An Evolutionary Path Planning Algorithm for Military Applications

1
An Evolutionary Path Planning Algorithm for
Military Applications

• Manoj K. Jha (Morgan State University)
• Cheng-Chieh Chen (Univ. of MD, College Park)
• Paul Schonfeld (Univ. of MD, College Park) Shinya
  Kikuchi (Virginia Tech.)

June 4th 2008 at SoSE IEEE Conference
2
Outline

• Introduction
• A 3-Dimensional (3D) highway alignment
  optimization (HAO) model
• Path Planning Optimization Problem for Military
  Applications
• Computational Results
• Conclusions

3
Introduction

• The evolutionary algorithm originally designed
  for optimizing 3-dimensional (3D) highway
  alignments is adapted and tested for real-time
  military path planning applications in a changing
  environment.
• In using GAs and GIS, the proposed path can be
  sufficiently described by a set of intermediate
  points (Pi) between given start and end points.

4
Introduction

• Both locations of cutting planes and locations of
  Pi along the planes are random.
• Associated costs and revenues are also
  calculated.

5
3D HAO Model

• The objective function consists of
  alignment-sensitive costs, such as user cost
  (CU), right-of-way cost (CR), pavement cost (CP),
  earthwork cost (CE) and structure cost (CS) as
  shown in Eq. (1).

6
3D HAO Model

• Genetic Encoding of Decision Variables
• In GAs the decision variables are encoded in
  strings of binary or real numbers, called
  chromosomes.
• In the HAO approach, real numbers are used to
  represent decision variables within the specified
  bounds.
• For an alignment represented by n points of
  intersections, the encoded chromosome is composed
  of 3n genes (for x, y, z values at each point
  of intersection along the alignment.)

7
3D HAO Model

• Genetic Operators
• Eight problem-specific genetic operators are
  designed 3, 5 to work on the encoded points of
  intersection rather than on individual genes.
• Those are uniform mutation, straight mutation,
  non-uniform mutation, whole non-uniform mutation,
  simple crossover, two-point crossover, arithmetic
  crossover, and heuristic crossover.

8
Identify Problem
Research Process
Formulate Objective Function and Constraints
Consider Uncertainty
Develop Solution Methodology
Genetic Algorithm Distance Based Other Techniques
Algorithms
Examples
Dynamic GIS Visualization
Testing / Evaluation / Simulation / Validation
Refinement
Project Complete
9
Path Planning Algorithm

• Path planning optimization problem for military
  applications

10
Path Planning Algorithm

• Assumed probabilities of destroying and getting
  destroyed by each target encountered

11
Path Planning Algorithm
12
Computational Results

• Optimized base case path (t50k, v100k, m5)
• The agent tends to move along a relatively short
  and direct path.

13
Computational Results

• Optimized path with additional southeastern
  target (t50k, v100k, m6)
• Since a new hostile target is added in the lower
  right side (i.e. the open circle), the
  optimal path shifts substantially
  leftward.

14
Computational Results

• Optimized path with higher v (v500k)
• Instead of closely confronting the hostile
  targets, the agent seeks to detour around them,
  while favoring its safety and probability of
  completing its mission.

15
Computational Results

• Optimized path with 10 targets (t50k, v100k)
• 10 hostile targets are randomly generated by GIS.
• The agent tends to avoid the most direct path
  near targets in the central area.

16
Computational Results

• Optimized path with 10 targets (t50k, v100k)

17
Computational Results

• Optimized path with changing probability
  functions (t50k, v100k, m5)
• In this case, the probability functions are
  changed. The dashed lines represent the original
  probabilities, and the solid lines illustrate the
  revised settings.
• Thus, the agents weapons are now more effective
  at shorter ranges and the targets are more
  effective at longer ranges.

18
Computational Results

• Optimized path with changing probability
  functions (t50k, v100k, m5)

19
Computational Results

• Optimized path with changing probability
  functions (t50k, v100k, m5)
• The agent tends to move within a balanced
  distance. If the agent moves too far from the
  target, the probability of getting destroyed
  will decrease. But if the agent moves
  too close, the cumulative travel
  distances and costs will both increase.

20
Conclusions

• Through a series of case studies, the model has
  shown its ability to provide promising results.
• A re-optimizing algorithm will be developed for
  the time-varying optimal path studies, for the
  remaining path from the current position at
  preset intervals or whenever significant new
  information becomes available.

21
References

• Chin, Y.T. et al., 2001. Vision Guided AGV Using
  Distance Transform, In Proceedings of the 32nd
  ISR (International Symposium on Robotics), Seoul,
  pp 1416-1421.
• Horng, J-H. and Li, J.T., 2000. Vehicle path
  planning by using adaptive constrained distance
  transformation, Pattern Recognition, 35, pp
  13271337.
• Garrido, S., Moreno, L. and Blanco, D., 2006.
  Voronoi Diagram and Fast Marching applied to Path
  Planning, In Proceedings of the 2006 IEEE
  International Conference on Robotics and
  Automation, Florida.
• Gupta, I. and Riordan, D., 2004, Path Planning
  for Mobile Robots using Fuzzy Logic, In
  Proceedings of the 28th Annual APICS Conference
  Mathematics-Statistics-Computer Science.
• Jarvis, R.A., 1984. Collision-Free Trajectory
  Planning Using Distance Transforms, In
  Proceedings of National Conference and Exhibition
  on Robotics 1984, Australia.
• Lebedev, D.V., Steil, J.J. and Ritter H., 2003. A
  Neural Network Model that Calculates Dynamic
  Distance Transform for Path Planning and
  Exploration in a Changing Environment,
  Proceedings of the 2003 IEEE International
  Conference on Robotics Automation, Taiwan.
• Marzouqi, M. S. and Jarvis, R. A., 2005. Covert
  Path Planning in Unknown Environments with Known
  or Suspected Sentries Locations, submitted to The
  IEEE International Conference on Robotics and
  Automation (ICRA), Spain.
• Marzouqi, M. S. and Jarvis, R. A., 2003. Covert
  Path Planning for Autonomous Robot Navigation in
  Known Environments , In Proceedings of the 2003
  Australasian Conference on Robotics Automation,
  Australia.
• Taylor, T., Geva, S. and Boles, W.W., 2005,
  Directed Exploration using a Modified Distance
  Transform, In Proceedings of the Digital Imaging
  Computing Techniques and Applications (DICTA),
  pp 53.
• Wang, L.C., Yong, L.S. and Ang, M.H.,Jr., 2002.
  Hybrid of global path planning and local
  navigation implemented on a mobile robot in
  indoor environment, In Proceedings of the 2002
  IEEE International Symposium on Intelligent
  Control.