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Maulik Bhatt

Publications and source records attributed to Maulik Bhatt.

14 recordsLinked to original sources

MIMIC-D: Multi-modal Imitation for MultI-agent Coordination with Decentralized Diffusion Policies

As robots become more integrated in society, their ability to coordinate with other robots and humans on multi-modal tasks (those with multiple valid solutions) is crucial. Such behaviors can be learned from expert demonstrations via imitation learning (IL), but when expert demonstrations are multi-modal, standard IL approaches usually average across modes or collapse to a single mode, preventing effective coordination. Being inspired by diffusion models' ability to capture complex multi-modal trajectory distributions in single-agent settings, we develop a diffusion-based framework for coordinated multi-modal behavior in multi-agent systems. However, existing multi-agent diffusion approaches typically require a centralized planner or explicit communication among agents. This assumption can fail in real-world scenarios where robots must operate independently or with agents like humans that they cannot directly communicate with. Therefore, we propose MIMIC-D, a joint training with decentralized execution paradigm for multi-modal multi-agent IL via diffusion. We jointly train all agents' policies with only local information to achieve implicit coordination. In simulation and hardware experiments, our method exhibits robust multi-modal coordination behavior in various tasks and environments, improving upon state-of-the-art baselines.

cs.RO

Multi-wavelength properties of $z\gtrsim 6$ LISA detectable events

We investigate the intrinsic and observational properties of $z\gtrsim 6$ galaxies hosting coalescing massive black holes (MBHs) that gives rise to gravitational waves (GWs) detectable with the Laser Interferometer Space Antenna (LISA). We adopt a zoom-in cosmological hydrodynamical simulation of galaxy formation and black hole (BH) co-evolution, zoomed-in on a $M_h \sim 10^{12}~\rm M_{\odot}$ dark matter halo at z = 6, which hosts a fast accreting super-massive black hole (SMBH) and a star-forming galaxy. Following the SMBH formation backward in time, we identify the merging events that concurred to its formation and we pick up the ones that are detectable with LISA. Among these LISA detectable events (LDEs), we select those that, based on their intrinsic properties are expected to be bright in one or more electromagnetic (EM) bands. We post-process these events with dust radiative transfer calculations to make predictions about their spectral energy distributions and continuum maps in the JWST to ALMA wavelength range. We compare the spectra arising from galaxies hosting the merging MBHs with those arising from AGN powered by single accreting BHs. We find that it will be impossible to identify an LDE from the continuum SEDs because of the absence of specific imprints from the merging MBHs. We also compute the profile of the H$_{\rm \alpha}$ line arising from LDEs, considering the contribution from their star-forming regions and the accreting MBHs. We find that the presence of two accreting MBHs would be difficult to infer even if both MBHs accrete at super-Eddington rates. We conclude that the combined detection of GW and EM signals from $z\gtrsim 6$ MBHs is challenging not only because of the poor sky-localization provided by LISA, but also because the loudest GW emitters are not massive enough to leave significant signatures in the emission lines arising from the broad line region.

astro-ph.GA

Red, hot, and very metal poor: extreme properties of a massive accreting black hole in the first 500 Myr

The James Webb Space Telescope (JWST) has recently discovered a new population of objects at high redshift referred to as `Little Red Dots' (LRDs). Their nature currently remains elusive, despite their surprisingly high inferred number densities. This emerging population of red point-like sources is reshaping our view of the early Universe and may shed light on the formation of high-redshift supermassive black holes. Here we present a spectroscopically confirmed LRD CANUCS-LRD-z8.6 at $z_{\rm spec}=8.6319\pm 0.0005$ hosting an Active Galactic Nucleus (AGN), using JWST data. This source shows the typical spectral shape of an LRD (blue UV and red optical continuum, unresolved in JWST imaging), along with broad H$\beta$ line emission, detection of high-ionization emission lines (CIV, NIV]) and very high electron temperature indicative of the presence of AGN. This is also combined with a very low metallicity ($Z<0.1 Z_\odot$). The presence of all these diverse features in one source makes CANUCS-LRD-z8.6 unique. We show that the inferred black hole mass of CANUCS-LRD-z8.6 ($M_{\rm BH}=1.0^{+0.6}_{-0.4}\times 10^{8}\rm ~M_\odot$) strongly challenges current standard theoretical models and simulations of black hole formation, and forces us to adopt `ad hoc' prescriptions. Indeed if massive seeds, or light seeds with super-Eddington accretion, are considered, the observed BH mass of CANUCS-LRD-z8.6 at $z=8.6$ can be reproduced. Moreover, the black hole is over-massive compared to its host, relative to the local $M_{\rm BH}-M_*$ relations, pointing towards an earlier and faster evolution of the black hole compared to its host galaxy.

astro-ph.GA

Understanding and Imitating Human-Robot Motion with Restricted Visual Fields

When working around other agents such as humans, it is important to model their perception capabilities to predict and make sense of their behavior. In this work, we consider agents whose perception capabilities are determined by their limited field of view, viewing range, and the potential to miss objects within their viewing range. By considering the perception capabilities and observation model of agents independently from their motion policy, we show that we can better predict the agents' behavior; i.e., by reasoning about the perception capabilities of other agents, one can better make sense of their actions. We perform a user study where human operators navigate a cluttered scene while scanning the region for obstacles with a limited field of view and range. We show that by reasoning about the limited observation space of humans, a robot can better learn a human's strategy for navigating an environment and navigate with minimal collision with dynamic and static obstacles. We also show that this learned model helps it successfully navigate a physical hardware vehicle in real-time. Code available at https://github.com/labicon/HRMotion-RestrictedView.

cs.RO

MultiNash-PF: A Particle Filtering Approach for Computing Multiple Local Generalized Nash Equilibria in Trajectory Games

Modern robotic systems frequently engage in complex multi-agent interactions, many of which are inherently multi-modal, i.e., they can lead to multiple distinct outcomes. To interact effectively, robots must recognize the possible interaction modes and adapt to the one preferred by other agents. In this work, we propose MultiNash-PF, an efficient algorithm for capturing the multimodality in multi-agent interactions. We model interaction outcomes as equilibria of a game-theoretic planner, where each equilibrium corresponds to a distinct interaction mode. Our framework formulates interactive planning as Constrained Potential Trajectory Games (CPTGs), in which local Generalized Nash Equilibria (GNEs) represent plausible interaction outcomes. We propose to integrate the potential game approach with implicit particle filtering, a sample-efficient method for non-convex trajectory optimization. We utilize implicit particle filtering to identify the coarse estimates of multiple local minimizers of the game's potential function. MultiNash-PF then refines these estimates with optimization solvers, obtaining different local GNEs. We show through numerical simulations that MultiNash-PF reduces computation time by up to 50\% compared to a baseline. We further demonstrate the effectiveness of our algorithm in real-world human-robot interaction scenarios, where it successfully accounts for the multi-modal nature of interactions and resolves potential conflicts in real-time.

cs.RO

To What Extent do Open-loop and Feedback Nash Equilibria Diverge in General-Sum Linear Quadratic Dynamic Games?

Dynamic games offer a versatile framework for modeling the evolving interactions of strategic agents, whose steady-state behavior can be captured by the Nash equilibria of the games. Nash equilibria are often computed in feedback, with policies depending on the state at each time, or in open-loop, with policies depending only on the initial state. Empirically, open-loop Nash equilibria (OLNE) could be more efficient to compute, while feedback Nash equilibria (FBNE) often encode more complex interactions. However, it remains unclear exactly which dynamic games yield FBNE and OLNE that differ significantly and which do not. To address this problem, we present a principled comparison study of OLNE and FBNE in linear quadratic (LQ) dynamic games. Specifically, we prove that the OLNE strategies of an LQ dynamic game can be synthesized by solving the coupled Riccati equations of an auxiliary LQ game with perturbed costs. The construction of the auxiliary game allows us to establish conditions under which OLNE and FBNE coincide and derive an upper bound on the deviation between FBNE and OLNE of an LQ game.

eess.SY

Is GN-z11 powered by a super-Eddington massive black hole?

Observations of $z \sim 6$ quasars powered by supermassive black holes (SMBHs; $M_{\rm BH} \sim 10^{8-10}\, M_\odot$) challenge our current understanding of early black hole (BH) formation and evolution. The advent of the James Webb Space Telescope (JWST) has enabled the study of massive BHs (MBHs; $M_{\rm BH}\sim 10^{6-7} \ \mathrm{M}_\odot$) up to $z\sim 11$, thus bridging the properties of $z\sim 6$ quasars to their ancestors. The JWST spectroscopic observations of GN-z11, a well-known $z=10.6$ star-forming galaxy, have been interpreted with the presence of a super-Eddington (Eddington ratio $\equiv \,λ_{\rm Edd}\sim 5.5$) accreting MBH. To test this hypothesis, we used a zoom-in cosmological simulation of galaxy formation and BH co-evolution. We first tested the simulation results against the observed probability distribution function (PDF) of $λ_{\rm Edd}$ found in $z\sim 6$ quasars. Then, in the simulation we selected the BHs that satisfy the following criteria: (a) $10 < z < 11 $, (b) $M_{\rm BH} > 10^6 \ \mathrm{M}_\odot$. Next, we apply the extreme value statistics to the PDF of $λ_{\rm Edd}$ resulting from the simulation and we find that the probability of observing a $z\sim 10-11$ MBH accreting with $λ_{\rm Edd} \sim 5.5$ in the volume surveyed by JWST is very low ($<0.2\%$). We compared our predictions with those in the literature, and discuss the main limitations of our work. Our simulation cannot explain the JWST observations of GN-z11. This might be due to (i) poor resolution and statistics in simulations, (ii) simplistic sub-grid models (e.g. BH accretion and seeding), (iii) uncertainties in the data analysis and interpretation.

astro-ph.GA

Strategic Decision-Making in Multi-Agent Domains: A Weighted Constrained Potential Dynamic Game Approach

In interactive multi-agent settings, decision-making and planning are challenging mainly due to the agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving constrained dynamic games and determining the interaction outcome in the form of generalized Nash Equilibria (GNE) pose computational challenges due to the need for solving constrained coupled optimal control problems. In this paper, we address this challenge by proposing to leverage the special structure of many real-world multi-agent interactions. More specifically, our key idea is to leverage constrained dynamic potential games, which are games for which GNE can be found by solving a single constrained optimal control problem associated with minimizing the potential function. We argue that constrained dynamic potential games can effectively facilitate interactive decision-making in many multi-agent interactions. We will identify structures in realistic multi-agent interactive scenarios that can be transformed into weighted constrained potential dynamic games (WCPDGs). We will show that the GNE of the resulting WCPDG can be obtained by solving a single constrained optimal control problem. We will demonstrate the effectiveness of the proposed method through various simulation studies and show that we achieve significant improvements in solve time compared to state-of-the-art game solvers. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.

cs.RO

Efficient Constrained Multi-Agent Trajectory Optimization using Dynamic Potential Games

Although dynamic games provide a rich paradigm for modeling agents' interactions, solving these games for real-world applications is often challenging. Many real-world interactive settings involve general nonlinear state and input constraints that couple agents' decisions with one another. In this work, we develop an efficient and fast planner for interactive trajectory optimization in constrained setups using a constrained game-theoretical framework. Our key insight is to leverage the special structure of agents' objective and constraint functions that are common in multi-agent interactions for fast and reliable planning. More precisely, we identify the structure of agents' cost and constraint functions under which the resulting dynamic game is an instance of a constrained dynamic potential game. Constrained dynamic potential games are a class of games for which instead of solving a set of coupled constrained optimal control problems, a constrained Nash equilibrium, i.e. a Generalized Nash equilibrium, can be found by solving a single constrained optimal control problem. This simplifies constrained interactive trajectory optimization significantly. We compare the performance of our method in a navigation setup involving four planar agents and show that our method is on average 20 times faster than the state-of-the-art. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.

cs.RO

RAPID: Autonomous Multi-Agent Racing using Constrained Potential Dynamic Games

In this work, we consider the problem of autonomous racing with multiple agents where agents must interact closely and influence each other to compete. We model interactions among agents through a game-theoretical framework and propose an efficient algorithm for tractably solving the resulting game in real time. More specifically, we capture interactions among multiple agents through a constrained dynamic game. We show that the resulting dynamic game is an instance of a simple-to-analyze class of games. Namely, we show that our racing game is an instance of a constrained dynamic potential game. An important and appealing property of dynamic potential games is that a generalized Nash equilibrium of the underlying game can be computed by solving a single constrained optimal control problem instead of multiple coupled constrained optimal control problems. Leveraging this property, we show that the problem of autonomous racing is greatly simplified and develop RAPID (autonomous multi-agent RAcing using constrained PotentIal Dynamic games), a racing algorithm that can be solved tractably in real-time. Through simulation studies, we demonstrate that our algorithm outperforms the state-of-the-art approach. We further show the real-time capabilities of our algorithm in hardware experiments.

eess.SY

Asymptotically Stable Optimal Multi-rate Rigid Body Attitude Estimation based on Lagrange-d'Alembert Principle

The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.

eess.SY

Discrete-time Rigid Body Pose Estimation based on Lagrange-d'Alembert principle

The problem of rigid body pose estimation is treated in discrete-time via discrete Lagrange-d'Alembert principle and discrete Lyapunov methods. The position and attitude of the rigid body are to be estimated simultaneously with the help of vision and inertial sensors. For the discrete-time estimation of pose, the continuous-time rigid body kinematics equations are discretized appropriately. We approach the pose estimation problem as minimising the energies stored in the errors of estimated quantities. With the help of measurements obtained through optical sensors, artificial rotational and translation potential energy-like terms have been designed. Similarly, artificial rotational and translation kinetic energy-like terms have been devised using inertial sensor measurements. This allows us to construct a discrete-time Lagrangian as the difference of the kinetic and potential energy like terms, to which a Lagrange-d'Alembert principle is applied to obtain an optimal pose estimation filter. The dissipation terms in the optimal filter are designed through discrete-Lyapunov analysis on a suitably constructed Morse-Lyapunov function and the overall scheme is proven to be almost globally asymptotically stable. The filtering scheme is simulated using noisy sensor data to verify the theoretical properties.

math.OC

Rigid Body Geometric Attitude Estimator using Multi-rate Sensors

A geometric estimator is proposed for the rigid body attitude under multi-rate measurements using discrete-time Lyapunov stability analysis in this work. The angular velocity measurements are assumed to be sampled at a higher rate compared to the attitude. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. In the case when measurements are absent, a discrete-time model for attitude kinematics is assumed in order to propagate the measurements. A discrete-time Lyapunov function is constructed as the sum of a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. A filtering scheme is obtained by discrete-time stability analysis using a suitable Lyapunov function. The analysis shows that the filtering scheme is exponentially stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. Simulation results exhibit convergence of the estimated states to a bounded neighborhood of the actual states.

eess.SY

Production of secondary particles in heavy nuclei interactions in supernova remnants

Depending on their type, supernova remnants may have ejecta material with high abundance of heavy elements such as carbon or oxygen. In addition, core-collapse supernovae explode in the wind material of their progenitor star that may also have a high abundance of heavy elements. Hadronic collisions in these enriched media spawn the production of gamma rays, neutrinos, and secondary electrons with spectra that cannot be scaled from those calculated for pp collisions, potentially leading to erroneous results. We used Monte-Carlo event generators to calculate the differential production rate of particles such as gamma rays, neutrinos, and secondary electrons for H, He, C, and O nuclei as projectiles and as target material. The cross sections and the multiplicity spectra are separately computed for each of the 16 combinations of projectile and target. We describe characteristic effects of heavy nuclei in the shape and normalization of the spectra of various particles produced.

astro-ph.HE