Kendric Ortiz | University of New Mexico (original) (raw)

Papers by Kendric Ortiz

This material is based upon work supported by the National Science Foundation under Awards No. 18... more This material is based upon work supported by the National Science Foundation under Awards No. 1836952 and 1836900. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

arXiv (Cornell University), Jun 2, 2022

Variability in human response creates non-trivial challenges for modeling and control of human-au... more Variability in human response creates non-trivial challenges for modeling and control of human-automation systems. As autonomy becomes pervasive, methods that can accommodate human variability will become paramount, to ensure efficiency, safety, and high levels of performance. We propose an easily computable modeling framework which takes advantage of a metric to assess variability in individual human response in a dynamic task that subjects repeat over several trials. Our approach is based in a transformation of observed trajectories to a reproducing kernel Hilbert space, which captures variability in human response as a distribution embedded within the Hilbert space. We evaluate the similarity across responses via the maximum mean discrepancy, which measures the distance between distributions within the Hilbert space. We apply this metric to a difficult driving task designed to elucidate differences across subjects. We conducted a pilot study with 6 subjects in an advanced driving simulator, in which subjects were tasked with collision avoidance of an obstacle in the middle of the road, around a blind corner, in a nighttime scenario, while steering only with the non-dominant hand.

2022 IEEE Conference on Control Technology and Applications (CCTA)

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information), Mar 1, 2020

Code for the paper, "Learning Approximate Forward Reachable Sets Using Separating Kernels,&q... more Code for the paper, "Learning Approximate Forward Reachable Sets Using Separating Kernels," L4DC 2021.

Automatica

In this paper, we compute finite sample bounds for data-driven approximations of the solution to ... more In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides probabilistic assurances of safety for stochastic systems in a model-free manner. By implicitly embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can approximate the safety probabilities for stochastic systems with arbitrary stochastic disturbances as simple matrix operations and inner products. We present finite sample bounds for pointbased approximations of the safety probabilities through construction of probabilistic confidence bounds that are state-and input-dependent. One advantage of this approach is that the bounds are responsive to non-uniformly sampled data, meaning that tighter bounds are feasible in regions of the state-and input-space with more observations. We numerically evaluate the approach, and demonstrate its efficacy on a neural network-controlled pendulum system.

Code for the paper, "SReachTools Kernel Module: Data-Driven Stochastic Reachability Using Hi... more Code for the paper, "SReachTools Kernel Module: Data-Driven Stochastic Reachability Using Hilbert Space Embeddings of Distributions," HSCC 2021.

ArXiv, 2020

We compute finite sample bounds for approximations of the solution to stochastic reachability pro... more We compute finite sample bounds for approximations of the solution to stochastic reachability problems computed using kernel distribution embeddings, a non-parametric machine learning technique. Our approach enables assurances of safety from observed data, through construction of probabilistic violation bounds on the computed stochastic reachability probability. By embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can compute the safety probabilities for systems with arbitrary disturbances as simple matrix operations and inner products. We present finite sample bounds for the approximation using elements from statistical learning theory. We numerically evaluate the approach, and demonstrate its efficacy on neural net-controlled pendulum system.

ArXiv, 2020

We present algorithms for performing data-driven stochastic reachability as an addition to SReach... more We present algorithms for performing data-driven stochastic reachability as an addition to SReachTools, an open-source stochastic reachability toolbox. Our method leverages a class of machine learning techniques known as kernel embeddings of distributions to approximate the safety probabilities for a wide variety of stochastic reachability problems. By representing the probability distributions of the system state as elements in a reproducing kernel Hilbert space, we can learn the "best fit" distribution via a simple regularized least-squares problem, and then compute the stochastic reachability safety probabilities as simple linear operations. This technique admits finite sample bounds and has known convergence in probability. We implement these methods as part of SReachTools, and demonstrate their use on a double integrator system, on a million-dimensional repeated planar quadrotor system, and a cart-pole system with a black-box neural network controller.

GLOBECOM 2020 - 2020 IEEE Global Communications Conference, 2020

In this paper an Unmanned Aerial Vehicles (UAVs) - enabled dynamic multi-target tracking and data... more In this paper an Unmanned Aerial Vehicles (UAVs) - enabled dynamic multi-target tracking and data collection framework is presented. Initially, a holistic reputation model is introduced to evaluate the targets’ potential in offloading useful data to the UAVs. Based on this model, and taking into account UAVs and targets tracking and sensing characteristics, a dynamic intelligent matching between the UAVs and the targets is performed. In such a setting, the incentivization of the targets to perform the data offloading is based on an effort-based pricing that the UAVs offer to the targets. The emerging optimization problem towards determining each target’s optimal amount of offloaded data and the corresponding effort-based price that the UAV offers to the target, is treated as a Stackelberg game between each target and the associated UAV. The properties of existence, uniqueness and convergence to the Stackelberg Equilibrium are proven. Detailed numerical results are presented highligh...

We present a data-driven method for computing approximate forward reachable sets using separating... more We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as an element in a reproducing kernel Hilbert space using a data-driven approach. Kernel methods provide a computationally efficient representation for the classifier that is the solution to a regularized least squares problem. The solution converges almost surely as the sample size increases, and admits known finite sample bounds. This approach is applicable to stochastic systems with arbitrary disturbances and neural network verification problems by treating the network as a dynamical system, or by considering neural network controllers as part of a closed-loop system. We present our technique on several examples, including a spacecraft rendezvous and docking problem, and two nonlinear system benchmarks with neural network controllers.

This material is based upon work supported by the National Science Foundation under Awards No. 18... more This material is based upon work supported by the National Science Foundation under Awards No. 1836952 and 1836900. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

arXiv (Cornell University), Jun 2, 2022

Variability in human response creates non-trivial challenges for modeling and control of human-au... more Variability in human response creates non-trivial challenges for modeling and control of human-automation systems. As autonomy becomes pervasive, methods that can accommodate human variability will become paramount, to ensure efficiency, safety, and high levels of performance. We propose an easily computable modeling framework which takes advantage of a metric to assess variability in individual human response in a dynamic task that subjects repeat over several trials. Our approach is based in a transformation of observed trajectories to a reproducing kernel Hilbert space, which captures variability in human response as a distribution embedded within the Hilbert space. We evaluate the similarity across responses via the maximum mean discrepancy, which measures the distance between distributions within the Hilbert space. We apply this metric to a difficult driving task designed to elucidate differences across subjects. We conducted a pilot study with 6 subjects in an advanced driving simulator, in which subjects were tasked with collision avoidance of an obstacle in the middle of the road, around a blind corner, in a nighttime scenario, while steering only with the non-dominant hand.

2022 IEEE Conference on Control Technology and Applications (CCTA)

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information), Mar 1, 2020

Code for the paper, "Learning Approximate Forward Reachable Sets Using Separating Kernels,&q... more Code for the paper, "Learning Approximate Forward Reachable Sets Using Separating Kernels," L4DC 2021.

Automatica

In this paper, we compute finite sample bounds for data-driven approximations of the solution to ... more In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides probabilistic assurances of safety for stochastic systems in a model-free manner. By implicitly embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can approximate the safety probabilities for stochastic systems with arbitrary stochastic disturbances as simple matrix operations and inner products. We present finite sample bounds for pointbased approximations of the safety probabilities through construction of probabilistic confidence bounds that are state-and input-dependent. One advantage of this approach is that the bounds are responsive to non-uniformly sampled data, meaning that tighter bounds are feasible in regions of the state-and input-space with more observations. We numerically evaluate the approach, and demonstrate its efficacy on a neural network-controlled pendulum system.

Code for the paper, "SReachTools Kernel Module: Data-Driven Stochastic Reachability Using Hi... more Code for the paper, "SReachTools Kernel Module: Data-Driven Stochastic Reachability Using Hilbert Space Embeddings of Distributions," HSCC 2021.

ArXiv, 2020

We compute finite sample bounds for approximations of the solution to stochastic reachability pro... more We compute finite sample bounds for approximations of the solution to stochastic reachability problems computed using kernel distribution embeddings, a non-parametric machine learning technique. Our approach enables assurances of safety from observed data, through construction of probabilistic violation bounds on the computed stochastic reachability probability. By embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can compute the safety probabilities for systems with arbitrary disturbances as simple matrix operations and inner products. We present finite sample bounds for the approximation using elements from statistical learning theory. We numerically evaluate the approach, and demonstrate its efficacy on neural net-controlled pendulum system.

ArXiv, 2020

We present algorithms for performing data-driven stochastic reachability as an addition to SReach... more We present algorithms for performing data-driven stochastic reachability as an addition to SReachTools, an open-source stochastic reachability toolbox. Our method leverages a class of machine learning techniques known as kernel embeddings of distributions to approximate the safety probabilities for a wide variety of stochastic reachability problems. By representing the probability distributions of the system state as elements in a reproducing kernel Hilbert space, we can learn the "best fit" distribution via a simple regularized least-squares problem, and then compute the stochastic reachability safety probabilities as simple linear operations. This technique admits finite sample bounds and has known convergence in probability. We implement these methods as part of SReachTools, and demonstrate their use on a double integrator system, on a million-dimensional repeated planar quadrotor system, and a cart-pole system with a black-box neural network controller.

GLOBECOM 2020 - 2020 IEEE Global Communications Conference, 2020

In this paper an Unmanned Aerial Vehicles (UAVs) - enabled dynamic multi-target tracking and data... more In this paper an Unmanned Aerial Vehicles (UAVs) - enabled dynamic multi-target tracking and data collection framework is presented. Initially, a holistic reputation model is introduced to evaluate the targets’ potential in offloading useful data to the UAVs. Based on this model, and taking into account UAVs and targets tracking and sensing characteristics, a dynamic intelligent matching between the UAVs and the targets is performed. In such a setting, the incentivization of the targets to perform the data offloading is based on an effort-based pricing that the UAVs offer to the targets. The emerging optimization problem towards determining each target’s optimal amount of offloaded data and the corresponding effort-based price that the UAV offers to the target, is treated as a Stackelberg game between each target and the associated UAV. The properties of existence, uniqueness and convergence to the Stackelberg Equilibrium are proven. Detailed numerical results are presented highligh...

We present a data-driven method for computing approximate forward reachable sets using separating... more We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as an element in a reproducing kernel Hilbert space using a data-driven approach. Kernel methods provide a computationally efficient representation for the classifier that is the solution to a regularized least squares problem. The solution converges almost surely as the sample size increases, and admits known finite sample bounds. This approach is applicable to stochastic systems with arbitrary disturbances and neural network verification problems by treating the network as a dynamical system, or by considering neural network controllers as part of a closed-loop system. We present our technique on several examples, including a spacecraft rendezvous and docking problem, and two nonlinear system benchmarks with neural network controllers.