A stochastic approach to Dubins feedback control for target tracking

Anderson, Ross P.; Milutinović, Dejan

doi:10.1109/iros.2011.6094760

Cited by 17 publications

(12 citation statements)

References 25 publications

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“…A noncontinuous grid decomposition strategy for planning parameterized paths for UAVs is proposed in [60] with the objective to localize a single target by maximizing the probability of detection when the target motion is modeled as a Markov process. Standoff tracking techniques are commonly used to control the agent to achieve a desired standoff configuration from the target usually by orbiting around it [26], [61], [62]. A probabilistic planning approach for localizing a group of targets using vision sensors is detailed in [63].…”

Section: B Motion Planning For Target Localizationmentioning

confidence: 99%

Real-Time Area Coverage and Target Localization Using Receding-Horizon Ergodic Exploration

et al. 2018

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Abstract-Although a number of solutions exist for the problems of coverage, search and target localization-commonly addressed separately-whether there exists a unified strategy that addresses these objectives in a coherent manner without being application-specific remains a largely open research question. In this paper, we develop a receding-horizon ergodic control approach, based on hybrid systems theory, that has the potential to fill this gap. The nonlinear model predictive control algorithm plans real-time motions that optimally improve ergodicity with respect to a distribution defined by the expected information density across the sensing domain. We establish a theoretical framework for global stability guarantees with respect to a distribution. Moreover, the approach is distributable across multiple agents, so that each agent can independently compute its own control while sharing statistics of its coverage across a communication network. We demonstrate the method in both simulation and in experiment in the context of target localization, illustrating that the algorithm is independent of the number of targets being tracked and can be run in real-time on computationally limited hardware platforms.

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Section: B Motion Planning For Target Localizationmentioning

confidence: 99%

Real-Time Area Coverage and Target Localization Using Receding-Horizon Ergodic Exploration

et al. 2018

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“…the gap between the best (smallest) and second-best response. ∆(x) measures the difficulty in ascertaining C(x): for locations where µ (1) − µ (2) is big, we do not need high fidelity, since the respective minimal response surface is easy to identify; conversely for locations where µ (1) − µ (2) is small we need more precision. Accordingly, we wish to preferentially sample where ∆(x) is small.…”

Section: Summary Of Approachmentioning

confidence: 99%

“…In terms of design over L, exploration suggests to spend the budget on learning the responses offering the biggest information gain. Namely, substantial benefits are available by discriminating over the sampling indices through locally concentrating on the (two) most promising surfaces µ (1) , µ (2) . This strategy is much more efficient than the naive equal sampling of each Y .…”

Section: Summary Of Approachmentioning

confidence: 99%

Sequential Design for Ranking Response Surfaces

Hu¹,

Ludkovski²

2017

SIAM/ASA J. Uncertainty Quantification

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Abstract. Motivated by the problem of estimating optimal feedback policy maps in stochastic control applications, we propose and analyze sequential design methods for ranking several response surfaces. Namely, given L ≥ 2 response surfaces over a continuous input space X , the aim is to efficiently find the index of the minimal response across the entire X . The response surfaces are not known and have to be noisily sampled one-at-a-time, requiring joint experimental design both in space and response-index dimensions.To generate sequential design heuristics we investigate Bayesian stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging metamodels. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.Key words. sequential design, response surface modeling, stochastic kriging, sequential uncertainty reduction, expected improvement 1. Introduction. A central step in stochastic control problems concerns estimating expected costs-to-go that are used to approximate the optimal feedback control. In simulation approaches to this question, costs-to-go are sampled by generating trajectories of the stochastic system and then regressed against current system state. The resulting Q-values are finally ranked to find the action that minimizes expected costs.When simulation is expensive, computational efficiency and experimental design become important. Sequential strategies rephrase learning the costs-to-go as another dynamic program, with actions corresponding to the sampling decisions. In this article, we explore a Bayesian formulation of this sequential design problem. The ranking objective imposes a novel loss function which mixes classification and regression criteria. Moreover, the presence of multiple stochastic samplers (one for each possible action) and a continuous input space necessitates development of targeted response surface methodologies. In particular, a major innovation is modeling in parallel the spatial correlation within each Q-value, while utilizing a multi-armed bandit perspective for picking which sampler to call next.To obtain a tractable approximation of the Q-values, we advocate the use of Gaussian process metamodels, viewing the latent response surfaces as realizations of a Gaussian random field. Consequently, the ranking criterion is formulated in terms of the posterior uncertainty about each Q-value. Thus, we connect metamodel uncertainty to the sampling decisions, akin to the discretestate frameworks of ranking-and-selection and multi-armed bandits. Our work brings forth a new link between emulation of stochastic simulators and stochastic control, offering a new class of approximate dynamic programming algorithms.

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“…Anderson and Milutinović present an innovative approach to the standoff tracking problem by solving the problem using stochastic optimal control [13]. Modeling the target as a Brownian particle (and the UAV as a deterministic Dubins vehicle), the authors employ specialized value iteration techniques to minimize the expected cost of the total squared distance error discounted over an infinite horizon.…”

Section: Related Workmentioning

confidence: 99%

“…While the existing literature offers methods for target tracking using continuous-time feedback control laws [6][7][8][9][10][11][12] or optimization based methods [13][14][15], these individual works make assumptions that simplify the UAV dynamics, target motion, and/or sensor visibility constraints, thereby hindering the feasibility of a real world implementation with actual hardware. This paper has detailed the design of two optimization-based control policies for vision-based target tracking, where strict trajectories must be flown by an underactuated UAV to maintain visibility and proximity to an unpredictable ground target.…”

Section: Overall Conclusion and Future Workmentioning

confidence: 99%

Vision-based target tracking with a small UAV: Optimization-based control strategies

Quintero

Hespanha

2014

Control Engineering Practice

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This paper considers the problem of a small, fixed-wing UAV equipped with a gimbaled camera autonomously tracking an unpredictable moving ground vehicle. Thus, the UAV must maintain close proximity to the ground target and simultaneously keep the target in its camera's visibility region. To achieve this objective robustly, two novel optimizationbased control strategies are developed. The first assumes an evasive target motion while the second assumes a stochastic target motion. The resulting optimal control policies have been successfully flight tested, thereby demonstrating the efficacy of both approaches in a real-world implementation and highlighting the advantages of one approach over the other.

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A stochastic approach to Dubins feedback control for target tracking

Cited by 17 publications

References 25 publications

Real-Time Area Coverage and Target Localization Using Receding-Horizon Ergodic Exploration

Real-Time Area Coverage and Target Localization Using Receding-Horizon Ergodic Exploration

Sequential Design for Ranking Response Surfaces

Vision-based target tracking with a small UAV: Optimization-based control strategies

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