arXiv subjects

Vaibhav Srivastava

Publications and source records attributed to Vaibhav Srivastava.

At least 37 records · Page 2Linked to original sources

arXiv2024

Assistance-Seeking in Human-Supervised Autonomy: Role of Trust and Secondary Task Engagement (Extended Version)

Using a dual-task paradigm, we explore how robot actions, performance, and the introduction of a secondary task influence human trust and engagement. In our study, a human supervisor simultaneously engages in a target-tracking task while supervising a mobile manipulator performing an object collection task. The robot can either autonomously collect the object or ask for human assistance. The human supervisor also has the choice to rely upon or interrupt the robot. Using data from initial experiments, we model the dynamics of human trust and engagement using a linear dynamical system (LDS). Furthermore, we develop a human action model to define the probability of human reliance on the robot. Our model suggests that participants are more likely to interrupt the robot when their trust and engagement are low during high-complexity collection tasks. Using Model Predictive Control (MPC), we design an optimal assistance-seeking policy. Evaluation experiments demonstrate the superior performance of the MPC policy over the baseline policy for most participants.

cs.RO↗

arXiv2024

Online Reduced-Order Data-Enabled Predictive Control

Data-enabled predictive control (DeePC) has garnered significant attention for its ability to achieve safe, data-driven optimal control without relying on explicit system models. Traditional DeePC methods use pre-collected input/output (I/O) data to construct Hankel matrices for online predictive control. However, in systems with evolving dynamics or insufficient pre-collected data, incorporating real-time data into the DeePC framework becomes crucial to enhance control performance. This paper proposes an online DeePC framework for time-varying systems (i.e., systems with evolving dynamics), enabling the algorithm to update the Hankel matrix online by adding real-time informative signals. By exploiting the minimum non-zero singular value of the Hankel matrix, the developed online DeePC selectively integrates informative data and effectively captures evolving system dynamics. Additionally, a numerical singular value decomposition technique is introduced to reduce the computational complexity for updating a reduced-order Hankel matrix. Simulation results on two cases, a linear time-varying system and the vehicle anti-rollover control, demonstrate the effectiveness of the proposed online reduced-order DeePC framework.

eess.SY↗

arXiv2024

A High-Gain Observer Approach to Robust Trajectory Estimation and Tracking for a Multi-rotor UAV

Using the context of trajectory estimation and tracking for multi-rotor unmanned aerial vehicles (UAVs), we explore the challenges in applying high-gain observers to highly dynamic systems. The multi-rotor will operate in the presence of external disturbances and modeling errors. At the same time, the reference trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume the only measurements that are available are the position and orientation of the multi-rotor and the position of the reference system. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the unmeasured multi-rotor states, modeling errors, external disturbances, and the reference trajectory. We design a robust output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. The proposed control method is rigorously analyzed to establish its stability properties. Finally, we illustrate our theoretical results through numerical simulation and experimental validation in which a multi-rotor tracks a moving ground vehicle with an unknown trajectory and dynamics and successfully lands on the vehicle while in motion.

eess.SY↗

arXiv2024

Fostering Human Learning in Sequential Decision-Making: Understanding the Role of Evaluative Feedback

Cognitive rehabilitation, STEM (science, technology, engineering, and math) skill acquisition, and coaching games such as chess often require tutoring decision-making strategies. The advancement of AI-driven tutoring systems for facilitating human learning requires an understanding of the impact of evaluative feedback on human decision-making and skill development. To this end, we conduct human experiments using Amazon Mechanical Turk to study the influence of evaluative feedback on human decision-making in sequential tasks. In these experiments, participants solve the Tower of Hanoi puzzle and receive AI-generated feedback while solving it. We examine how this feedback affects their learning and skill transfer to related tasks. Additionally, treating humans as noisy optimal agents, we employ maximum entropy inverse reinforcement learning to analyze the effect of feedback on the implicit human reward structure that guides their decision making. Lastly, we explore various computational models to understand how people incorporate evaluative feedback into their decision-making processes. Our findings underscore that humans perceive evaluative feedback as indicative of their long-term strategic success, thus aiding in skill acquisition and transfer in sequential decision-making tasks. Moreover, we demonstrate that evaluative feedback fosters a more structured and organized learning experience compared to learning without feedback. Furthermore, our results indicate that providing intermediate goals alone does not significantly enhance human learning outcomes.

cs.HC↗

arXiv2024

Human Motor Learning Dynamics in High-dimensional Tasks

Conventional approaches to enhancing movement coordination, such as providing instructions and visual feedback, are often inadequate in complex motor tasks with multiple degrees of freedom (DoFs). To effectively address coordination deficits in such complex motor systems, it becomes imperative to develop interventions grounded in a model of human motor learning; however, modeling such learning processes is challenging due to the large DoFs. In this paper, we present a computational motor learning model that leverages the concept of motor synergies to extract low-dimensional learning representations in the high-dimensional motor space and the internal model theory of motor control to capture both fast and slow motor learning processes. We establish the model's convergence properties and validate it using data from a target capture game played by human participants. We study the influence of model parameters on several motor learning trade-offs such as speed-accuracy, exploration-exploitation, satisficing, and flexibility-performance, and show that the human motor learning system tunes these parameters to optimize learning and various output performance metrics.

eess.SY↗

arXiv2023

On Multi-Fidelity Impedance Tuning for Human-Robot Cooperative Manipulation

We examine how a human-robot interaction (HRI) system may be designed when input-output data from previous experiments are available. In particular, we consider how to select an optimal impedance in the assistance design for a cooperative manipulation task with a new operator. Due to the variability between individuals, the design parameters that best suit one operator of the robot may not be the best parameters for another one. However, by incorporating historical data using a linear auto-regressive (AR-1) Gaussian process, the search for a new operator's optimal parameters can be accelerated. We lay out a framework for optimizing the human-robot cooperative manipulation that only requires input-output data. We establish how the AR-1 model improves the bound on the regret and numerically simulate a human-robot cooperative manipulation task to show the regret improvement. Further, we show how our approach's input-output nature provides robustness against modeling error through an additional numerical study.

cs.RO↗

arXiv2023

Structural Properties of Optimal Fidelity Selection Policies for Human-in-the-loop Queues

We study optimal fidelity selection for a human operator servicing a queue of homogeneous tasks. The agent can service a task with a normal or high fidelity level, where fidelity refers to the degree of exactness and precision while servicing the task. Therefore, high-fidelity servicing results in higher-quality service but leads to larger service times and increased operator tiredness. We treat the human cognitive state as a lumped parameter that captures psychological factors such as workload and fatigue. The operator's service time distribution depends on her cognitive dynamics and the fidelity level selected for servicing the task. Her cognitive dynamics evolve as a Markov chain in which the cognitive state increases with high probability whenever she is busy and decreases while resting. The tasks arrive according to a Poisson process and the operator is penalized at a fixed rate for each task waiting in the queue. We address the trade-off between high-quality service of the task and consequent penalty due to a subsequent increase in queue length using a discrete-time Semi-Markov Decision Process framework. We numerically determine an optimal policy and the corresponding optimal value function. Finally, we establish the structural properties of an optimal fidelity policy and provide conditions under which the optimal policy is a threshold-based policy.

cs.HC↗

arXiv2023

A Multi-Fidelity Bayesian Approach to Safe Controller Design

Safely controlling unknown dynamical systems is one of the biggest challenges in the field of control. Oftentimes, an approximate model of a system's dynamics exists which provides beneficial information for the selection of controls. However, differences between the approximate and true systems present challenges as well as safety concerns. We propose an algorithm called SAFE-SLOPE to safely evaluate points from a Gaussian process model of a function when its Lipschitz constant is unknown. We establish theoretical guarantees for the performance of SAFE-SLOPE and quantify how multi-fidelity modeling improves the algorithm's performance. Finally, we demonstrate how SAFE-SLOPE achieves lower cumulative regret than a naive sampling method by applying it to find the control gains of a linear time-invariant system.

eess.SY↗

arXiv2023

Coupled Evolutionary Behavioral and Disease Dynamics under Reinfection Risk

We study the interplay between epidemic dynamics and human decision making for epidemics that involve reinfection risk; in particular, the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed game-theoretic setting, individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. For the SIS epidemic, we fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system for both SIS and SIRI models. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.

eess.SY↗

arXiv2022

Deterministic Sequencing of Exploration and Exploitation for Reinforcement Learning

We propose Deterministic Sequencing of Exploration and Exploitation (DSEE) algorithm with interleaving exploration and exploitation epochs for model-based RL problems that aim to simultaneously learn the system model, i.e., a Markov decision process (MDP), and the associated optimal policy. During exploration, DSEE explores the environment and updates the estimates for expected reward and transition probabilities. During exploitation, the latest estimates of the expected reward and transition probabilities are used to obtain a robust policy with high probability. We design the lengths of the exploration and exploitation epochs such that the cumulative regret grows as a sub-linear function of time.

cs.LG↗

arXiv2022

SIS Epidemic Spreading under Multi-layer Population Dispersal in Patchy Environments

We study SIS epidemic spreading models under population dispersal on multi-layer networks. We consider a patchy environment in which each patch comprises individuals belonging to different classes. Individuals disperse to other patches on a multi-layer network in which each layer corresponds to a class. The dispersal on each layer is modeled by a Continuous Time Markov Chain (CTMC). At each time, individuals disperse according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS model. We establish the existence of various equilibria under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We also derive simple conditions that highlight the influence of the multi-layer network on the stability of these equilibria. For this model, we study optimal intervention strategies using a convex optimization framework. Finally, we numerically illustrate the influence of the multi-layer network structure and the effectiveness of the optimal intervention strategies.

math.OC↗

arXiv2022

Towards Modeling Human Motor Learning Dynamics in High-Dimensional Spaces

Designing effective rehabilitation strategies for upper extremities, particularly hands and fingers, warrants the need for a computational model of human motor learning. The presence of large degrees of freedom (DoFs) available in these systems makes it difficult to balance the trade-off between learning the full dexterity and accomplishing manipulation goals. The motor learning literature argues that humans use motor synergies to reduce the dimension of control space. Using the low-dimensional space spanned by these synergies, we develop a computational model based on the internal model theory of motor control. We analyze the proposed model in terms of its convergence properties and fit it to the data collected from human experiments. We compare the performance of the fitted model to the experimental data and show that it captures human motor learning behavior well.

eess.SY↗

arXiv2022

Epidemic Propagation under Evolutionary Behavioral Dynamics: Stability and Bifurcation Analysis

We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the probability of becoming infected but it comes with a cost that is weighed with the instantaneous risk of becoming infected. An infected individual adopting protection transmits a new infection with a smaller probability compared to an unprotected infected individual. We focus on the replicator evolutionary dynamics to model the evolution of protection decisions by susceptible and infected subpopulations. We completely characterize the existence and local stability of the equilibria of the resulting coupled epidemic and replicator dynamics. We further show how the stability of different equilibrium points gets exchanged as certain parameters change. Finally, we investigate the system behavior under timescale separation between the epidemic and the evolutionary dynamics.

eess.SY↗

arXiv2021

Online Estimation and Coverage Control with Heterogeneous Sensing Information

Heterogeneous multi-robot sensing systems are able to characterize physical processes more comprehensively than homogeneous systems. Access to multiple modalities of sensory data allow such systems to fuse information between complementary sources and learn richer representations of a phenomenon of interest. Often, these data are correlated but vary in fidelity, i.e., accuracy (bias) and precision (noise). Low-fidelity data may be more plentiful, while high-fidelity data may be more trustworthy. In this paper, we address the problem of multi-robot online estimation and coverage control by combining low- and high-fidelity data to learn and cover a sensory function of interest. We propose two algorithms for this task of heterogeneous learning and coverage -- namely Stochastic Sequencing of Multi-fidelity Learning and Coverage (SMLC) and Deterministic Sequencing of Multi-fidelity Learning and Coverage (DMLC) -- and prove that they converge asymptotically. In addition, we demonstrate the empirical efficacy of SMLC and DMLC through numerical simulations.

cs.RO↗

arXiv2021

Cloud-Assisted Nonlinear Model Predictive Control for Finite-Duration Tasks

Cloud computing creates new possibilities for control applications by offering powerful computation and storage capabilities. In this paper, we propose a novel cloud-assisted model predictive control (MPC) framework in which we systematically fuse a cloud MPC that uses a high-fidelity nonlinear model but is subject to communication delays with a local MPC that exploits simplified dynamics (due to limited computation) but has timely feedback. Unlike traditional cloud-based control that treats the cloud as powerful, remote, and sole controller in a networked-system control setting, the proposed framework aims at seamlessly integrating the two controllers for enhanced performance. In particular, we formalize the fusion problem for finite-duration tasks by explicitly considering model mismatches and errors due to request-response communication delays. We analyze stability-like properties of the proposed cloud-assisted MPC framework and establish approaches to robustly handling constraints within this framework in spite of plant-model mismatch and disturbances. A fusion scheme is then developed to enhance control performance while satisfying stability-like conditions, the efficacy of which is demonstrated with multiple simulation examples, including an automotive control example to show its industrial application potentials.

eess.SY↗

arXiv2021

Multi-Robot Gaussian Process Estimation and Coverage: A Deterministic Sequencing Algorithm and Regret Analysis

We study the problem of distributed multi-robot coverage over an unknown, nonuniform sensory field. Modeling the sensory field as a realization of a Gaussian Process and using Bayesian techniques, we devise a policy which aims to balance the tradeoff between learning the sensory function and covering the environment. We propose an adaptive coverage algorithm called Deterministic Sequencing of Learning and Coverage (DSLC) that schedules learning and coverage epochs such that its emphasis gradually shifts from exploration to exploitation while never fully ceasing to learn. Using a novel definition of coverage regret which characterizes overall coverage performance of a multi-robot team over a time horizon $T$, we analyze DSLC to provide an upper bound on expected cumulative coverage regret. Finally, we illustrate the empirical performance of the algorithm through simulations of the coverage task over an unknown distribution of wildfires.

cs.RO↗

arXiv2021

In-flight actuator failure recovery of a hexrotor via multiple models and extended high-gain observers

We study an in-flight actuator failure recovery problem for a hexrotor UAV. The hexrotor may experience external disturbances and modeling error, which are accounted for in the control design and distinguished from an actuator failure. A failure of any one actuator occurs during flight and must be identified quickly and accurately. This is achieved through the use of a multiple-model, multiple extended high-gain observer (EHGO) based output feedback control strategy. The family of EHGOs are responsible for estimating states, disturbances, and are used to select the appropriate model based on the system dynamics after a failure has occurred. The proposed method is theoretically analyzed and validated through simulations and experiments.

eess.SY↗

arXiv2021

Phase Reduction and Synchronization of Coupled Noisy Oscillators

We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any internal fluctuations, and (2) a coupling noise which is generated by interactions with other systems. After providing sufficient conditions that foster synchronization in networks of general noisy systems, we focus on weakly coupled networks of noisy oscillators and, using the first- and second-order phase response curves (PRCs), we derive a reduced order stochastic differential equation to describe the corresponding phase evolutions. Finally, we derive synchronization conditions based on the PRCs and illustrate the theoretical results on a couple of models.

math.DS↗