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Many books have been written on modelling, simulation and control of four-wheeled vehicles (cars, in particular). However, due to the very specific and different dynamics of two-wheeled vehicles, it is very difficult to reuse previous knowledge gained on cars for two-wheeled vehicles.

Modelling, Simulation and Control of Two-Wheeled Vehicles presents all of the unique features of two-wheeled vehicles, comprehensively covering the main methods, tools and approaches to address the modelling, simulation and control design issues. With contributions from leading researchers, this book also offers a perspective on the future trends in the field, outlining the challenges and the industrial and academic development scenarios. Extensive reference to real-world problems and experimental tests is also included throughout.

Key features:

• The first book to cover all aspects of two-wheeled vehicle dynamics and control
• Collates cutting-edge research from leading international researchers in the field
• Covers motorcycle control – a subject gaining more and more attention both from an academic and an industrial viewpoint
• Covers modelling, simulation and control, areas that are integrated in two-wheeled vehicles, and therefore must be considered together in order to gain an insight into this very specific field of research
• Presents analysis of experimental data and reports on the results obtained on instrumented vehicles.

Modelling, Simulation and Control of Two-Wheeled Vehicles is a comprehensive reference for those in academia who are interested in the state of the art of two-wheeled vehicles, and is also a useful source of information for industrial practitioners.

Mara Tanelli was born in Lodi, Italy, in 1978. She is an Assistant Professor of Automatic Control at the Dipartimento di Elettronica, Informazione e Bioingegneria of the Politecnico di Milano, Italy, where she obtained the Laurea degree in Computer Engineering in 2003 and the Ph.D. in Information Engineering in 2007. She also holds a M.Sc. in Computer Science from the University of Illinois at Chicago. Her main research interests focus on control systems design for vehicles, energy management of electric vehicles, control for energy aware IT systems and sliding mode control. She is co-author of more than 100 peer-reviewed scientific publications and 7 patents in the above research aras. She is also co-author of the monograph “Active braking control systems design for vehicles”, published in 2010 by Springer.

Matteo Corno was born in Italy in 1980. He received his Master of Science degree in Computer and Electrical Engineering (University of Illinois) and his Ph.D. cum laude degree with a thesis on active stability control of two-wheeled vehicles (Politecnico di Milano) in 2005 and 2009. He is currently an Assistant Professor with the Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Italy. In 2011, his paper “On Optimal Motorcycle Braking” was awarded the best-paper prize for Control Engineering Practice, published in the period 2008-2010. In 2012 and 2013, he co-founded two highly innovative start-ups: E-Novia and Zehus. His current research interests include dynamics and control of vehicles, Lithium-ion battery modelling, estimation and control and modelling and control of human powered electric vehicles. He held research positions at Thales Alenia Space, University of Illinois, Harley Davidson, University of Minnesota, Johannes Kepler University in Linz, and TU Delft.

Born in Manerbio, Italy, in 1968, Sergio Savaresi holds an MSc in Electrical Engineering and a PhD in Systems and Control Engineering, both from the Politecnico di Milano, and an MSc in Applied Mathematics from Università Cattolica. After receiving the PhD, he was a consultant for McKinsey&Co, Milan Office. He is Full Professor in Automatic Control since 2006.  He has been visiting scholar at Lund University, Sweden, University of Twente, The Netherlans, Canberra National University, Australia, Minnesota University at Minneapolis, USA, Johannes Kepler University, Linz, Austria. He is Associate Editor of several international journals and he has been in the International Program Committee of many International Conferences. His main research interests are in the areas of vehicles control, automotive systems, data analysis and modeling, non-linear control, and industrial control applications. He is the head of the MoVE research group at the Politecnico di Milano, active in many public and industrial projects in all vehicle-related areas.

Part One Two-wheeled Vehicles Modelling and Simulation 1

1 Motorcycle Dynamics 3

1.1 Kinematics 3

1.1.1 Basics of motorcycle kinematics 3

1.1.2 Handlebar steering angle and kinematic steering angle 6

1.2 Tyres 7

1.2.1 Contact forces and torques 7

1.2.2 Steady-state behavior 9

1.2.3 Dynamic behavior 12

1.3 Suspensions 14

1.3.1 Suspension forces 14

1.3.2 Suspensions layout 14

1.3.3 Equivalent stiffness and damping 16

1.4 In-Plane Dynamics 19

1.4.1 Pictch, bounce and hops modes 19

1.4.2 Powertrain 23

1.4.3 Engine-to-slip dynamics 25

1.4.4 Chatter 28

1.5 Out-of-Plane Dynamics 30

1.5.1 Roll equilibrium 30

1.5.2 Motorcycle countersteering 31

1.5.3 Weave, wobble & capsize 34

1.6 In-Plane and Out-of-Plane Coupled Dynamics 41

References 42

2 Dynamic Modeling of Riderless Motorcycles for Agile Maneuvers 43

2.1 Introduction 44

2.2 Related Work 45

2.3 Motorcycle Dynamics 46

2.3.1 Geometry and kinematics relationships 46

2.3.2 Motorcycle dynamics 49

2.4 Tire Dynamics Models 51

2.4.1 Tire kinematics relationships 52

2.4.2 Modeling of frictional forces 53

2.4.3 Combined tire and motorcycle dynamics models 54

2.5 Conclusion 55

References 56

3 Identification and Analysis of Motorcycle Engine-to-Slip Dynamics 59

3.1 Introduction 59

3.2 Experimental Setup 60

3.3 Identification of Engine-to-Slip Dynamics 61

3.3.1 Relative Slip 73

3.3.2 Throttle Dynamics 73

3.4 Engine-to-Slip Dynamics Analysis 74

3.4.1 Throttle and Spark Advance Control 74

3.4.2 Motorcycle Benchmarking 76

3.5 Road Surface Sensitivity 79

3.6 Velocity Sensitivity 80

3.7 Conclusions 81

References 81

4 Virtual rider design: optimal maneuver definition and tracking 83

4.1 Introduction 83

4.2 Principles of minimum time trajectory computation 86

4.2.1 Tire modeling 87

4.2.2 Engine and drivetrain modeling 88

4.2.3 Brake modeling 89

4.2.4 Wheelie and stoppie 90

4.3 Computing the optimal velocity profile for a point-mass motorcycle 90

4.3.1 Computing the optimal velocity profile for a realistic motorcycle 96

4.3.2 Application to a realistic motorcycle model 100

4.4 The virtual rider 101

4.4.1 The sliding plane motorcycle model 101

4.5 Dynamic inversion: from flatland to state-input trajectories 104

4.5.1 Quasi-static motorcycle trajectory 104

4.5.2 Approximate inversion by trajectory optimization 106

4.6 Closed-loop control: executing the planned trajectory 107

4.6.1 Maneuver regulation 107

4.6.2 Shaping the closed loop response 112

4.6.3 Interfacing the maneuver regulation controller with the multi-body motorycle model 113

4.7 Conclusions 115

References 116

5 The Optimal Manoeuvre 119

5.1 The Optimal Manoeuvre Concept: Manoeuvrability and Handling 121

5.1.1 Optimal Manoeuvre Mathematically Formalised 123

5.1.2 The Optimal Manoeuvre explained with linearized motorcycle models 124

5.2 Optimal Manoeuvre as a Solution of an Optimal Control Problem 134

5.2.1 The Pontryagin minimum principle 137

5.2.2 General formulation of Unconstrained Optimal control 137

5.2.3 Exact solution of a linearized motorcycle model 139

5.2.4 Numerical solution and approximate Pontryagin 143

5.3 Applications of Optimal Manoeuvre to Motorcycle Dynamics 146

5.3.1 Modelling rider’s skills and preferences with the Optimal Manoeuvre 146

5.3.2 Minimum lap time manoeuvres 148

5.4 Conclusions 150

References 152

6 Active Biomechanical Rider Model for Motorcycle Simulation 155

6.1 Human Biomechanics and Motor Control 156

6.1.1 Biomechanics 157

6.1.2 Motor Control 159

6.2 The Model 161

6.2.1 The Human Body Model: 161

6.2.2 The Motorcycle Model 166

6.2.3 Steering the Motorcycle 166

6.3 Simulations and Results 168

6.3.1 Rider’s Vibration Response 168

6.3.2 Lane Change Maneuver 171

6.3.3 Path Following Performance 171

6.3.4 Influence of Physical Fitness 171

6.3.5 Analyzing Weave Mode 177

6.3.6 Provoking Wobble Mode 177

6.3.7 Road Excitation and Ride Comfort 179

6.4 Conclusions 179

References 180

7 A Virtual-Reality Framework for the Hardware-in-the-Loop Motorcycle Simulation 183

7.1 Introduction 183

7.2 Architecture of the Motorcycle Simulator 184

7.2.1 Motorcycle Mock-up and Sensors 184

7.2.2 Realtime Multibody Model 185

7.2.3 Simulator Cues 186

7.2.4 Virtual Scenario 188

7.3 Tuning and validation 188

7.3.1 Objective validation 190

7.3.2 Subjective Validation 191

7.4 Application examples 192

7.4.1 Hardware & Human in the Loop testing of Advanced Rider Assistance Systems 192

7.4.2 Training and road education 194

References 194

Part Two Two-wheeled Vehicles Control and Estimation Problems 197

8 Traction Control Systems Design: A Systematic Approach 199

8.1 Introduction 199

8.2 Wheel slip dynamics 202

8.3 Traction Control System Design 206

8.3.1 Supervisor 207

8.3.2 Slip Reference Generation 208

8.3.3 Control Law Design 208

8.3.4 Transition Recognition 211

8.4 Fine tuning and Experimental Validation 212

8.5 Conclusions 219

References 220

9 Motorcycle Dynamic Modes and Passive Steering Compensation 223

9.1 Introduction 223

9.2 Motorcycle Main Oscillatory Modes and Dynamic Behaviour 224

9.3 Motorcycle Standard Model 226

9.4 Characteristics of the StandardMachine OscillatoryModes and the Influence of Steering Damping 228

9.5 Compensator Frequency Response Design 231

9.6 Suppression of Burst Oscillations 234

9.6.1 Simulated Bursting 234

9.6.2 Acceleration Analysis 237

9.6.3 Compensator Design and Performance 238

9.7 Conclusions 241

References 243

10 Semi-active steering damper control for two-wheeled vehicles 245

10.1 Introduction and motivation 245

10.2 Steering dynamics analysis 247

10.2.1 Model parameters estimation 250

10.2.2 Comparison between vertical and steering dynamics 253

10.3 Control strategies for semi-active steering dampers 254

10.3.1 Rotational sky-hook and ground-hook 255

10.3.2 Closed-loop performance analysis 258

10.4 Validation on challenging maneuvers 259

10.4.1 Performance evaluation method 259

10.4.2 Validation of the control algorithms 260

10.5 Experimental results 269

10.6 Concluding remarks 271

References 271

11 Semi-Active suspensions control in two-wheeled vehicles: a case study 275

11.1 Introduction and Problem Statement 275

11.2 The Semi-Active Actuator 276

11.3 The Quarter-Car Model: a Description of a Semi-Active Suspension System 280

11.4 Evaluation Methods for Semi-Active Suspension Systems 281

11.5 Semi-active Control Strategies 283

11.5.1 Skyhook Control 283

11.5.2 Mix-1-Sensor Control 284

11.5.3 The Groundhook Control 284

11.6 Experimental Set-up 285

11.7 Experimental Evaluation 287

11.8 Concluding Remarks 293

References 294

12 Autonomous Control of Riderless Motorcycles 297

12.1 Introduction 297

12.2 Trajectory Tracking Control Systems Design 298

12.2.1 External/Internal convertible dynamical systems 298

12.2.2 Trajectory tracking control 301

12.2.3 Simulation Results 305

12.3 Path-Following Control System Design 308

12.3.1 Modeling of tire/road friction forces 309

12.3.2 Path-Following Maneuvering Design 310

12.3.3 Simulation Results 312

12.4 Conclusion 316

References 319

13 Estimation problems in two-wheeled vehicles 323

13.1 Introduction 323

13.2 Roll angle estimation 324

13.2.1 Vehicle attitude and reference frames 326

13.2.2 Experimental set-up 329

13.2.3 Accelerometer-based roll angle estimation 330

13.2.4 Use of the frequency separation principle 332

13.3 Vehicle speed estimation 334

13.3.1 Speed estimation during traction maneuvers 335

13.3.2 Experimental setup 335

13.3.3 Kalman filter based frequency split estimation of vehicle speed 336

13.3.4 Experimental Validation 339

13.4 Suspension Stroke Estimation 340

13.4.1 Problem Statement and Estimation Law 342

13.4.2 Experimental Results 344

13.5 Concluding remarks 347

References 347