Optimal Timing Control in Mode Transition Systems

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GRITS Lab
Optimal Timing Control in Mode Transition Systems
Henrik Axelsson Georgia Robotics and
IntelligentSystems Laboratory (GRITS Lab)July
15, 2004Advisors Dr. Magnus Egerstedt and Dr.
Yorai Wardi
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Summary

• Introduction
• Motivation
• Gradient Formula
• Example
• Robotics Application
• Conclusions
• Future Work

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Introduction Problem I
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Introduction Problem II

• Consider inserting new switches.

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Motivation

• Control module switching among several processes.
• Control module collecting data sequentially from
  a number of sensors.
• Avoid obstacles for mobile robots.

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Gradient Formula
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Half-time

• Introduction
• Motivation
• Gradient Formula
• Example
• Robotics Application
• Conclusions
• Future Work

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Gradient-Descent Algorithm

• Optimization algorithm optimal
  switching-times

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Example I
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Robotics Application
Goal
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Conclusion

• Gradient formulae together with algorithm.
• Scheduling, i.e., to answer the question of what
  dynamics to use at a certain time.
• Optimal mode transition in robotics systems.

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Future Work

• Design discrete optimization algorithm.
• Prove convergence for the discrete algorithm-
  Theory of Consistent Approximations.
• Develop optimality criteria for scheduling
  problem in the 8 dimensional case.
• Apply to real-time robotics applications.

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Questions?