Technical Brief

Stochastic Model Predictive Control for Guided Projectiles Under Impact Area Constraints

[+] Author and Article Information
Jonathan Rogers

Assistant Professor
Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 19, 2013; final manuscript received June 25, 2014; published online October 21, 2014. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 137(3), 034503 (Oct 21, 2014) (8 pages) Paper No: DS-13-1453; doi: 10.1115/1.4028084 History: Received November 19, 2013; Revised June 25, 2014

The dynamics of guided projectile systems are inherently stochastic in nature. While deterministic control algorithms such as impact point prediction (IPP) may prove effective in many scenarios, the probability of impacting obstacles and constrained areas within an impact zone cannot be accounted for without accurate uncertainty modeling. A stochastic model predictive guidance algorithm is developed, which incorporates nonlinear uncertainty propagation to predict the impact probability density in real-time. Once the impact distribution is characterized, the guidance system aim point is computed as the solution to an optimization problem. The result is a guidance law that can achieve minimum miss distance while avoiding impact area constraints. Furthermore, the acceptable risk of obstacle impact can be quantified and tuned online. Example trajectories and Monte Carlo simulations demonstrate the effectiveness of the proposed stochastic control formulation in comparison to deterministic guidance schemes.

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Fig. 2

Deterministic and stochastic impact point prediction guidance. Deterministic guidance follows the solid path; stochastic guidance follows the dashed path.

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Fig. 1

Diagram of impact point prediction guidance parameters

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Fig. 7

Obstacle geometry, defilade case

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Fig. 8

Aim point evolution for stochastic IPP guidance, defilade case

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Fig. 9

Range versus altitude and zoom view of target area, defilade example case

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Fig. 10

Obstacle impact probability versus εp, defilade case

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Fig. 4

Aim point evolution, for example scenario

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Fig. 5

Monte Carlo dispersion patterns and mean-centered CEP rings for varying εp, example geometry

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Fig. 6

Obstacle impact probability versus εp, for example scenario

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Fig. 3

Obstacle geometry, example scenario




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