1 Dynamic Optimization Challenges in Autonomous Vehicle Systems Fernando Lobo Pereira, João Borges de Sousa Faculdade de Engenharia da Universidade do Porto (FEUP) Presented by Jorge Estrela da Silva (Phd student at FEUP) OMPC 2013 - Summer School and Workshop on Optimal and Model Predictive Control September 9-13, 2013 Bayreuth, Germany
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Dynamic Optimization Challenges in Autonomous Vehicle Systems
Fernando Lobo Pereira, João Borges de Sousa
Faculdade de Engenharia da Universidade do Porto (FEUP)
Presented by
Jorge Estrela da Silva (Phd student at FEUP)
OMPC 2013 - Summer School and Workshop on
Optimal and Model Predictive Control
September 9-13, 2013
Bayreuth, Germany
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Acknowledgment The contents of this presentation builds on the effort of the LSTS researchers
• Coordination layer – pick feasible task with higher added value
• Maneuver layer – control synthesis (feedback optimization)
Structural Arrangement
• Activities logically organized to ensure task/mission completion
Systems Engineering Process
Transformation of objectives, requirements & constraints into a
System-Solution
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An Application Scenario
Two AUV teams Positioning service (L team)
Finding the minimum of a scalar field (S team)
Teams have to coordinate activities Intra-team control:
provide a service satisfying technological constraints & requirements.
Inter-team control:
implement a model of coordination (L team must “follow” S team)
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Search team Coordinated gradient following
Invariance problem
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Some dynamic optimization developments by LSTS members
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Dynamic optimization developments
Moored sensors
Autonomous surface vehicle
Surface buoy
Navigation beacon
Oceanographic sensors
Moored sensors
Drifters
AUV
AUV
UAV UAV
AUV
UAV
Control station
Control station
Control station
AUV
Value Function based coordination
Model Predictive Control
Dynamic Programming based controllers J. Estrela da Silva, J. Borges de Sousa, A dynamic programming based path-following controller for autonomous vehicles, Control and Intelligent Systems, Vol. 39, No. 4, 2011
J. Estrela da Silva, J. Borges de Sousa, Dynamic Programming Techniques for Feedback Control, IFAC18th World Congress, Milano, Italy, August 28 - September 2, 2011.
J. Estrela da Silva, J. Borges de Sousa, F. Lobo Pereira, “Experimental results with value function based control of an AUV”, NGCUV 2012 Workshop, Porto, Portugal, April 10-12, 2012.
F. Lobo Pereira, J. Borges de Sousa, R. Gomes, P. Calado, MPC based coordinated control of Autonomous Underwater Vehicles, ICIAM, Vancouver, July 18-22, 2011
F. Lobo Pereira, “Reach set formulation of a model predictive control scheme”, MTNS 2012, 20th Melbourne, Australia, July 9-13, 2012.
J. Borges de Sousa, F. Lobo Pereira, A set-valued framework for coordinated motion control of networked vehicles, Journal of Computer and Systems Sciences International, 2006
F. Lobo Pereira, J. Borges de Sousa, Coordinated Control of Networked Vehicles: An Autonomous Underwater Systems, Automation and Remote Control, 2004
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Dynamic programming based controllers Jorge Estrela da Silva, João Sousa, Fernando Lobo Pereira
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Problem formulation
Differential game (upper value solution)
• Subject to:
• Optimal cost to reach a target:
Adversarial (maximizing) input models disturbances and model
uncertainty
Input sequence a(.) is piecewise constant
0
0
non-anticipative
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The approach: dynamic programming for sampled data systems
Value function: the main object of the dynamic
programming (DP) approach:
“Optimal cost to reach” - value function is time independent.
Infinite horizon (more delicate) – assume that solution converges to
V(x)+ct.
Approach: value function based feedback synthesis
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Value function computation
In general, it is not possible to find an analytical expression
for the value function.
• Numerical methods are required.
Numerical computation of the value function is expensive,
but not impossible for systems of low dimension.
• And, for the considered problems, this can be done at the design
stage.
Our solver is based on the semi-Lagrangian (SL) numerical
scheme by Falcone and co-authors, see, e.g.,
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DP for sampled data systems
SL scheme: iteratively apply the DPP on each grid node
(value iteration)
Key to our approach: emulation of the behavior of the
computer system. - Time step = control period.
- Piecewise constant input sequences (sample and hold).
x
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Implementation of the control law
What to store on the target computer?
• Numerical approximation of the value function
• Constant control on each grid cell
- Requires less computations (local optimization is avoided).
- May require more storage space, depending on the dimension of the
control input.
- In the former approach, the computed control is, in general, closer to