our proposed discrete-time approach and show that it agrees with recently proposed approximations to the continuous-time SB for GMM boundary distributions. We illustrate this new result through two numerical examples.

Evangelos Psomiadis, Dipankar Maity, Panagiotis Tsiotras

Collaborative navigation of heterogeneous robots in unknown environments poses significant challenges due to sensing, communication, and computational limitations. In this work, a lead robot navigates toward a target while a mobile sensor robot (e.g., a drone) assists by transmitting information about its locally observed environment under bandwidth constraints. We propose a framework that enables the sensor to jointly select its transmitted map points and navigation actions online, while also predicting unexplored regions of the environment. To this end, we present $β$-Sparse Gaussian Processes, a novel and robust variational sparse Gaussian Process model for task-aware inducing point selection. Furthermore, we develop an action-selection strategy that balances task relevance with exploration. Simulations on Mars and Earth maps show that the framework can reduce path cost by 18% relative to no communication and decrease transmitted information by 76% compared to raw-data transmission baselines.

Siddhartha Ganguly, George Rapakoulias, Panagiotis Tsiotras

We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schrödinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source--target component label. Consequently, the problem decomposes into Gaussian component-to-component Schrödinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dimensional entropic coupling problem with a Sinkhorn scaling form. We then analyze the projection obtained by discarding or forgetting the label. By construction, the projected law satisfies the original Gaussian-mixture endpoint constraints, but its relative entropy generally differs from the lifted relative entropy by a nonnegative conditional label-information gap. This gap reveals a path-space obstruction: the lifted optimizer cannot, in general, be identified with the direct unlabeled Schrödinger bridge after projection. We also derive the posterior-averaged Markov drift associated with the projected marginal flow, prove a kinetic-energy upper bound, and identify a common path-potential condition under which the projection gap vanishes. Several numerical illustrations showing density and shape control are recorded for a self-contained exposition.

Travis Driver, Kento Tomita, Koki Ho et al.

Hazard detection and avoidance is a key technology for future robotic small body sample return and lander missions. Current state-of-the-practice methods rely on high-fidelity, a priori terrain maps, which require extensive human-in-the-loop verification and expensive reconnaissance campaigns to resolve mapping uncertainties. We propose a novel safety mapping paradigm that leverages deep semantic segmentation techniques to predict landing safety directly from a single monocular image, thus reducing reliance on high-fidelity, a priori data products. We demonstrate precise and accurate safety mapping performance on real in-situ imagery of prospective sample sites from the OSIRIS-REx mission.

George Rapakoulias, Peter Garud, Lingjiong Zhu et al.

Diffusion models achieve strong generation quality, diversity, and distribution coverage, but their performance often comes with expensive inference. In this work, we propose Stochastic Transition-Map Distillation (STMD), a teacher-free framework for accelerating diffusion model inference while preserving probabilistic sample generation. In contrast to score-based diffusion models, whose denoising parametrization models the mean of the posterior distribution, STMD distills the full transition map associated with the sampling stochastic differential equation (SDE). We parameterize these SDE transitions with a conditional Mean Flow model, yielding a one- or few-step stochastic sampler that retains the transition structure of the underlying diffusion process. This perspective is especially useful for downstream tasks that require stochastic inference, such as diffusion posterior sampling, inverse problems, and energy-based fine-tuning. Compared to recent distillation methods, STMD requires no pretrained teacher, bi-level optimization, or trajectory simulation and caching, enabling efficient and scalable training. We derive convergence bounds for our method in the Wasserstein distance, providing a strong theoretical foundation for our approach, and validate STMD on various image generation examples on the MNIST, CIFAR-10, and CelebA datasets.

Dimitrios Moustroufis, Panagiotis Tsiotras

This paper addresses the problem of output-feedback covariance steering for stochastic, discrete-time, linear, time-invariant systems without knowledge of the system model. We employ a controllable, non-minimal state representation constructed from past inputs and outputs and convert the problem to one in state-feedback form. In this representation, the induced disturbance becomes temporally correlated, which requires explicit propagation of the cross-covariance between the state and disturbance processes. To handle the lack of a system model, we leverage persistently exciting data collected offline and formulate the mean and covariance steering problems using an indirect and a direct approach, respectively. The indirect formulation requires an estimate of the mean dynamics model, while the direct formulation relies on an estimate of the noise realization in the collected data. To this end, we present an estimation method suitable to handle temporally correlated noise, enabling consistent identification of both components. Using a convex relaxation, we convert the covariance steering problem to a semidefinite program that can be solved efficiently. We conduct numerical simulations to evaluate the performance of the developed framework.

Longxu Pan, Yue Guan, Daigo Shishika et al.

In this work, we introduce the Deceptive Resource Allocation Game (DRAG), which studies purposeful deception within a Bayesian game framework. In DRAG, a Defender allocates resources across the true asset and several decoys to influence an Attacker's beliefs and actions, with the goal of diverting the Attacker away from the true asset. We seek to characterize purposeful deception, whereby the Defender deceives only when doing so improves its performance. To this end, we solve for the Perfect Bayesian Nash Equilibrium (PBNE) of the corresponding game. We show that, despite the coupled belief-policy interdependence, the problem admits an efficient, non-iterative linear programming formulation. Numerical results demonstrate that the resulting policies naturally balance effective allocation and belief manipulation, giving rise to purposeful and emergent deceptive behaviors.

Evangelos Psomiadis, Panagiotis Tsiotras

This paper addresses the problem of collaborative formation control for multi-agent systems with limited resources. We consider a team of robots tasked with achieving a desired formation from an arbitrary initial configuration. To reduce unnecessary control updates and conserve resources, we propose a distributed event-triggered formation controller. Unlike the well-studied linear formation control strategies, the proposed controller is nonlinear and relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a predefined threshold, ensuring system stability while minimizing actuation effort. We also employ a distributed control barrier function to guarantee inter-agent collision avoidance. The proposed controller is validated through extensive simulations and real-world experiments involving different formations, communication topologies, scalability tests, and variations in design parameters, while also being compared against periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control effort while preserving formation performance.

Lorenzo Ticozzi, Patricio A. Vela, Panagiotis Tsiotras

Reconstructing the shape of continuum manipulators from sparse, noisy sensor data is a challenging task, owing to the infinite-dimensional nature of such systems. Existing approaches broadly trade off between parametric methods that yield compact state representations but lack probabilistic structure, and Cosserat rod inference on factor graphs, which provides principled uncertainty quantification at the cost of a state dimension that grows with the spatial discretization. This letter combines the strength of both paradigms by estimating the coefficients of a low-dimensional Geometric Variable Strain (GVS) parameterization within a factor graph framework. A novel kinematic factor, derived from the Magnus expansion of the strain field, encodes the closed-form rod geometry as a prior constraint linking the GVS strain coefficients to the backbone pose variables. The resulting formulation yields a compact state vector directly amenable to model-based control, while retaining the modularity, probabilistic treatment and computational efficiency of factor graph inference. The proposed method is evaluated in simulation on a 0.4 m long tendon-driven continuum robot under three measurement configurations, achieving mean position errors below 2 mm for all three scenarios and demonstrating a sixfold reduction in orientation error compared to a Gaussian process regression baseline when only position measurements are available.

Travis Driver, Panagiotis Tsiotras

Missions to small celestial bodies rely heavily on optical feature tracking for characterization of and relative navigation around the target body. While techniques for feature tracking based on deep learning are a promising alternative to current human-in-the-loop processes, designing deep architectures that can operate onboard spacecraft is challenging due to onboard computational and memory constraints. This paper introduces a novel deep local feature description architecture that leverages binary convolutional neural network layers to significantly reduce computational and memory requirements. We train and test our models on real images of small bodies from legacy and ongoing missions and demonstrate increased performance relative to traditional handcrafted methods. Moreover, we implement our models onboard a surrogate for the next-generation spacecraft processor and demonstrate feasible runtimes for online feature tracking.

Dongliang Zheng, Panagiotis Tsiotras

In this work, we introduce a new graph search algorithm, lazy edged based A* (LEA*), for robot motion planning. By using an edge queue and exploiting the idea of lazy search, LEA* is optimally vertex efficient similar to A*, and has improved edge efficiency compared to A*. LEA* is simple and easy to implement with minimum modification to A*, resulting in a very small overhead compared to previous lazy search algorithms. We also explore the effect of inflated heuristics, which results in the weighted LEA* (wLEA*). We show that the edge efficiency of wLEA* becomes close to LazySP and, thus is near-optimal. We test LEA* and wLEA* on 2D planning problems and planning of a 7-DOF manipulator. We perform a thorough comparison with previous algorithms by considering sparse, medium, and cluttered random worlds and small, medium, and large graph sizes. Our results show that LEA* and wLEA* are the fastest algorithms to find the plan compared to previous algorithms.

Juan-Diego Florez, Mehregan Dor, Panagiotis Tsiotras

We propose a standalone monocular visual Simultaneous Localization and Mapping (vSLAM) initialization pipeline for autonomous space robots. Our method, a state-of-the-art factor graph optimization pipeline, extends Structure from Small Motion (SfSM) to robustly initialize a monocular agent in spacecraft inspection trajectories, addressing visual estimation challenges such as weak-perspective projection and center-pointing motion, which exacerbates the bas-relief ambiguity, dominant planar geometry, which causes motion estimation degeneracies in classical Structure from Motion, and dynamic illumination conditions, which reduce the survivability of visual information. We validate our approach on realistic, simulated satellite inspection image sequences with a tumbling spacecraft and demonstrate the method's effectiveness over existing monocular initialization procedures.

Vignesh Sivaramakrishnan, Krishna C. Kalagarla, Rosalyn Devonport et al.

We present a neural network verification toolbox to 1) assess the probability of satisfaction of a constraint, and 2) synthesize a set expansion factor to achieve the probability of satisfaction. Specifically, the tool box establishes with a user-specified level of confidence whether the output of the neural network for a given input distribution is likely to be contained within a given set. Should the tool determine that the given set cannot satisfy the likelihood constraint, the tool also implements an approach outlined in this paper to alter the constraint set to ensure that the user-defined satisfaction probability is achieved. The toolbox is comprised of sampling-based approaches which exploit the properties of signed distance function to define set containment.

Travis Driver, Andrew Vaughan, Yang Cheng et al.

This paper proposes the incorporation of techniques from stereophotoclinometry (SPC) into a keypoint-based structure-from-motion (SfM) system to estimate the surface normal and albedo at detected landmarks to improve autonomous surface and shape characterization of small celestial bodies from in-situ imagery. In contrast to the current state-of-the-practice method for small body shape reconstruction, i.e., SPC, which relies on human-in-the-loop verification and high-fidelity a priori information to achieve accurate results, we forego the expensive maplet estimation step and instead leverage dense keypoint measurements and correspondences from an autonomous keypoint detection and matching method based on deep learning to provide the necessary photogrammetric constraints. Moreover, we develop a factor graph-based approach allowing for simultaneous optimization of the spacecraft's pose, landmark positions, Sun-relative direction, and surface normals and albedos via fusion of Sun sensor measurements and image keypoint measurements. The proposed framework is validated on real imagery of the Cornelia crater on Asteroid 4 Vesta, along with pose estimation and mapping comparison against an SPC reconstruction, where we demonstrate precise alignment to the SPC solution without relying on any a priori camera pose and topography information or humans-in-the-loop

George Rapakoulias, Ali Reza Pedram, Panagiotis Tsiotras

The Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy to drive a McKean-Vlassov stochastic differential equation from one probability measure to another. In the context of multi-agent control, the objective is to control the configuration of a swarm of identical, interacting cooperative agents, as captured by the time-varying probability measure of their state. Available methods for solving this problem for distributions with continuous support rely either on spatial discretizations of the problem's domain or on approximating optimal solutions using neural networks trained through stochastic optimization schemes. For agents following Linear Time Varying dynamics, and for Gaussian Mixture Model boundary distributions, we propose a highly efficient parameterization to approximate the optimal solutions of the corresponding MFSB in closed form, without any learning step. Our proposed approach consists of a mixture of elementary policies, each solving a Gaussian-to-Gaussian Covariance Steering problem from the components of the initial mixture to the components of the terminal mixture. Leveraging the semidefinite formulation of the Covariance Steering problem, the proposed solver can handle probabilistic constraints on the system's state while maintaining numerical tractability. We illustrate our approach on a variety of numerical examples.

Fangji Wang, Panagiotis Tsiotras

Branch-and-bound with preactivation splitting has been shown highly effective for deterministic verification of neural networks. In this paper, we extend this framework to the probabilistic setting. We propose BaB-prob that iteratively divides the original problem into subproblems by splitting preactivations and leverages linear bounds computed by linear bound propagation to bound the probability for each subproblem. We prove soundness and completeness of BaB-prob for feedforward-ReLU neural networks. Furthermore, we introduce the notion of uncertainty level and design two efficient strategies for preactivation splitting, yielding BaB-prob-ordered and BaB+BaBSR-prob. We evaluate BaB-prob on untrained networks, MNIST and CIFAR-10 models, respectively, and VNN-COMP 2025 benchmarks. Across these settings, our approach consistently outperforms state-of-the-art approaches in medium- to high-dimensional input problems.

Travis Driver, Andrew Vaughan, Yang Cheng et al.

Image-based surface reconstruction and characterization is crucial for missions to small celestial bodies, as it informs mission planning, navigation, and scientific analysis. However, current state-of-the-practice methods, such as stereophotoclinometry (SPC), rely heavily on human-in-the-loop verification and high-fidelity a priori information. This paper proposes Photoclinometry-from-Motion (PhoMo), a novel framework that incorporates photoclinometry techniques into a keypoint-based structure-from-motion (SfM) system to estimate the surface normal and albedo at detected landmarks to improve autonomous surface and shape characterization of small celestial bodies from in-situ imagery. In contrast to SPC, we forego the expensive maplet estimation step and instead use dense keypoint measurements and correspondences from an autonomous keypoint detection and matching method based on deep learning. Moreover, we develop a factor graph-based approach allowing for simultaneous optimization of the spacecraft's pose, landmark positions, Sun-relative direction, and surface normals and albedos via fusion of Sun vector measurements and image keypoint measurements. The proposed framework is validated on real imagery taken by the Dawn mission to the asteroid 4 Vesta and the minor planet 1 Ceres and compared against an SPC reconstruction, where we demonstrate superior rendering performance compared to an SPC solution and precise alignment to a stereophotogrammetry (SPG) solution without relying on any a priori camera pose and topography information or humans-in-the-loop.

Hemanth Manjunatha, Panagiotis Tsiotras

Deep learning has revolutionized autonomous driving by enabling vehicles to perceive and interpret their surroundings with remarkable accuracy. This progress is attributed to various deep learning models, including Mediated Perception, Behavior Reflex, and Direct Perception, each offering unique advantages and challenges in enhancing autonomous driving capabilities. However, there is a gap in research addressing integrating these approaches and understanding their relevance in diverse driving scenarios. This study introduces three distinct neural network models corresponding to Mediated Perception, Behavior Reflex, and Direct Perception approaches. We explore their significance across varying driving conditions, shedding light on the strengths and limitations of each approach. Our architecture fuses information from the base, future latent vector prediction, and auxiliary task networks, using global routing commands to select appropriate action sub-networks. We aim to provide insights into effectively utilizing diverse modeling strategies in autonomous driving by conducting experiments and evaluations. The results show that the ensemble model performs better than the individual approaches, suggesting that each modality contributes uniquely toward the performance of the overall model. Moreover, by exploring the significance of each modality, this study offers a roadmap for future research in autonomous driving, emphasizing the importance of leveraging multiple models to achieve robust performance.

Hemanth Manjunatha, Andrey Pak, Dimitar Filev et al.

Autonomous driving has received a great deal of attention in the automotive industry and is often seen as the future of transportation. The development of autonomous driving technology has been greatly accelerated by the growth of end-to-end machine learning techniques that have been successfully used for perception, planning, and control tasks. An important aspect of autonomous driving planning is knowing how the environment evolves in the immediate future and taking appropriate actions. An autonomous driving system should effectively use the information collected from the various sensors to form an abstract representation of the world to maintain situational awareness. For this purpose, deep learning models can be used to learn compact latent representations from a stream of incoming data. However, most deep learning models are trained end-to-end and do not incorporate any prior knowledge (e.g., from physics) of the vehicle in the architecture. In this direction, many works have explored physics-infused neural network (PINN) architectures to infuse physics models during training. Inspired by this observation, we present a Kalman filter augmented recurrent neural network architecture to learn the latent representation of the traffic flow using front camera images only. We demonstrate the efficacy of the proposed model in both imitation and reinforcement learning settings using both simulated and real-world datasets. The results show that incorporating an explicit model of the vehicle (states estimated using Kalman filtering) in the end-to-end learning significantly increases performance.

Dongliang Zheng, Panagiotis Tsiotras

In this work, we develop the Batch Belief Trees (BBT) algorithm for motion planning under motion and sensing uncertainties. The algorithm interleaves between batch sampling, building a graph of nominal trajectories in the state space, and searching over the graph to find belief space motion plans. By searching over the graph, BBT finds sophisticated plans that will visit (and revisit) information-rich regions to reduce uncertainty. One of the key benefits of this algorithm is the modified interplay between exploration and exploitation. Instead of an exhaustive search (exploitation) after one exploration step, the proposed algorithm uses batch samples to explore the state space and, in addition, does not require exhaustive search before the next iteration of batch sampling, which adds flexibility.The algorithm finds motion plans that converge to the optimal one as more samples are added to the graph. We test BBT in different planning environments. Our numerical investigation confirms that BBT finds non-trivial motion plans and is faster compared with previous similar methods.

Ji Yin, Zhiyuan Zhang, Evangelos Theodorou et al.

This paper presents a novel control approach for autonomous systems operating under uncertainty. We combine Model Predictive Path Integral (MPPI) control with Covariance Steering (CS) theory to obtain a robust controller for general nonlinear systems. The proposed Covariance-Controlled Model Predictive Path Integral (CC-MPPI) controller addresses the performance degradation observed in some MPPI implementations owing to unexpected disturbances and uncertainties. Namely, in cases where the environment changes too fast or the simulated dynamics during the MPPI rollouts do not capture the noise and uncertainty in the actual dynamics, the baseline MPPI implementation may lead to divergence. The proposed CC-MPPI controller avoids divergence by controlling the dispersion of the rollout trajectories at the end of the prediction horizon. Furthermore, the CC-MPPI has adjustable trajectory sampling distributions that can be changed according to the environment to achieve efficient sampling. Numerical examples using a ground vehicle navigating in challenging environments demonstrate the proposed approach.

Dongliang Zheng, Panagiotis Tsiotras

Sampling-based motion planning algorithms such as RRT* are well-known for their ability to quickly find an initial solution and then converge to the optimal solution asymptotically. However, the convergence rate can be slow for highdimensional planning problems, particularly for dynamical systems where the sampling space is not just the configuration space but the full state space. In this paper, we introduce the idea of using a partial-final-state-free (PFF) optimal controller in kinodynamic RRT* [1] to reduce the dimensionality of the sampling space. Instead of sampling the full state space, the proposed accelerated kinodynamic RRT*, called Kino-RRT*, only samples part of the state space, while the rest of the states are selected by the PFF optimal controller. We also propose a delayed and intermittent update of the optimal arrival time of all the edges in the RRT* tree to decrease the computation complexity of the algorithm. We tested the proposed algorithm using 4-D and 10-D state-space linear systems and showed that Kino-RRT* converges much faster than the kinodynamic RRT* algorithm.

Jaein Lim, Siddhartha Srinivasa, Panagiotis Tsiotras

We present an incremental search algorithm, called Lifelong-GLS, which combines the vertex efficiency of Lifelong Planning A* (LPA*) and the edge efficiency of Generalized Lazy Search (GLS) for efficient replanning on dynamic graphs where edge evaluation is expensive. We use a lazily evaluated LPA* to repair the cost-to-come inconsistencies of the relevant region of the current search tree based on the previous search results, and then we restrict the expensive edge evaluations only to the current shortest subpath as in the GLS framework. The proposed algorithm is complete and correct in finding the optimal solution in the current graph, if one exists. We also show that the search returns a bounded suboptimal solution, if an inflated heuristic edge weight is used and the tree repairing propagation is truncated early for faster search. Finally, we show the efficiency of the proposed algorithm compared to the standard LPA* and the GLS algorithms over consecutive search episodes in a dynamic environment. For each search, the proposed algorithm reduces the edge evaluations by a significant amount compared to the LPA*. Both the number of vertex expansions and the number of edge evaluations are reduced substantially compared to GLS, as the proposed algorithm utilizes previous search results to facilitate the new search.

Dongliang Zheng, Jack Ridderhof, Panagiotis Tsiotras et al.

A new belief space planning algorithm, called covariance steering Belief RoadMap (CS-BRM), is introduced, which is a multi-query algorithm for motion planning of dynamical systems under simultaneous motion and observation uncertainties. CS-BRM extends the probabilistic roadmap (PRM) approach to belief spaces and is based on the recently developed theory of covariance steering (CS) that enables guaranteed satisfaction of terminal belief constraints in finite-time. The nodes in the CS-BRM are sampled in belief space and represent distributions of the system states. A covariance steering controller steers the system from one BRM node to another, thus acting as an edge controller of the corresponding belief graph that ensures belief constraint satisfaction. After the edge controller is computed, a specific edge cost is assigned to that edge. The CS-BRM algorithm allows the sampling of non-stationary belief nodes, and thus is able to explore the velocity space and find efficient motion plans. The performance of CS-BRM is evaluated and compared to a previous belief space planning method, demonstrating the benefits of the proposed approach.

Kelsey P. Hawkins, Ali Pakniyat, Panagiotis Tsiotras

Two novel numerical estimators are proposed for solving forward-backward stochastic differential equations (FBSDEs) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. In contrast to the current numerical approaches which are based on the discretization of the continuous-time FBSDE, we propose a converse approach, namely, we obtain a discrete-time approximation of the on-policy value function, and then we derive a discrete-time estimator that resembles the continuous-time counterpart. The proposed approach allows for the construction of higher accuracy estimators along with error analysis. The approach is applied to the policy improvement step in reinforcement learning. Numerical results and error analysis are demonstrated using (i) a scalar nonlinear stochastic optimal control problem and (ii) a four-dimensional linear quadratic regulator (LQR) problem. The proposed estimators show significant improvement in terms of accuracy in both cases over Euler-Maruyama-based estimators used in competing approaches. In the case of LQR problems, we demonstrate that our estimators result in near machine-precision level accuracy, in contrast to previously proposed methods that can potentially diverge on the same problems.

Sagar Suhas Joshi, Seth Hutchinson, Panagiotis Tsiotras

Sampling-based algorithms solve the path planning problem by generating random samples in the search-space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased towards exploration to acquire information about the search-space. In contrast, this work proposes an optimization-based procedure that generates new samples to improve the cost-to-come value of vertices in a neighborhood. The application of proposed algorithm adds an exploitative-bias to sampling and results in a faster convergence to the optimal solution compared to other state-of-the-art sampling techniques. This is demonstrated using benchmarking experiments performed fora variety of higher dimensional robotic planning tasks.

Daniel T. Larsson, Dipankar Maity, Panagiotis Tsiotras

In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from information-theoretic signal compression, specifically the information bottleneck (IB) method, to pose a graph abstraction problem as an optimal encoder search over the space of multi-resolution trees. The abstractions emerge in a task-relevant manner as a function of agent information-processing constraints, and are not provided to the system a priori. We detail our formulation and show how the problem can be realized as an integer linear program. A non-trivial numerical example is presented to demonstrate the utility in employing our approach to obtain hierarchical tree abstractions for resource-limited agents.

Jaein Lim, Panagiotis Tsiotras

Both geometric and semantic information of the search space is imperative for a good plan. We encode those properties in a weighted colored graph (geometric information in terms of edge weight and semantic information in terms of edge and vertex color), and propose a generalized A* to find the shortest path among the set of paths with minimal inclusion of low-ranked color edges. We prove the completeness and optimality of this Class-Ordered A* (COA*) algorithm with respect to the hereto defined notion of optimality. The utility of COA* is numerically validated in a ternary graph with feasible, infeasible, and unknown vertices and edges for the cases of a 2D mobile robot, a 3D robotic arm, and a 5D robotic arm with limited sensing capabilities. We compare the results of COA* to that of the regular A* algorithm, the latter of which finds the shortest path regardless of uncertainty, and we show that the COA* dominates the A* solution in terms of finding less uncertain paths.

Yue Guan, Qifan Zhang, Panagiotis Tsiotras

We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the regularized Q-function, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm's ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic hyper-parameter scheduling scheme to further expedite convergence. Empirical results applied to a number of stochastic games verify that the proposed algorithm converges to the Nash equilibrium, while exhibiting a major speed-up over existing algorithms.

Kelsey P. Hawkins, Ali Pakniyat, Evangelos Theodorou et al.

We propose a numerical method for the computation of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. By the use of the Girsanov change of probability measures, it is demonstrated how a rapidly-exploring random tree (RRT) method can be utilized for the forward integration pass, as long as the controlled drift terms are appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of the constructed RRT. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method is developed to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories. The results of the proposed methodology are demonstrated on linear and nonlinear stochastic optimal control problems with non-quadratic running costs, which reveal significant convergence improvements over previous FBSDE-based numerical solution methods.

Venkata Ramana Makkapati, Panagiotis Tsiotras

In this paper, we address pursuit-evasion problems involving multiple pursuers and multiple evaders. The pursuer and the evader teams are assumed to be heterogeneous, in the sense that each team has agents with different speed capabilities. The pursuers are all assumed to be following a constant bearing strategy. A dynamic divide and conquer approach, where at every time instant each evader is assigned to a set of pursuers based on the instantaneous positions of all the players, is introduced to solve the multi-agent pursuit problem. In this regard, the corresponding multi-pursuer single-evader problem is analyzed first. Assuming that the evader can follow any strategy, a dynamic task allocation algorithm is proposed for the pursuers. The algorithm is based on the well-known Apollonius circle and allows the pursuers to allocate their resources in an intelligent manner while guaranteeing the capture of the evader in minimum time. The proposed algorithm is then extended to assign pursuers in multi-evader settings that is proven to capture all the evaders in finite time.

Sagar Suhas Joshi, Seth Hutchinson, Panagiotis Tsiotras

Anytime sampling-based methods are an attractive technique for solving kino-dynamic motion planning problems. These algorithms scale well to higher dimensions and can efficiently handle state and control constraints. However, an intelligent exploration strategy is required to accelerate their convergence and avoid redundant computations. Using ideas from reachability analysis, this work defines a "Time-Informed Set", that focuses the search for time-optimal kino-dynamic planning after an initial solution is found. Such a Time-Informed Set (TIS) includes all trajectories that can potentially improve the current best solution and hence exploration outside this set is redundant. Benchmarking experiments show that an exploration strategy based on the TIS can accelerate the convergence of sampling-based kino-dynamic motion planners.

R. Connor Lawson, Linda Wills, Panagiotis Tsiotras

Sampling-based planning has become a de facto standard for complex robots given its superior ability to rapidly explore high-dimensional configuration spaces. Most existing optimal sampling-based planning algorithms are sequential in nature and cannot take advantage of wide parallelism available on modern computer hardware. Further, tight synchronization of exploration and exploitation phases in these algorithms limits sample throughput and planner performance. Policy Iteration RRT# (PI-RRT#) exposes fine-grained parallelism during the exploitation phase, but this parallelism has not yet been evaluated using a concrete implementation. We first present a novel GPU implementation of PI-RRT#'s exploitation phase and discuss data structure considerations to maximize parallel performance. Our implementation achieves 3-4x speedup over a serial PI-RRT# implementation for a 77.9% decrease in overall planning time on average. As a second contribution, we introduce the Batched-Extension RRT# algorithm, which loosens the synchronization present in PI-RRT# to realize independent 12.97x and 12.54x speedups under serial and parallel exploitation, respectively.

Hemanth Sarabu, Venkata Ramana Makkapati, Vinodhini Comandur et al.

We address the issue of safe optimal path planning under parametric uncertainties using a novel regularizer that allows trading off optimality with safety. The proposed regularizer leverages the notion that collisions may be modeled as constraint violations in an optimal control setting in order to produce open-loop trajectories with reduced risk of collisions. The risk of constraint violation is evaluated using a state-dependent relevance function and first-order variations in the constraint function with respect to parametric variations. The approach is generic and can be adapted to any optimal control formulation that deals with constraints under parametric uncertainty. Simulations using a holonomic robot avoiding multiple dynamic obstacles with uncertain velocities are used to demonstrate the effectiveness of the proposed approach. Finally, we introduce the car vs. train problem to emphasize the dependence of the resultant risk aversion behavior on the form of the constraint function used to derive the regularizer.

Sagar Suhas Joshi, Panagiotis Tsiotras

Asymptotically optimal sampling-based planners require an intelligent exploration strategy to accelerate convergence. After an initial solution is found, a necessary condition for improvement is to generate new samples in the so-called "Informed Set". However, Informed Sampling can be ineffective in focusing search if the chosen heuristic fails to provide a good estimate of the solution cost. This work proposes an algorithm to sample the "Relevant Region" instead, which is a subset of the Informed Set. The Relevant Region utilizes cost-to-come information from the planner's tree structure, reduces dependence on the heuristic, and further focuses the search. Benchmarking tests in uniform and general cost-space settings demonstrate the efficacy of Relevant Region sampling.

Justin Zheng, Kazuhide Okamoto, Panagiotis Tsiotras

This work proposes a new self-driving framework that uses a human driver control model, whose feature-input values are extracted from images using deep convolutional neural networks (CNNs). The development of image processing techniques using CNNs along with accelerated computing hardware has recently enabled real-time detection of these feature-input values. The use of human driver models can lead to more "natural" driving behavior of self-driving vehicles. Specifically, we use the well-known two-point visual driver control model as the controller, and we use a top-down lane cost map CNN and the YOLOv2 CNN to extract feature-input values. This framework relies exclusively on inputs from low-cost sensors like a monocular camera and wheel speed sensors. We experimentally validate the proposed framework on an outdoor track using a 1/5th-scale autonomous vehicle platform.

Brian Goldfain, Paul Drews, Changxi You et al.

This article presents AutoRally, a 1$:$5 scale robotics testbed for autonomous vehicle research. AutoRally is designed for robustness, ease of use, and reproducibility, so that a team of two people with limited knowledge of mechanical engineering, electrical engineering, and computer science can construct and then operate the testbed to collect real world autonomous driving data in whatever domain they wish to study. Complete documentation to construct and operate the platform is available online along with tutorials, example controllers, and a driving dataset collected at the Georgia Tech Autonomous Racing Facility. Offline estimation algorithms are used to determine parameters for physics-based dynamics models using an adaptive limited memory joint state unscented Kalman filter. Online vehicle state estimation using a factor graph optimization scheme and a convolutional neural network for semantic segmentation of drivable surface are presented. All algorithms are tested with real world data from the fleet of six AutoRally robots at the Georgia Tech Autonomous Racing Facility tracks, and serve as a demonstration of the robot$'$s capabilities.

Daniel T. Larsson, Daniel Braun, Panagiotis Tsiotras

In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework ignores computational limitations while searching for optimal policies, essentially assuming that the acting agent is perfectly rational and aims for exact optimality. Using the free-energy, a variational principle is introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programming (DP) and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment.

Oktay Arslan, Panagiotis Tsiotras

Recent progress in randomized motion planners has led to the development of a new class of sampling-based algorithms that provide asymptotic optimality guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals that the so-called "rewiring" step in these algorithms can be interpreted as a local policy iteration (PI) step (i.e., a local policy evaluation step followed by a local policy improvement step) so that asymptotically, as the number of samples tend to infinity, both algorithms converge to the optimal path almost surely (with probability 1). Policy iteration, along with value iteration (VI) are common methods for solving dynamic programming (DP) problems. Based on this observation, recently, the RRT$^{\#}$ algorithm has been proposed, which performs, during each iteration, Bellman updates (aka "backups") on those vertices of the graph that have the potential of being part of the optimal path (i.e., the "promising" vertices). The RRT$^{\#}$ algorithm thus utilizes dynamic programming ideas and implements them incrementally on randomly generated graphs to obtain high quality solutions. In this work, and based on this key insight, we explore a different class of dynamic programming algorithms for solving shortest-path problems on random graphs generated by iterative sampling methods. These class of algorithms utilize policy iteration instead of value iteration, and thus are better suited for massive parallelization. Contrary to the RRT* algorithm, the policy improvement during the rewiring step is not performed only locally but rather on a set of vertices that are classified as "promising" during the current iteration. This tends to speed-up the whole process. The resulting algorithm, aptly named Policy Iteration-RRT$^{\#}$ (PI-RRT$^{\#}$) is the first of a new class of DP-inspired algorithms for randomized motion planning that utilize PI methods.

Oktay Arslan, Karl Berntorp, Panagiotis Tsiotras

Motion planning under differential constraints, kinodynamic motion planning, is one of the canonical problems in robotics. Currently, state-of-the-art methods evolve around kinodynamic variants of popular sampling-based algorithms, such as Rapidly-exploring Random Trees (RRTs). However, there are still challenges remaining, for example, how to include complex dynamics while guaranteeing optimality. If the open-loop dynamics are unstable, exploration by random sampling in control space becomes inefficient. We describe a new sampling-based algorithm, called CL-RRT#, which leverages ideas from the RRT# algorithm and a variant of the RRT algorithm that generates trajectories using closed-loop prediction. The idea of planning with closed-loop prediction allows us to handle complex unstable dynamics and avoids the need to find computationally hard steering procedures. The search technique presented in the RRT# algorithm allows us to improve the solution quality by searching over alternative reference trajectories. Numerical simulations using a nonholonomic system demonstrate the benefits of the proposed approach.

Wei Sun, Evangelos Theodorou, Panagiotis Tsiotras

We present one of the first algorithms on model based reinforcement learning and trajectory optimization with free final time horizon. Grounded on the optimal control theory and Dynamic Programming, we derive a set of backward differential equations that propagate the value function and provide the optimal control policy and the optimal time horizon. The resulting policy generalizes previous results in model based trajectory optimization. Our analysis shows that the proposed algorithm recovers the theoretical optimal solution on linear low dimensional problem. Finally we provide application results on nonlinear systems.

Oktay Arslan, Evangelos Theodorou, Panagiotis Tsiotras

This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value function that satisfies a nonlinear partial differential equation, namely, the Hamilton-Jacobi-Bellman equation. This nonlinear PDE must be solved backwards in time, and this computation is intractable for large scale systems. Under certain assumptions, and after applying a logarithmic transformation, an alternative characterization of the optimal policy can be given in terms of a path integral. Path Integral (PI) based control methods have recently been shown to provide elegant solutions to a broad class of stochastic optimal control problems. One of the implementation challenges with this formalism is the computation of the expectation of a cost functional over the trajectories of the unforced dynamics. Computing such expectation over trajectories that are sampled uniformly may induce numerical instabilities due to the exponentiation of the cost. Therefore, sampling of low-cost trajectories is essential for the practical implementation of PI-based methods. In this paper, we use incremental sampling-based algorithms to sample useful trajectories from the unforced system dynamics, and make a novel connection between Rapidly-exploring Random Trees (RRTs) and information-theoretic stochastic optimal control. We show the results from the numerical implementation of the proposed approach to several examples.

Oktay Arslan, Panagiotis Tsiotras

Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), and the Probabilistic Road Maps (PRMs) have become very popular recently, owing to their implementation simplicity and their advantages in handling high-dimensional problems. Although these algorithms work very well in practice, the quality of the computed solution is often not good, i.e., the solution can be far from the optimal one. A recent variation of RRT, namely the RRT* algorithm, bypasses this drawback of the traditional RRT algorithm, by ensuring asymptotic optimality as the number of samples tends to infinity. Nonetheless, the convergence rate to the optimal solution may still be slow. This paper presents a new incremental sampling-based motion planning algorithm based on Rapidly-exploring Random Graphs (RRG), denoted RRT# (RRT "sharp") which also guarantees asymptotic optimality but, in addition, it also ensures that the constructed spanning tree of the geometric graph is consistent after each iteration. In consistent trees, the vertices which have the potential to be part of the optimal solution have the minimum cost-come-value. This implies that the best possible solution is readily computed if there are some vertices in the current graph that are already in the goal region. Numerical results compare with the RRT* algorithm.