Near-Optimal Missile Avoidance Trajectories via Receding Horizon Control

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Near-Optimal Missile Avoidance Trajectories via
Receding Horizon Control

• Janne Karelahti, Kai Virtanen, and
• Tuomas Raivio
• Systems Analysis Laboratory
• Helsinki University of Technology, Finland

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Goal avoid a closing missile
Criterion max capture time min closing
velocity max miss distance max guidance
effort max gimbal angle max tracking rate
Select the most suitable criterion
Controls wanted in a feedback form Receding
Horizon Control cost-to-go approximation
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Problem overview

• Some physical constraints of the missile system
• Lags in the missile guidance system dynamics
• Seeker heads gimbal angle limit
• Seeker heads tracking rate limit
• Limited energy supply of the missile control
  system

Target aircraft
Gimbal angle
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Problem overview

• Assumptions
• The vehicles receive perfect state information
  about each other
• The vehicles are modeled as 3-DOF point-masses
• Target aircrafts angular velocities and
  accelerations are limited
• The missile utilizes proportional navigation
• The missile has a single lag guidance system

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Optimal Control Problem

• The target aircraft minimizes/maximizes
• subject to

State equations
Control/state constraints
Terminal constraint
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Receding horizon control scheme

• The target makes decisions at
• Lets define
  and
• Set k 0. Set the initial state x0 and initial
  controls u0.
• Solve the optimal controls over tk, tkT by
  min./maximizing
• Set and solve by
  implementing for
• If the missile has reached its target set, stop.
• Set k k 1 and go to step 2.

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Criteria ctg. approximation

• Capture time
• Closing velocity
• Miss distance
• Control effort
• Gimbal angle
• Tracking rate

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Optimal controls over tkT

• The direct shooting method
• Time discretization
• Explicit integration of the state at
  by using
• The resulting NLP problem
• is solved by SNOPT SQP-solver

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Numerical results
Capture time maximization
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Numerical results
Miss distance maximization
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Numerical results
Capture time maximization
Miss distance maximization
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Conclusions

• The scheme provides near-optimal feedback
  controls in virtually real-time
• Launch state maps provide a way for selecting the
  most effective performance measure for the
  current state
• Additional research topics
• Evaluation of the realism of the optimal
  trajectories by inverse simulation
• Uncertainty about the missile establishes a need
  for automatic identification of the missile
  parameters (e.g. guidance law)