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An Analysis of Policies from Stochastic Linear Quadratic Gaussian in Robotics Problems with State- and Control-Dependent Noise

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Abstract

Among all the mathematical frameworks used in the control and robotics communities to handle uncertainties, the stochastic variants of optimal control frameworks are appealing, in particular because of the existence of efficient tools to solve them computationally, such as dynamic programming. However, in many cases, because of their formulation as a classical optimization problem, it may be difficult to ponder the expected solutions for a given choice of the objective function to minimize. In this paper, we perform an in-depth analysis of the behavior of the policies obtained from solving Stochastic Linear Quadratic Gaussian problems, thinking in particular in robot motion planning applications. To perform this analysis, we assume simplified linear systems perturbed by Gaussian noise, with state-dependend and control-dependent components, and objective functions summing up control-related and state-related costs. We provide (1) useful bounds for understanding the effect of the objective function parameters, (2) insights on what the expected paths of system should be and (3) results on the optimal choice of the planning horizon.

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References

  1. Anderson, B.D.O., Moore, J.B.: Optimal control: linear quadratic methods. Prentice-Hall, Inc., Upper Saddle River (1990)

    MATH  Google Scholar 

  2. Bai, H., Hsu, D., Lee, W.S.: Integrated perception and planning in the continuous space: A pomdp approach. Int. J. Robot. Res. 33(9), 1288–1302 (2014)

    Article  Google Scholar 

  3. Barraquand, J., Ferbach, P.: Motion planning with uncertainty: the information space approach. In: 1995. Proceedings., 1995 IEEE International Conference on Robotics and Automation, vol. 2, pp 1341–1348 (1995)

  4. Bertsekas, D.P.: Dynamic programming and optimal control. Volume I. Athena Scientific optimization and computation series. Mass. Athena Scientific, Belmont (2005)

    Google Scholar 

  5. Candido, S., Davidson, J.C., Hutchinson, S.: Exploiting domain knowledge in planning uncertain robot systems modeled as POMDPs. In: Proceedings of IEEE Int. Conf. on Robotics and Automation, ICRA 2010, Anchorage, pp 3596–3603 (2010)

  6. Kaelbling, L., Littman, M., Cassandra, A.: Planning and acting in partially observable stochastic domains. Artif. Intell. 101(1-2), 99–134 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kurniawati, H., Du, Y., Hsu, D., Lee, W.S.: Motion planning under uncertainty for robotic tasks with long time horizons. Int. J. Robot. Res. 30(3), 308–323 (2011)

    Article  MATH  Google Scholar 

  8. LaValle, S.M., Hutchinson, S.A.: An objective-based framework for motion planning under sensing and control uncertainties. Int. J. Robot. Res. 17(1), 19–42 (1998)

    Article  Google Scholar 

  9. Smith, C.R., Cheeseman, P.: On the representation and estimation of spatial uncertainty. Int. J. Robot. Res. 5(4), 56–68 (1986)

    Article  Google Scholar 

  10. Taylor, K., LaValle, S.M.: Intensity-based navigation with global guarantees. Auton. Robot. 36(4), 349–364 (2014)

    Article  Google Scholar 

  11. Thrun, S.: Monte Carlo POMDPs. In: Solla, S.A., Leen, T.K., Muller, K.-R. (eds.) Advances in Neural Information Processing Systems 12, pp 1064–1070. MIT Press, Cambridge (2000)

  12. Todorov, E.: A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems. In: Proceedings of the 2005, American Control Conference, pp 300–306 (2005)

  13. van den Berg, J., Abbeel, P., Goldberg, K.: LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information. Int. J. Robot. Res. 30(7), 895–913 (2011)

    Article  Google Scholar 

  14. van den Berg, J., Patil, S., Alterovitz, R.: Motion planning under uncertainty using iterative local optimization in belief space. Int. J. Robot. Res. 31(11), 1263–1278 (2012)

    Article  Google Scholar 

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas (CIMAT), Guanajuato, México

    Hugo Carlos, Jean-Bernard Hayet & Rafael Murrieta-Cid

Authors
  1. Hugo Carlos
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  2. Jean-Bernard Hayet
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  3. Rafael Murrieta-Cid
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Correspondence to Hugo Carlos.

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Carlos, H., Hayet, JB. & Murrieta-Cid, R. An Analysis of Policies from Stochastic Linear Quadratic Gaussian in Robotics Problems with State- and Control-Dependent Noise. J Intell Robot Syst 92, 85–106 (2018). https://doi.org/10.1007/s10846-017-0736-x

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  • DOI: https://doi.org/10.1007/s10846-017-0736-x

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