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Optimal Timing Control in Mode Transition Systems

GRITS Lab. Optimal Timing Control in Mode Transition Systems. Henrik Axelsson Georgia Robotics and Intelligent Systems Laboratory (GRITS Lab) July 15, 2004 Advisors Dr. Magnus Egerstedt and Dr. Yorai Wardi. Summary. Introduction Motivation Gradient Formula Example Robotics Application

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Optimal Timing Control in Mode Transition Systems

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  1. 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

  2. Summary • Introduction • Motivation • Gradient Formula • Example • Robotics Application • Conclusions • Future Work Henrik Axelsson - GritsLab, July 2004

  3. Introduction – Problem I Henrik Axelsson - GritsLab, July 2004

  4. Introduction – Problem II • Consider inserting new switches. Henrik Axelsson - GritsLab, July 2004

  5. Motivation • Control module switching among several processes. • Control module collecting data sequentially from a number of sensors. • Avoid obstacles for mobile robots*. Henrik Axelsson - GritsLab, July 2004

  6. Gradient Formula Henrik Axelsson - GritsLab, July 2004

  7. Half-time • Introduction • Motivation • Gradient Formula • Example • Robotics Application • Conclusions • Future Work Henrik Axelsson - GritsLab, July 2004

  8. Gradient-Descent Algorithm • Optimization algorithm optimal switching-times Henrik Axelsson - GritsLab, July 2004

  9. Example I Henrik Axelsson - GritsLab, July 2004

  10. Robotics Application Goal Henrik Axelsson - GritsLab, July 2004

  11. 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. Henrik Axelsson - GritsLab, July 2004

  12. Future Work • Design discrete optimization algorithm. • Prove convergence for the discrete algorithm:- Theory of Consistent Approximations. • Develop optimality criteria for scheduling problem in the ∞ dimensional case. • Apply to real-time robotics applications. Henrik Axelsson - GritsLab, July 2004

  13. Questions? Henrik Axelsson - GritsLab, July 2004

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