Nonlinear control of vehicles and robots / by Béla Lantos, Lőrinc Márton.

Includes bibliographical references (pages 447-453) and index.

1. Introduction-- 1.1. Basic Notions, Background-- 1.2. A Short History-- 1.3. Control Systems for Vehicles and Robots, Research Motivation-- 1.4. Outline of the Following Chapters-- 2. Basic Nonlinear Control Methods-- 2.1. Nonlinear System Classes-- 2.1.1. State Equation of Nonlinear Systems-- 2.1.2. Holonomic and Nonholonomic Systems-- 2.1.3. Differentially Flat Systems-- 2.2. Dynamic Model of Simple Systems-- 2.2.1. Dynamic Model of Inverted Pendulum-- 2.2.2. Car Active Suspension Model-- 2.2.3. The Model of the 2 DOF Robot Arm-- 2.3. Stability of Nonlinear Systems-- 2.3.1. Stability Definitions-- 2.3.2. Lyapunov Stability Theorems-- 2.3.3. Barbalat Lemmas-- 2.3.4. Stability of Interconnected Passive Systems-- 2.4. Input-Output Linearization-- 2.5. Flatness Control-- 2.6. Backstepping-- 2.7. Sliding Control-- 2.7.1. Sliding Control of Second Order Systems-- 2.7.2. Control Chattering-- 2.7.3. Sliding Control of Robot-- 2.8. Receding Horizon Control-- 2.8.1. Nonlinear Receding Horizon Control-- 2.8.2. Nonlinear RHC Control of 2D Crane-- 2.8.3. RHC Based on Linearization at Each Horizon-- 2.9. Closing Remarks-- 3. Dynamic Models of Ground, Aerial and Marine Robots-- 3.1. Dynamic Model of Rigid Body-- 3.1.1. Dynamic Model Based on Newton-Euler Equations-- 3.1.2. Kinematic Model Using Euler (RPY) Angles-- 3.1.3. Kinematic Model Using Quaternion-- 3.2. Dynamic Model of Industrial Robot-- 3.2.1. Recursive Computation of the Kinematic Quantities-- 3.2.2. Robot Dynamic Model Based on Appell's Equation-- 3.2.3. Robot Dynamic Model Based on Lagrange's Equation-- 3.2.4. Dynamic Model of SCARA Robot-- 3.3. Dynamic Model of Car-- 3.3.1. Nonlinear Model of Car-- 3.3.2. Input Affine Approximation of the Dynamic Model-- 3.3.3. Linearized Model for Constant Velocity-- 3.4. Dynamic Model of Airplane-- 3.4.1. Coordinate Systems for Navigation-- 3.4.2. Airplane Kinematics-- 3.4.3. Airplane Dynamics-- 3.4.4. Wind-Axes Coordinate System-- 3.4.5. Gravity Effect-- 3.4.6. Aerodynamic Forces and Torques-- 3.4.7. Gyroscopic Effect of Rotary Engine-- 3.4.8. State Equationsof Airplane-- 3.4.9. Linearization of the Nonlinear Airplane Model-- 3.4.10. Parametrization of Aerodynamic and Trust Forces and Moments-- 3.5. Dynamic Model of Surface and Underwater Ships-- 3.5.1. Rigid Body Equationof Ship-- 3.5.2. Hydrodynamic Forces and Moments-- 3.5.3. Restoring Forces and Moments-- 3.5.4. Ballast Systems-- 3.5.5. Wind, Wave and Current Models-- 3.5.6. Kinematic Model-- 3.5.7. Dynamic Model in Body Frame-- 3.5.8. Dynamic Model in NED Frame-- 3.6. Closing Remarks-- 4. Nonlinear Control of Industrial Robots-- 4.1. Decentralized Three-Loop Cascade Control-- 4.1.1. Dynamic Model of DC Motor-- 4.1.2. Design of Three-Loop Cascade Controller-- 4.1.3. Approximation of Load Inertia and Disturbance Torque-- 4.2. Computed Torque Technique-- 4.3. Nonlinear Decoupling in Cartesian Space-- 4.3.1. Computation of Equivalent Forces and Torques-- 4.3.2. Computation of Equivalent Joint Torques-- 4.3.3. Robot Dynamic Model in Cartesian Space-- 4.3.4. Nonlinear Decoupling of the Free Motion-- 4.4. Hybrid Position and Force Control-- 4.4.1. Generalized Task Specification Matrices-- 4.4.2. Hybrid Position/Force Control Law-- 4.5. Self-Tuning Adaptive Control-- 4.5.1. Independent Parameters of Robot Dynamic Model-- 4.5.2. Control and Adaptation Laws-- 4.5.3. Simulation Results for 2-DOF Robot-- 4.5.4. Identification Strategy-- 4.6. Robust Backstepping Control in Case of Nonsmooth Path-- 4.6.1. Gradient Update Laws for Speed Error-- 4.6.2. Control of 2-DOF Robot Arm Along Rectangle Path-- 4.7. Closing Remarks-- 5. Nonlinear Control of Cars-- 5.1. Control Concept of Collision Avoidance System (CAS)-- 5.2. Path Design Using Elastic Band-- 5.3. Reference Signal Design for Control-- 5.4. Nonlinear Dynamic Model-- 5.5. Differential Geometry Based Control Algorithm-- 5.5.1. External State Feedback Design-- 5.5.2. Stability Proof of Zero Dynamics-- 5.5.3. Simulation Results Using DGAMethod-- 5.6. Receding Horizon Control-- 5.6.1. Nominal Values and Perturbations-- 5.6.2. RHCOptimization Using End Constraint-- 5.7. State Estimation Using GPSand IMU-- 5.8. Simulation Resultswith RHCControl and State Estimation-- 5.9. Software Implementations-- 5.9.1. Standalone Programs-- 5.9.2. Quick Prototype Designfor Target Processors-- 5.10. Closing Remarks --

6. Nonlinear Control of Airplanes and Helicopters-- 6.1. Receding Horizon Control of the Longitudinal Motion of an Airplane-- 6.1.1. Robust Internal Stabilization Using Disturbance Observer-- 6.1.2. High Level Receding Horizon Control-- 6.1.3. Simulation Results with External RHC and Internal Disturbance Observer-- 6.2. Backstepping Control of an Indoor Quadrotor Helicopter-- 6.2.1. Dynamic Model of the Quadrotor Helicopter-- 6.2.2. Sensor System of the Helicopter-- 6.2.3. State Estimation Using Vision and Inertial Measurements-- 6.2.4. Backstepping Control Algorithm-- 6.2.5. Embedded Control Realization-- 6.3. Closing Remarks-- 7. Nonlinear Control of Surface Ships-- 7.1. Control System Structure-- 7.1.1. Reference Path Design-- 7.1.2. Line-of-Sight Guidance-- 7.1.3. Filtering Wave Disturbances-- 7.1.4. State Estimation Using IMUand GPS-- 7.2. Acceleration Feedback and Nonlinear PD-- 7.3. Nonlinear Decoupling-- 7.3.1. Nonlinear Decoupling in Body Frame-- 7.3.2. Nonlinear Decoupling in NED Frame-- 7.4. Adaptive Feedback Linearization-- 7.5. MIMO Backstepping in 6 DOF-- 7.6. Constrained Control Allocation-- 7.7. Simulation Results-- 7.8. Closing Remarks-- 8. Formation Control of Vehicles-- 8.1. Selected Approaches in Formation Control of Vehicles-- 8.2. Stabilization of Ground Vehicles Using Potential Field Method-- 8.2.1. Low Level Linearizing Controller-- 8.2.2. High Level Formation Controller-- 8.2.3. Passivity Based Formation Stabilization-- 8.3. Simulation Results for UGVs-- 8.4. Stabilization of Marine Vehicles Using Passivity Theory-- 8.4.1. Problem Formulation for Synchronized Path Following-- 8.4.2. Control Structure-- 8.4.3. Stability Proof Based on Passivity Theory-- 8.5. Simulation Results for UMVs-- 8.6. Closing Remarks-- 9. Modeling Nonsmooth Nonlinearities in Mechanical Systems-- 9.1. Modeling and Stability of Nonsmooth Systems-- 9.1.1. Modeling and Stability of Switched Systems-- 9.1.2. Modeling, Solution and Stability of Differential Inclusions-- 9.2. Static Friction Models-- 9.2.1. Stick-Slip Motion-- 9.2.2. Friction-Induced Dead Zone-- 9.3. Dynamic Friction Models-- 9.3.1. Classic Dynamic Friction Models-- 9.3.2. Modified and Advanced Dynamic Friction Models-- 9.4. Piecewise Linearly Parameterized Friction Model-- 9.4.1. Parameter Equivalence with the Tustin Model-- 9.4.2. Modeling Errors-- 9.4.3. Incorporating the Dynamic Effects-- 9.5. Backlash in Mechanical Systems-- 9.6. Closing Remarks-- 10. Mechanical Control Systems with Nonsmooth Nonlinearities-- 10.1. Switched System Model of Mechanical Systems with Stribeck Friction and Backlash-- 10.2. Motion Control-- 10.2.1. Stabilizing Control-- 10.2.2. Extension of the Control Law for Tracking-- 10.2.3. Simulation Results-- 10.3. Friction and Backlash Induced Limit Cycle Around Zero Velocity-- 10.3.1. Chaotic Measures for Nonlinear Analysis-- 10.3.2. Simulation Measurements-- 10.4. Friction Generated Limit Cycle Around Stribeck Velocities-- 10.4.1. Simulation Results-- 10.4.2. Experimental Measurements-- 10.5. Closing Remarks-- 11. Model Based Identification and Adaptive Compensation of Nonsmooth Nonlinearities-- 11.1. Friction and Backlash Measurement and Identification in Robotic Manipulators-- 11.1.1. Friction Measurement and Identification-- 11.1.2. Backlash Measurement-- 11.1.3. Velocity Control for Measurements-- 11.1.4. Experimental Measurements-- 11.2. Friction Measurement and Identification in Hydraulic Actuators-- 11.2.1. Mathematical Model of Hydraulic Actuators-- 11.2.2. Friction Measurement and Identification-- 11.2.3. Experimental Measurements-- 11.3. Nonlinear Control of a Ball and Beam System Using Coulomb Friction Compensation-- 11.3.1. Adaptive Friction Identification-- 11.3.2. Nonlinear Control Algorithm for the Ball and Beam System-- 11.3.3. Experimental Evaluations-- 11.4. Adaptive Payload and Friction Compensation in Robotic Manipulators-- 11.4.1. Simulation Results-Adaptive Friction Compensation in the Presence of Backlash-- 11.4.2. Experimental Measurements-- 11.5. Closing Remarks-- 12. Conclusions and Future Research Directions-- 12.1. Summary-- 12.2. Future Research Directions-- Appendix A. Kinematic and Dynamic Foundations of Physical Systems-- A. Orientation Description Using Rotations and Quaternion-- A. Homogeneous Transformations-- A. Orientation Description Using Rotations-- A. Orientation Description Using Quaternion-- A. Solutionof the Inverse Orientation Problem-- A. Differentiation Rule in Moving Coordinate System-- A. Inertia Parametersof Rigid Objects-- A. Lagrange, Appell and Newton-Euler Equations-- A. Lagrange Equation-- A. Appell Equation-- A. Newton-Euler Equations-- A. Robot Kinematics-- A. Denavit-Hartenberg Form-- A. Direct Kinematic Problem-- A. Inverse Kinematic Problem-- A. Robot Jacobian-- Appendix B. Basis of Differential Geometry for Control Problems-- B. Lie Derivatives, Submanifold, Tangent Space-- B. Frobenius Theorem-- B. Local Reachability and Observability-- B. Input/Output Linearization, Zero Dynamics.

"Tracking of autonomous vehicles and the high-precision positioning of robotic manipulators require advanced modeling techniques and control algorithms. Controller design should take into account any model nonlinearities. Nonlinear Control of Vehicles and Robots develops a unified approach to the dynamic modeling of robots in terrestrial, aerial and marine environments. To begin with, the main classes of nonlinear systems and stability methods are summarized. Basic nonlinear control methods useful in manipulator and vehicle control - linearization, backstepping, sliding-mode and receding-horizon control - are presented. Formation control of ground robots and ships is discussed. The second part of the book deals with the modeling and control of robotic systems in the presence of non-smooth nonlinearities including analysis of their influence on the performance of motion control systems. Robust adaptive tracking control of robotic systems with unknown payload and friction in the presence of uncertainties is treated. Theoretical (guaranteed stability, guaranteed tracking precision, boundedness of all signals in the control loop) and practical (implementability) aspects of the control algorithms under discussion are detailed. Examples are included throughout the book allowing the reader to apply the control and modeling techniques in their own research and development work. Some of these examples demonstrate state estimation based on the use of advanced sensors such as Inertial Measurement System, Global Positioning System and vision systems as part of the control system. Nonlinear Control of Vehicles and Robots will interest academic researchers studying the control of robots and industrial research and development engineers and graduate students wishing to become familiar with modern control algorithms and modeling techniques for the most common mechatronics systems: vehicles and robot manipulators."--Publisher's website.

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