Operations Research for Unmanned Systems

Jeffrey Cares is an author, entrepreneur and thought-leader in military innovation.  He consults to the most senior levels of the international defense industry and is a leading researcher in collective robotics and networked warfare. He lectures internationally at senior service colleges on the future of combat, and he develops and conducts military and business war games. Harvard Business Review selected Jeff's research to the Top 20 list of "Breakthrough Ideas for 2006," and he has been featured in such Information Age bellwethers as Wired and Fast Company. A combat veteran of the first Gulf War, Jeff's military career included multiple command tours, over a decade of service on four-star staffs, service in the Pentagon and all Fleet Headquarters, and joint and combined operations worldwide. He is a retired Navy Captain. John Dickmann, Jr is a retired U.S. Navy submarine officer. A graduate of the U.S. Naval Academy, he served on active duty for 22 years in both attack and ballistic missile submarines, with shore assignments in both technical and policy organizations. Following his Navy career, he attended the Massachusetts Institute of Technology, earning a Ph.D. in Engineering Systems. His research focuses on architectures of complex socio-technical systems, emphasizing operational flexibility. He has conducted studies and analysis for the Naval Sea Systems Command, DARPA, the Office of the Secretary of Defense and numerous commercial customers.

About the contributors xiii

Acknowledgements xix

1 Introduction 1

1.1 Introduction 1

1.2 Background and Scope 3

1.3 About the Chapters 4

References 6

2 The In‐Transit Vigilant Covering Tour Problem for Routing Unmanned Ground Vehicles 7

2.1 Introduction 7

2.2 Background 8

2.3 CTP for UGV Coverage 9

2.4 The In‐Transit Vigilant Covering Tour Problem 9

2.5 Mathematical Formulation 11

2.6 Extensions to Multiple Vehicles 14

2.7 Empirical Study 15

2.8 Analysis of Results 21

2.9 Other Extensions 24

2.10 Conclusions 25

Author Statement 25

References 25

3 Near‐Optimal Assignment of UAVs to Targets Using a Market‐Based Approach 27

3.1 Introduction 27

3.2 Problem Formulation 29

3.2.1 Inputs 29

3.2.2 Various Objective Functions 29

3.2.3 Outputs 31

3.3 Literature 31

3.3.1 Solutions to the MDVRP Variants 31

3.3.2 Market‐Based Techniques 33

3.4 The Market‐Based Solution 34

3.4.1 The Basic Market Solution 36

3.4.2 The Hierarchical Market 37

3.4.2.1 Motivation and Rationale 37

3.4.2.2 Algorithm Details 40

3.4.3 Adaptations for the Max‐Pro Case 41

3.4.4 Summary 41

3.5 Results 42

3.5.1 Optimizing for Fuel‐Consumption (Min‐Sum) 43

3.5.2 Optimizing for Time (Min‐Max) 44

3.5.3 Optimizing for Prioritized Targets (Max‐Pro) 47

3.6 Recommendations for Implementation 51

3.7 Conclusions 52

Appendix 3.A A Mixed Integer Linear Programming (MILP) Formulation 53

3.A.1 Sub-tour Elimination Constraints 54

References 55

4 Considering Mine Countermeasures Exploratory Operations Conducted by Autonomous Underwater Vehicles 59

4.1 Background 59

4.2 Assumptions 61

4.3 Measures of Performance 62

4.4 Preliminary Results 64

4.5 Concepts of Operations 64

4.5.1 Gaps in Coverage 64

4.5.2 Aspect Angle Degradation 64

4.6 Optimality with Two Different Angular Observations 65

4.7 Optimality with N Different Angular Observations 66

4.8 Modeling and Algorithms 67

4.8.1 Monte Carlo Simulation 67

4.8.2 Deterministic Model 67

4.9 Random Search Formula Adapted to AUVs 68

4.10 Mine Countermeasures Exploratory Operations 70

4.11 Numerical Results 71

4.12 Non‐uniform Mine Density Distributions 72

4.13 Conclusion 74

Appendix 4.A Optimal Observation Angle between Two AUV Legs 75

Appendix 4.B Probabilities of Detection 78

References 79

5 Optical Search by Unmanned Aerial Vehicles: Fauna Detection Case Study 81

5.1 Introduction 81

5.2 Search Planning for Unmanned Sensing Operations 82

5.2.1 Preliminary Flight Analysis 84

5.2.2 Flight Geometry Control 85

5.2.3 Images and Mosaics 86

5.2.4 Digital Analysis and Identification of Elements 88

5.3 Results 91

5.4 Conclusions 92

Acknowledgments 94

References 94

6 A Flight Time Approximation Model for Unmanned Aerial Vehicles: Estimating the Effects of Path Variations and Wind 95

Nomenclature 95

6.1 Introduction 96

6.2 Problem Statement 97

6.3 Literature Review 97

6.3.1 Flight Time Approximation Models 97

6.3.2 Additional Task Types to Consider 98

6.3.3 Wind Effects 99

6.4 Flight Time Approximation Model Development 99

6.4.1 Required Mathematical Calculations 100

6.4.2 Model Comparisons 101

6.4.3 Encountered Problems and Solutions 102

6.5 Additional Task Types 103

6.5.1 Radius of Sight Task 103

6.5.2 Loitering Task 105

6.6 Adding Wind Effects 108

6.6.1 Implementing the Fuel Burn Rate Model 110

6.7 Computational Expense of the Final Model 111

6.7.1 Model Runtime Analysis 111

6.7.2 Actual versus Expected Flight Times 113

6.8 Conclusions and Future Work 115

Acknowledgments 117

References 117

7 Impacts of Unmanned Ground Vehicles on Combined Arms Team Performance 119

7.1 Introduction 119

7.2 Study Problem 120

7.2.1 Terrain 120

7.2.2 Vehicle Options 122

7.2.3 Forces 122

7.2.3.1 Experimental Force 123

7.2.3.2 Opposition Force 123

7.2.3.3 Civilian Elements 123

7.2.4 Mission 124

7.3 Study Methods 125

7.3.1 Closed‐Loop Simulation 125

7.3.2 Study Measures 126

7.3.3 System Comparison Approach 128

7.4 Study Results 128

7.4.1 Basic Casualty Results 128

7.4.1.1 Low Density Urban Terrain Casualty Only Results 128

7.4.1.2 Dense Urban Terrain Casualty‐Only Results 130

7.4.2 Complete Measures Results 131

7.4.2.1 Low Density Urban Terrain Results 131

7.4.2.2 Dense Urban Terrain Results 132

7.4.2.3 Comparison of Low and High Density Urban Results 133

7.4.3 Casualty versus Full Measures Comparison 135

7.5 Discussion 136

References 137

8 Processing, Exploitation and Dissemination: When is Aided/Automated Target Recognition “Good Enough” for Operational Use? 139

8.1 Introduction 139

8.2 Background 140

8.2.1 Operational Context and Technical Issues 140

8.2.2 Previous Investigations 141

8.3 Analysis 143

8.3.1 Modeling the Mission 144

8.3.2 Modeling the Specific Concept of Operations 145

8.3.3 Probability of Acquiring the Target under the Concept of Operations 146

8.3.4 Rational Selection between Aided/Automated Target Recognition and Extended Human Sensing 147

8.3.5 Finding the Threshold at which Automation is Rational 148

8.3.6 Example 148

8.4 Conclusion 149

Acknowledgments 151

Appendix 8.A 151

Ensuring [Q ] * decreases as ζ* increases 152

References 152

9 Analyzing a Design Continuum for Automated Military Convoy Operations 155

9.1 Introduction 155

9.2 Definition Development 156

9.2.1 Human Input Proportion (H) 156

9.2.2 Interaction Frequency 157

9.2.3 Complexity of Instructions/Tasks 157

9.2.4 Robotic Decision‐Making Ability (R) 157

9.3 Automation Continuum 157

9.3.1 Status Quo (SQ) 158

9.3.2 Remote Control (RC) 158

9.3.3 Tele‐Operation (TO) 158

9.3.4 Driver Warning (DW) 158

9.3.5 Driver Assist (DA) 158

9.3.6 Leader‐Follower (LF) 159

9.3.6.1 Tethered Leader‐Follower (LF1) 159

9.3.6.2 Un‐tethered Leader‐Follower (LF2) 159

9.3.6.3 Un‐tethered/Unmanned/Pre‐driven Leader‐Follower (LF3) 159

9.3.6.4 Un‐tethered/Unmanned/Uploaded Leader‐Follower (LF4) 159

9.3.7 Waypoint (WA) 159

9.3.7.1 Pre‐recorded “Breadcrumb” Waypoint (WA1) 160

9.3.7.2 Uploaded “Breadcrumb” Waypoint (WA2) 160

9.3.8 Full Automation (FA) 160

9.3.8.1 Uploaded “Breadcrumbs” with Route Suggestion Full Automation (FA1) 160

9.3.8.2 Self‐Determining Full Automation (FA2) 160

9.4 Mathematically Modeling Human Input Proportion (H) versus System Configuration 161

9.4.1 Modeling H versus System Configuration Methodology 161

9.4.2 Analyzing the Results of Modeling H versus System Configuration 165

9.4.3 Partitioning the Automation Continuum for H versus System Configuration into Regimes and Analyzing the Results 168

9.5 Mathematically Modeling Robotic Decision‐Making Ability (R) versus System Configuration 169

9.5.1 Modeling R versus System Configuration Methodology 169

9.5.2 Mathematically Modeling R versus System Configuration When Weighted by H 171

9.5.3 Partitioning the Automation Continuum for R (Weighted by H) versus System Configuration into Regimes 175

9.5.4 Summarizing the Results of Modeling H versus System Configuration and R versus System Configuration When Weighted by H 177

9.6 Mathematically Modeling H and R 178

9.6.1 Analyzing the Results of Modeling H versus R 178

9.7 Conclusion 180

9.A System Configurations 180

10 Experimental Design for Unmanned Aerial Systems Analysis: Bringing Statistical Rigor to UAS Testing 187

10.1 Introduction 187

10.2 Some UAS History 188

10.3 Statistical Background for Experimental Planning 189

10.4 Planning the UAS Experiment 192

10.4.1 General Planning Guidelines 192

10.4.2 Planning Guidelines for UAS Testing 193

10.4.2.1 Determine Specific Questions to Answer 194

10.4.2.2 Determine Role of the Human Operator 194

10.4.2.3 Define and Delineate Factors of Concern for the Study 195

10.4.2.4 Determine and Correlate Response Data 196

10.4.2.5 Select an Appropriate Design 196

10.4.2.6 Define the Test Execution Strategy 198

10.5 Applications of the UAS Planning Guidelines 199

10.5.1 Determine the Specific Research Questions 199

10.5.2 Determining the Role of Human Operators 199

10.5.3 Determine the Response Data 200

10.5.4 Define the Experimental Factors 200

10.5.5 Establishing the Experimental Protocol 201

10.5.6 Select the Appropriate Design 202

10.5.6.1 Verifying Feasibility and Practicality of Factor Levels 202

10.5.6.2 Factorial Experimentation 202

10.5.6.3 The First Validation Experiment 203

10.5.6.4 Analysis: Developing a Regression Model 204

10.5.6.5 Software Comparison 204

10.6 Conclusion 205

Acknowledgments 205

Disclaimer 205

References 205

11 Total Cost of Ownership (TOC): An Approach for Estimating UMAS Costs 207

11.1 Introduction 207

11.2 Life Cycle Models 208

11.2.1 DoD 5000 Acquisition Life Cycle 208

11.2.2 ISO 15288 Life Cycle 208

11.3 Cost Estimation Methods 210

11.3.1 Case Study and Analogy 210

11.3.2 Bottom‐Up and Activity Based 211

11.3.3 Parametric Modeling 212

11.4 UMAS Product Breakdown Structure 212

11.4.1 Special Considerations 212

11.4.1.1 Mission Requirements 214

11.4.2 System Capabilities 214

11.4.3 Payloads 214

11.5 Cost Drivers and Parametric Cost Models 215

11.5.1 Cost Drivers for Estimating Development Costs 215

11.5.1.1 Hardware 215

11.5.1.2 Software 218

11.5.1.3 Systems Engineering and Project Management 218

11.5.1.4 Performance‐Based Cost Estimating Relationship 220

11.5.1.5 Weight‐Based Cost Estimating Relationship 223

11.5.2 Proposed Cost Drivers for DoD 5000.02 Phase Operations and Support 224

11.5.2.1 Logistics – Transition from Contractor Life Support (CLS) to Organic Capabilities 224

11.5.2.2 Training 224

11.5.2.3 Operations – Manned Unmanned Systems Teaming (MUM‐T) 225

11.6 Considerations for Estimating Unmanned Ground Vehicle Costs 225

11.7 Additional Considerations for UMAS Cost Estimation 230

11.7.1 Test and Evaluation 230

11.7.2 Demonstration 230

11.8 Conclusion 230

Acknowledgments 231

References 231

12 Logistics Support for Unmanned Systems 233

12.1 Introduction 233

12.2 Appreciating Logistics Support for Unmanned Systems 233

12.2.1 Logistics 234

12.2.2 Operations Research and Logistics 236

12.2.3 Unmanned Systems 240

12.3 Challenges to Logistics Support for Unmanned Systems 242

12.3.1 Immediate Challenges 242

12.3.2 Future Challenges 242

12.4 Grouping the Logistics Challenges for Analysis and Development 243

12.4.1 Group A – No Change to Logistics Support 243

12.4.2 Group B – Unmanned Systems Replacing Manned Systems and Their Logistics Support Frameworks 244

12.4.3 Group C – Major Changes to Unmanned Systems Logistics 247

12.5 Further Considerations 248

12.6 Conclusions 251

References 251

13 Organizing for Improved Effectiveness in Networked Operations 255

13.1 Introduction 255

13.2 Understanding the IACM 256

13.3 An Agent‐Based Simulation Representation of the IACM 259

13.4 Structure of the Experiment 260

13.5 Initial Experiment 264

13.6 Expanding the Experiment 265

13.7 Conclusion 269

Disclaimer 270

References 270

14 An Exploration of Performance Distributions in Collectives 271

14.1 Introduction 271

14.2 Who Shoots How Many? 272

14.3 Baseball Plays as Individual and Networked Performance 273

14.4 Analytical Questions 275

14.5 Imparity Statistics in Major League Baseball Data 277

14.5.1 Individual Performance in Major League Baseball 278

14.5.2 Interconnected Performance in Major League Baseball 281

14.6 Conclusions 285

Acknowledgments 286

References 286

15 Distributed Combat Power: The Application of Salvo Theory to Unmanned Systems 287

15.1 Introduction 287

15.2 Salvo Theory 288

15.2.1 The Salvo Equations 288

15.2.2 Interpreting Damage 289

15.3 Salvo Warfare with Unmanned Systems 290

15.4 The Salvo Exchange Set and Combat Entropy 291

15.5 Tactical Considerations 292

15.6 Conclusion 293

References 294

Index 295