Journal of Global Optimization

, Volume 73, Issue 2, pp 389–410 | Cite as

Robot path planning in a dynamic environment with stochastic measurements

  • Adriano Zanin ZambomEmail author
  • Brian Seguin
  • Feifei Zhao


We study the problem of trajectory planning for autonomous vehicles designed to minimize the travel distance while avoiding moving obstacles whose position and speed are not known. Because, in practice, observations from sensors have measurement errors, the stochasticity of the data is modeled using maximum likelihood estimators, which are shown to be consistent as the sample size increases. To comply with the kinematic constraints of the vehicle, we consider smooth trajectories that can be represented by a linear combination of B-spline basis functions, transforming the infinite-dimensional problem into a finite-dimensional one. Moreover, a smooth penalty function is added to the travel distance, transforming the constrained optimization problem into an unconstrained one. The planned stochastic trajectory, obtained from the minimization problem with stochastic confidence regions, is shown to converge almost surely to the deterministic one as the number of sensor observations increases. Finally, we present two simulation studies to demonstrate the proposed method.


Autonomous vehicle B-splines Kinematics Constrained optimization Moving obstacle avoidance 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Adriano Zanin Zambom
    • 1
    Email author
  • Brian Seguin
    • 2
  • Feifei Zhao
    • 2
  1. 1.Department of MathematicsCalifornia State University NorthridgeNorthridgeUSA
  2. 2.Department of Mathematics and StatisticsLoyola University ChicagoChicagoUSA

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