Uncertainty in motion planning

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Uncertainty in motion planning

• Behrouz Haji Soleimani
• Dr. Moradi

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Outline

• What is uncertainty?
• Some examples
• Solutions to uncertainty
• Ignoring uncertainty
• Markov Decision Process (MDP)
• Stochastic Motion Roadmap
• A detailed example
• Conclusion

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What is uncertainty?

• Uncertainty in sensing
• the current state of the robot and workspace is
  not known with certainty
• Predictability
• the future state of the robot and workspace
  cannot be deterministically predicted even when
  the current state and future actions are known

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Uncertainty in sensing

• It is not the world that is imperfect, it is our
  knowledge of it

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Predictability

• Uncertainty in workspace
• Uncertainty in goal location
• Dynamic environments with moving obstacles
• Uncertainty in robots motion

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Uncertainty example

• A robot with imperfect sensing must reach a goal
  location among moving obstacles (dynamic world)

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Uncertainty example

• Robot created at Stanfords ARL Lab to study
  issues in robot control and planning in
  no-gravity space environment
• air thrusters
• gas tank
• air bearing

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Uncertainty in motion
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Uncertainty in motion
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Markov Decision Process (MDP)

• MDP is a general approach to considering
  uncertainty
• Determines model of the environment
• Descretizes state space
• Requires explicitly defining transition
  probabilities between states
• We can use dynamic programming to solve the MDP

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Stochastic Motion Roadmap

• Combines a roadmap representation of
  configuration space with the theory of MDPs
• Maximizes the probability of success
• Uses sampling to
• learn the configuration space (represented as
  states)
• learn the stochastic motion model (represented as
  state transition probabilities)
• Discretizes state space
• Discretizes actions

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Stochastic Motion Roadmap

• Learning Phase
• Selecting random sample of discrete states
• Sample the robots motion model to build a
  Stochastic Motion Roadmap (SMR)
• Calculating transition probabilities for each
  action
• Query Phase
• Specify initial and goal states
• Roadmap is used to find a feasible path
• Possibly optimizing some criteria such as minimum
  length

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Building the roadmap
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Building the roadmap
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Maximizing probability of success

• build an n n transition probability matrix P(u)
  for each u U
• For each tuple (s, t, p) , we set
  equals the probability of
  transitioning from state s to state t given that
  action u is performed

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Maximizing probability of success
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Maximizing probability of success

• It is an MDP and has the form of the Bellman
  equation
• Where and
• It can be optimally solved using infinite
  horizon dynamic programming

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A detailed example
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A detailed example
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A detailed example
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A detailed example
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Conclusion

• Uncertainty has a great effect on successfully
  reaching the goal
• MDP can consider uncertainty in the model
• SMR combines PRM and MDP to handle uncertainty
• SMR maximizes the probability of success
• SMR makes balance between path safety and minimum
  length
• Continuous actions in SMR is still an open
  question

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References

• 1 R. Alterovitz, T. Simeon, and K. Goldberg,
  The Stochastic Motion Roadmap A Sampling
  Framework for Planning with Markov Motion
  Uncertainty 2007
• 2 R. Alterovitz, M. Branicky, and K. Goldberg,
  Constant-curvature motion planning under
  uncertainty with applications in image-guided
  medical needle steering, in Workshop on the
  Algorithmic Foundations of Robotics, July 2006.
• 3 R. Alterovitz, A. Lim, K. Goldberg, G. S.
  Chirikjian, and A. M. Okamura, Steering flexible
  needles under Markov motion uncertainty, in
  Proc. IEEE/RSJ Int. Conf. on Intelligent Robots
  and Systems (IROS), Aug. 2005, pp. 120125.
• 4 B. Bouilly, T. Simeon, and R. Alami, A
  numerical technique for planning motion
  strategies of a mobile robot in presence of
  uncertainty, in Proc. IEEE Int. Conf. on
  Robotics and Automation (ICRA), Nagoya, Japan,
  May 1995.

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Questions ?
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Thank you