application of geometrical extrapolation method based hybrid system controller on pursuit-avoidance...
Post on 22-Dec-2015
222 views
TRANSCRIPT
![Page 1: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/1.jpg)
APPLICATION OF GEOMETRICAL APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED EXTRAPOLATION METHOD BASED
HYBRID SYSTEM CONTROLLER ON HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL PURSUIT-AVOIDANCE DIFFERENTIAL
GAMEGAME
Ginzburg Pavel and Slavnaya Lyudmila
Supervisory by Dr. Mark Moulin
![Page 2: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/2.jpg)
List of contents:
Optimal control and Hamiltonian formalism Hybrid control Intuitive Geometrical Controller Circle Extrapolation Controller Second Order Approximation in Geometrical
Extrapolation Nonlinear Heading Estimator The Supper Hybrid Controller Conclusion
![Page 3: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/3.jpg)
Hamiltonian Formalism
![Page 4: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/4.jpg)
System representation
![Page 5: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/5.jpg)
Solutions of Backward Reachable Set
Capture radius 5Linear velocities 5
Angular velocities 1
Capture radius 5Linear velocities 5
Angular velocity Evader 2Angular velocity Pursuer 1
Capture radius 5Linear velocities 5
Angular velocity Evader 1Angular velocity Pursuer 2
![Page 6: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/6.jpg)
Open loop via closed loop control
Open loop:+ Safe for initial condition check - Sensitive to measurement noise - Non flexible to task changing - Slow and massive calculation (offline ) - And more…
Closed loop: + Safe control + Online and fast calculations - Non optimal
![Page 7: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/7.jpg)
Intuitive Geometrical Controller
Plane division to provide control signal
Problematic situation for Simple Controller
![Page 8: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/8.jpg)
Results of Intuitive Geometrical Controller
Initial conditions (-2, 2, π/2)
Initial conditions (-2, 2, π/3) Control signal output
Control signal output
![Page 9: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/9.jpg)
Circle Extrapolation Controller
Red Cross – estimated positionBlue Star – measurement data, stored in controller memory
Assumptions:
- The opponent control signal unchanged during the sampling
Principe:
- 3 points define the only one circle
- Forth point is the opponent estimated position
-Controller chooses the optimal output depends on the estimated position
- Each step correction provided (like Kalman filter measurement correction)
![Page 10: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/10.jpg)
Results of Circle Extrapolation Controller
Initial conditions (-2, 2, π/2) Control signal output
Initial conditions (-2, 2, π/3) Control signal output
![Page 11: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/11.jpg)
Second Order Approximation in Geometrical Extrapolation
![Page 12: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/12.jpg)
Results Geometrical Extrapolation Controller
Initial conditions (-2, 2, π/3)
Initial conditions (-2, 2, π/2) Control signal output
Control signal output
![Page 13: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/13.jpg)
Geometrical Extrapolation Controller used by both players
Border point (0, 3.44, -π)Applied control signals
Applied control signalsBorder point (2, 1.42, -π/2)
(0, 3, -π)
(1.6, 1, -π/2)
![Page 14: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/14.jpg)
Results Geometrical Extrapolation Controller with “arctan”
“Sign” function replaced by “Arctangent”
Initial conditions (-2, 2, π/2) Control signal output
Control signal output Initial conditions (-2, 2, π/3)
![Page 15: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/15.jpg)
Noise in coordinate measurement
1 variance noiseBorder point (2, 1.42, -π/2)
0.1 variance noiseBorder point (2, 1.42, -π/2)
![Page 16: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/16.jpg)
Nonlinear Heading Estimator Assumptions: - The opponent heading signal unchanged during the sampling Principe: - 5 points is a trade off between noise filtering and device flexibilityController provides the most fitted line (MSE)
Red points – measurement dataBlue lines – calculated slopes, the estimator output
![Page 17: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/17.jpg)
Performances of Nonlinear Heading Estimator
Constant control input (0), noisy case (0.01 variance)
no noise exist
Constant control input (0.1), noisy case (0.01 variance).
![Page 18: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/18.jpg)
The Supper Hybrid Controller
Idea:- fitting noisy data to estimated orbit - verify the noise level by R-condition checking - choose more successful controller
implementation
Travels between hybrids controllers (double hybridism exists)
![Page 19: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/19.jpg)
Conclusions
Advantages of Hybrid Control Implementation The geometrical extrapolation method in
Hybrid system provides wise plane division Noise filtering using The Method More levels in Hybrid Implementation
![Page 20: APPLICATION OF GEOMETRICAL EXTRAPOLATION METHOD BASED HYBRID SYSTEM CONTROLLER ON PURSUIT-AVOIDANCE DIFFERENTIAL GAME Ginzburg Pavel and Slavnaya Lyudmila](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649d785503460f94a5a491/html5/thumbnails/20.jpg)
Directions
Non linear filtering (fit the surface to measurement data)
Analytical approximated solution of HJB equations
More complex differential games General case