Planning and Optimization of Dynamic Systems: A HigherOrder Approach

1
Planning and Optimization of Dynamic Systems A
Higher-Order Approach

• Sunil K. Agrawal, Ph.D.
• Associate Professor of Mechanical Engineering
• University of Delaware, Newark, DE 19716
• http//mechsys4.me.udel.edu

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Problem Statement

• Develop computationally efficient algorithms for
  feasible and/or optimal planning of dynamic
  systems.
• State equations
• Path and end constraints
• Cost functional

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Motivation
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Higher-Order systems

• Canonical transformation of state equations using
  linear and nonlinear systems theory

• Controllable linear time-invariant systems
• Classes of time-varying, time-periodic systems
• Feedback linearizable nonlinear systems
• Classes of nonholonomic systems
• Differentially flat systems

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Outline

• Systems without inequality constraints
• feasible planning admissible forms
• optimal planning variational theory
• Systems with inequality constraints
• feasible planning polytopic approximation
• optimal planning Pontryagin extensions, Mayers
  problems, Computation comparisons

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Higher-Order Systems Examples
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Higher-Order Systems Examples
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Feasible Trajectories without Inequalities
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Optimal Trajectories without InequalitiesFeedback
Linearizable Systems
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Example Flexible Joint
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Experiment Free-floating Robot
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Feasible Planning Inequalities

0
)
,
(
u
x
c
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Experiment Predator-Prey
c
m
2



y
y
y
x




y
x
1
2
k
k
2
2
T


0


d
y
y
y
C



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Example PUMA 560
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Optimal Planning InequalitiesPontryagins
Extensions
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Higher-Order ToolboxesComputation Comparisons
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Conclusions Challenges

• Higher-Order approach is computationally
  effective for classes of dynamic systems
• Extensions to systems with partial higher-order
  structures
• Handling singularities of transformations
• Extensions to systems that do not admit
  higher-order structures

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Acknowledgments

• Ph.D. students Faiz, Xu, Annapragada,
  Veeraklaew, Ferreira
• MS students Bhattacharya, Claewplodtook
• Post-docs Visitors Schlemmer, Pfister,
  Burkhardt, Murray
• NSF, AFOSR, Humboldt Foundation