Modelling, Simulation and Control of Two-Wheeled Vehicles

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