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Optimization-based Control for Bearing-only Target Search with a Mobile Vehicle

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Pith's one-line read A normalized bi-objective optimization solved in closed form steers a Dubins vehicle to a stationary target using only bearing measurements, with and without global position.

arxiv 1908.00380 v1 pith:MMTVYJKI submitted 2019-08-01 eess.SY cs.SY

Zhuo Li , Keyou You , Shiji Song , Anke Xue This is my paper · ORCID
classification eess.SYcs.SY
keywords positioncontrollertargetvehiclemobileoptimizationoptimization-basedproblem
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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The reading

This paper studies a robot that must reach a stationary target whose location is unknown. The robot only measures the direction, or bearing, to the target, and that measurement is noisy. It moves like a Dubins vehicle, meaning constant speed with limited turning. The authors split the robot's motion into a radial part, toward the target, and a tangential part, around it. That split turns a complicated two-goal control problem into a one-variable optimization problem. The two goals are to reduce uncertainty about the target position and to reduce distance to the target. A single parameter, beta, sets the balance between them. The main theoretical result gives, for each range of beta, an explicit or nearly explicit formula for the best radial speed, and the heading follows from simple geometry. A recursive least-squares estimator feeds the current target estimate into this formula, using the certainty-equivalence idea: pretend the estimate is the truth. Simulations show spiral trajectories that converge near the target, both with GPS and without GPS, using only compass readings and local bearings. The method is cheap to compute and needs no global position. The main caveats are that the estimator is acknowledged to be biased, the closed-loop 'as fast as possible' claim is not proven, and the simulations lack error bars and comparisons to existing methods.
Extended reading notes

Core claim

Theorem 1 gives the exact minimizer of the normalized bi-objective optimization problem (17) for every beta regime, and the certainty-equivalence controller built from this minimizer and a recursive least-squares estimator (Algorithms 1-3) drives the discrete-time Dubins vehicle to approach the unknown stationary target, both with and without global position information, as shown in the simulations.

Load-bearing premise

The controller's near-optimality for the actual closed loop is assumed via the certainty-equivalence principle: the true target range r, bearing phi, and position used in Theorem 1 and equation (10) are replaced by estimates from Algorithms 1 or 3. The estimator is derived under the small-noise approximation sin(m-phi) about m-phi and by ignoring the 1/r(i) weight in the least-squares objective, and the paper states the estimator 'might be biased'. No suboptimality bound or closed-loop convergence proof is given, so the 'as fast as possible' claim is not established for the implemented controller.

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Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The method introduces no new physical entities. The only hand-chosen number is the weighting parameter beta. The derivation assumes a standard Gaussian noise model, a stationary target, exact Dubins kinematics, and imports the CRLB from the cited literature. The two load-bearing approximations are the constancy of vr, vt, phi over one sampling period and certainty equivalence with a recursive estimator that the paper admits may be biased; both are unquantified.

free parameters (1)
  • beta (weighting parameter) = beta = 1 in the default simulation; studied in [0,6]
    User-selected relative weight of the control objective vs. the estimation objective. Not fitted to data, but the search time in Fig. 12 depends on it, and only heuristic guidance is given for choosing it.
assumptions (6)
  • domain assumption The bearing noise e(k) in (1) is zero-mean white Gaussian with known variance sigma^2.
    Used to justify the CRLB expression (5), the least-squares objectives (19)/(24), and the small-noise approximations; Section II-A.
  • domain assumption The target is stationary, and the vehicle obeys the discrete-time Dubins model (2) with constant forward speed and angular velocity held over the sampling interval.
    Problem setup in Section II-A; all geometry in Fig. 3 relies on exact circular-arc motion between samples.
  • standard math The D-optimal CRLB formula (5) from Theorem 1 of [10] is valid for the bearing-only measurement model.
    The estimation objective is imported from an external result; the paper does not re-derive or verify its conditions.
  • ad hoc to paper Within one sampling period, the radial velocity vr, tangential velocity vt, and true bearing phi are constant.
    Assumed in Section III-B after (8) to obtain the Euler-integrated relation (9), feeding the identities (13) and the reduced problem (15). Not exact, since the bearing changes as the vehicle turns.
  • ad hoc to paper The sine-for-error approximation in the Stansfield estimator, replacing m-phi by sin(m-phi), and the neglect of the 1/r(i) weight are accurate enough for the estimate to be usable.
    Section IV-A, Eq. (20)-(21); the paper explicitly notes the resulting estimator 'might be biased', so the closed-loop optimum is not guaranteed.
  • ad hoc to paper Certainty equivalence holds: replacing the true r, phi, pT in the optimal solution by the recursive least-squares estimates preserves near-optimal behavior.
    Invoked at the start of Section IV and used in Algorithm 2; no suboptimality bound or stability proof is provided.

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Pith. "Pith review of Optimization-based Control for Bearing-only Target Search with a Mobile Vehicle." pith.science (2026). https://pith.science/paper/MMTVYJKI

@misc{pith2026190800380,
  author       = {Pith},
  title        = {Pith review of: Optimization-based Control for Bearing-only Target Search with a Mobile Vehicle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MMTVYJKI}},
  note         = {Machine review of arXiv:1908.00380}
}
read the original abstract

This work aims to design an optimization-based controller for a discrete-time Dubins vehicle to approach a target with unknown position as fast as possible by only using bearing measurements. To this end, we propose a bi-objective optimization problem, which jointly considers the performance of estimating the unknown target position and controlling the mobile vehicle to a known position, and then adopt a weighted sum method with normalization to solve it. The controller is given based on the solution of the optimization problem in ties with a least-square estimate of the target position. Moreover, the controller does not need the vehicle's global position information. Finally, simulation results are included to validate the effectiveness of the proposed controller.

Figures

Figures reproduced from arXiv: 1908.00380 by the authors.

Figure 1
Figure 1. The bearing-only target search problem with a mobile vehicle. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The controller architecture for bearing-only target search. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. The bearing-only target search problem in the vehicle’s coordinate. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (7 more)
Figure 6
Figure 6. Figure 6: The trajectories of the vehicle and the estimated positions of the target [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: The trajectory of the vehicle and the estimated positions of the target [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 11
Figure 11. Figure 11: The trajectory of the vehicle and the estimated positions of the target [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 12
Figure 12. Figure 12: The time for target search with different values of [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]
Figure 10
Figure 10. Figure 10: The ranges between the vehicle and the estimated target with different [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 13
Figure 13. Figure 13: A possible case of ˙f(vr) and f(vr) curves. it holds that f(vz) is the minimum if β > 1. For β < 1, the minimum is the smaller one of f(vs) and f(vz) [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 15
Figure 15. Figure 15: A possible case of ˙f(vr) and f(vr) curves. then the minimum of f(vr) is the smaller one of f(vz) and f(vs). The function curves are shown in [PITH_FULL_IMAGE:figures/full_fig_p010_15.png]

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Works this paper leans on

33 extracted references · 31 canonical work pages

  1. [1]

    Optimal path planning with spatial-temporal mobility modeling for individual-based emergency guiding,

    L. W. Chen, J. H. Cheng, and Y . C. Tseng, “Optimal path planning with spatial-temporal mobility modeling for individual-based emergency guiding,” IEEE Transactions on Systems Man & Cybernetics: Systems , vol. 45, no. 12, pp. 1491–1501, 2015

    work page 2015

  2. [2]

    New potential field method for rough terrain path planning using genetic algorithm for a 6-wheel rover,

    R. Raja, A. Dutta, and K. Venkatesh, “New potential field method for rough terrain path planning using genetic algorithm for a 6-wheel rover,” Robotics and Autonomous Systems , vol. 72, pp. 295–306, 2015

    work page 2015

  3. [3]

    Path planning with spatiotemporal optimal stopping for stochastic mission monitoring,

    G. Best, W. Martens, and R. Fitch, “Path planning with spatiotemporal optimal stopping for stochastic mission monitoring,” IEEE Transactions on Robotics, vol. 33, no. 3, pp. 629–646, 2017

    work page 2017

  4. [4]

    Minimum time search for lost targets using cross entropy optimization,

    P. Lanillos, E. Besada-Portas, G. Pajares, and J. J. Ruz, “Minimum time search for lost targets using cross entropy optimization,” in International Conference on Intelligent Robots and Systems . IEEE, 2012, pp. 602– 609. 11

    work page 2012

  5. [5]

    ε⋆: An online coverage path planning algorithm,

    J. Song and S. Gupta, “ε⋆: An online coverage path planning algorithm,” IEEE Transactions on Robotics , vol. 34, no. 2, pp. 526–533, 2018

    work page 2018

  6. [6]

    Multi-UAV convoy protection: An optimal approach to path planning and coordination,

    X. C. Ding, A. R. Rahmani, and M. Egerstedt, “Multi-UAV convoy protection: An optimal approach to path planning and coordination,” IEEE Transactions on Robotics , vol. 26, no. 2, pp. 256–268, 2010

    work page 2010

  7. [7]

    Planning expected-time optimal paths for target search by robot,

    B. Zhang and S. Liu, “Planning expected-time optimal paths for target search by robot,” in World Congress on Intelligent Control and Automa- tion. IEEE, 2012, pp. 3881–3886

    work page 2012

  8. [8]

    C-FOREST: Parallel shortest path planning with superlinear speedup,

    M. Otte and N. Correll, “C-FOREST: Parallel shortest path planning with superlinear speedup,” IEEE Transactions on Robotics , vol. 29, no. 3, pp. 798–806, 2013

    work page 2013

Show all 33 references
  1. [9]

    Single-objective path planning for autonomous robots using reconfigurable analog VLSI,

    S. Koziol, R. Wunderlich, J. Hasler, and M. Stilman, “Single-objective path planning for autonomous robots using reconfigurable analog VLSI,” IEEE Transactions on Systems Man & Cybernetics: Systems , vol. 47, no. 7, pp. 1301–1314, 2017

    2017

  2. [10]

    Optimality analysis of sensor-target geometries in passive localization: Part 1 Bearing-only localization,

    A. N. Bishop, B. Fidan, B. D. Anderson, K. Dogancay, and P. N. Pathirana, “Optimality analysis of sensor-target geometries in passive localization: Part 1 Bearing-only localization,” in International Confer- ence on Intelligent Sensors, Sensor Networks and Information . IEEE, ...

    2007

  3. [11]

    Real-time area coverage and target localization using receding-horizon ergodic exploration,

    A. Mavrommati, E. Tzorakoleftherakis, I. Abraham, and T. D. Murphey, “Real-time area coverage and target localization using receding-horizon ergodic exploration,” IEEE Transactions on Robotics, vol. 34, no. 1, pp. 62–80, 2018

    2018

  4. [12]

    Optimal sensor placement for multiple target positioning with range-only measurements in two-dimensional scenarios,

    D. Moreno-Salinas, A. M. Pascoal, and J. Aranda, “Optimal sensor placement for multiple target positioning with range-only measurements in two-dimensional scenarios,” Sensors, vol. 13, no. 8, p. 10674, 2013

    2013

  5. [13]

    UAV path planning for passive emitter localization,

    K. Dogancay, “UAV path planning for passive emitter localization,” IEEE Transactions on Aerospace and Electronic systems , vol. 48, no. 2, pp. 1150–1166, 2012

    2012

  6. [14]

    Communication aware optimal sensor motion coordination for source localization,

    W. Meng, L. Xie, and W. Xiao, “Communication aware optimal sensor motion coordination for source localization,” IEEE Transactions on Instrumentation and Measurement, vol. 65, no. 11, pp. 2505–2514, 2016

    2016

  7. [15]

    Optimal exploratory paths for a mobile rover,

    F. Lorussi, A. Marigo, and A. Bicchi, “Optimal exploratory paths for a mobile rover,” in International Conference on Robotics and Automation. IEEE, 2001, pp. 2078–2083

    2001

  8. [16]

    Path planning to optimize observability in a planar uniform flow field,

    B. T. Hinson, M. K. Binder, and K. A. Morgansen, “Path planning to optimize observability in a planar uniform flow field,” in American Control Conference. IEEE, 2013, pp. 1392–1399

    2013

  9. [17]

    Optimal active sensing with process and measurement noise,

    M. Cognetti, P. Salaris, and P. R. Giordano, “Optimal active sensing with process and measurement noise,” in International Conference on Robotics and Automation . IEEE, 2018, pp. 2118–2125

    2018

  10. [18]

    Localization and cir- cumnavigation of a slowly moving target using bearing measurements,

    M. Deghat, I. Shames, B. D. Anderson, and C. Yu, “Localization and cir- cumnavigation of a slowly moving target using bearing measurements,” IEEE Transactions on Automatic Control, vol. 59, no. 8, pp. 2182–2188, 2014

    2014

  11. [19]

    Adaptive source localization based station keeping of autonomous vehicles,

    S. G ¨uler, s ¸FidanBar, S. Dasgupta, B. D. Anderson, and I. Shames, “Adaptive source localization based station keeping of autonomous vehicles,” IEEE Transactions on Automatic Control , vol. 62, no. 7, pp. 3122–3135, 2017

    2017

  12. [20]

    A novel real-time moving target tracking and path planning system for a quadrotor UAV in unknown unstructured outdoor scenes,

    Y . Liu, Q. Wang, H. Hu, and Y . He, “A novel real-time moving target tracking and path planning system for a quadrotor UAV in unknown unstructured outdoor scenes,” IEEE Transactions on Systems Man & Cybernetics: Systems, no. 99, pp. 1–11, 2018

    2018

  13. [21]

    Optimality analysis of sensor-target localization geometries,

    A. N. Bishop, B. Fidan, B. D. Anderson, K. Do ˘ganc ¸ay, and P. N. Pathirana, “Optimality analysis of sensor-target localization geometries,” Automatica, vol. 46, no. 3, pp. 479–492, 2010

    2010

  14. [22]

    The weighted sum method for multi- objective optimization: new insights,

    R. T. Marler and J. S. Arora, “The weighted sum method for multi- objective optimization: new insights,” Structural and multidisciplinary optimization, vol. 41, no. 6, pp. 853–862, 2010

    2010

  15. [23]

    Path planning for UAVs for max- imum information collection,

    H. Ergezer and K. Leblebicioglu, “Path planning for UAVs for max- imum information collection,” IEEE Transactions on Aerospace & Electronic Systems, vol. 49, no. 5, pp. 502–520, 2013

    2013

  16. [24]

    Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning,

    H. Duan and P. Qiao, “Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning,” International Journal of Intelligent Computing and Cybernetics, vol. 7, no. 1, pp. 24–37, 2014

    2014

  17. [25]

    A multiobjective path- planning algorithm with time windows for asset routing in a dynamic weather-impacted environment,

    D. Sidoti, G. V . Avvari, M. Mishra, L. Zhang, B. K. Nadella, J. E. Peak, J. A. Hansen, and K. R. Pattipati, “A multiobjective path- planning algorithm with time windows for asset routing in a dynamic weather-impacted environment,” IEEE Transactions on Systems Man & Cybernetic...

    2017

  18. [26]

    Path planning for active SLAM based on the D* algorithm with negative edge weights,

    I. Maurovi ´c, M. Seder, K. Lenac, and I. Petrovi ´c, “Path planning for active SLAM based on the D* algorithm with negative edge weights,” IEEE Transactions on Systems Man & Cybernetics: Systems , vol. 48, no. 8, pp. 1321–1331, 2018

    2018

  19. [27]

    Discrete-time stochastic source seeking via tuning of forward velocity,

    S. J. Liu and P. P. Zhang, “Discrete-time stochastic source seeking via tuning of forward velocity,” IFAC-PapersOnLine, vol. 48, no. 28, pp. 927–932, 2015

    2015

  20. [28]

    Minimum uncertainty robot navigation using information-guided pomdp planning,

    S. Candido and S. Hutchinson, “Minimum uncertainty robot navigation using information-guided pomdp planning,” in International Conference on Robotics and Automation . IEEE, 2011, pp. 6102–6108

    2011

  21. [29]

    Performance analysis of bearing-only target location algorithms,

    M. Gavish and A. J. Weiss, “Performance analysis of bearing-only target location algorithms,” IEEE Transactions on Aerospace and Electronic Systems, vol. 28, no. 3, pp. 817–828, 1992

    1992

  22. [30]

    Distributed source localization of multi-agent systems with bearing angle measurements,

    C. Lin, Z. Lin, R. Zheng, G. Yan, and G. Mao, “Distributed source localization of multi-agent systems with bearing angle measurements,” IEEE Transactions on Automatic Control, vol. 61, no. 4, pp. 1105–1110, 2016

    2016

  23. [31]

    Enclosing a target by nonholonomic mobile robots with bearing-only measurements,

    R. Zheng, Y . Liu, and D. Sun, “Enclosing a target by nonholonomic mobile robots with bearing-only measurements,” Automatica, vol. 53, pp. 400–407, 2015

    2015

  24. [32]

    H. L. V . Trees, Detection, Estimation, and Modulation Theory: Detec- tion, Estimation, and Linear Modulation Theory . Publishing House of Electronics Industry, 2003

    2003

  25. [33]

    On the bias of linear least squares algorithms for passive target localization,

    K. Do ˘ganc ¸ay, “On the bias of linear least squares algorithms for passive target localization,”Signal Processing, vol. 84, no. 3, pp. 475–486, 2004. Zhuo Li received the B.S. degree from the Depart- ment of Automation, Harbin Institute of Technology, Harbin, China, in 2016....

    2004

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